Perturbative approach to Markovian open quantum systems.
Li, Andy C Y; Petruccione, F; Koch, Jens
2014-05-08
The exact treatment of Markovian open quantum systems, when based on numerical diagonalization of the Liouville super-operator or averaging over quantum trajectories, is severely limited by Hilbert space size. Perturbation theory, standard in the investigation of closed quantum systems, has remained much less developed for open quantum systems where a direct application to the Lindblad master equation is desirable. We present such a perturbative treatment which will be useful for an analytical understanding of open quantum systems and for numerical calculation of system observables which would otherwise be impractical.
Investigating non-Markovian dynamics of quantum open systems
Chen, Yusui
Quantum open system coupled to a non-Markovian environment has recently attracted widespread interest for its important applications in quantum information processing and quantum dissipative systems. New phenomena induced by the non-Markovian environment have been discovered in variety of research areas ranging from quantum optics, quantum decoherence to condensed matter physics. However, the study of the non-Markovian quantum open system is known a difficult problem due to its technical complexity in deriving the fundamental equation of motion and elusive conceptual issues involving non-equilibrium dynamics for a strong coupled environment. The main purpose of this thesis is to introduce several new techniques of solving the quantum open systems including a systematic approach to dealing with non-Markovian master equations from a generic quantum-state diffusion (QSD) equation. In the first part of this thesis, we briefly introduce the non-Markovian quantum-state diffusion approach, and illustrate some pronounced non-Markovian quantum effects through numerical investigation on a cavity-QED model. Then we extend the non-Markovian QSD theory to an interesting model where the environment has a hierarchical structure, and find out the exact non-Markovian QSD equation of this model system. We observe the generation of quantum entanglement due to the interplay between the non-Markovian environment and the cavity. In the second part, we show an innovative method to obtain the exact non-Markovian master equations for a set of generic quantum open systems based on the corresponding non-Markovian QSD equations. Multiple-qubit systems and multilevel systems are discussed in details as two typical examples. Particularly, we derive the exact master equation for a model consisting of a three-level atom coupled to an optical cavity and controlled by an external laser field. Additionally, we discuss in more general context the mathematical similarity between the multiple
Colloquium: Non-Markovian dynamics in open quantum systems
Breuer, Heinz-Peter; Laine, Elsi-Mari; Piilo, Jyrki; Vacchini, Bassano
2016-04-01
The dynamical behavior of open quantum systems plays a key role in many applications of quantum mechanics, examples ranging from fundamental problems, such as the environment-induced decay of quantum coherence and relaxation in many-body systems, to applications in condensed matter theory, quantum transport, quantum chemistry, and quantum information. In close analogy to a classical Markovian stochastic process, the interaction of an open quantum system with a noisy environment is often modeled phenomenologically by means of a dynamical semigroup with a corresponding time-independent generator in Lindblad form, which describes a memoryless dynamics of the open system typically leading to an irreversible loss of characteristic quantum features. However, in many applications open systems exhibit pronounced memory effects and a revival of genuine quantum properties such as quantum coherence, correlations, and entanglement. Here recent theoretical results on the rich non-Markovian quantum dynamics of open systems are discussed, paying particular attention to the rigorous mathematical definition, to the physical interpretation and classification, as well as to the quantification of quantum memory effects. The general theory is illustrated by a series of physical examples. The analysis reveals that memory effects of the open system dynamics reflect characteristic features of the environment which opens a new perspective for applications, namely, to exploit a small open system as a quantum probe signifying nontrivial features of the environment it is interacting with. This Colloquium further explores the various physical sources of non-Markovian quantum dynamics, such as structured environmental spectral densities, nonlocal correlations between environmental degrees of freedom, and correlations in the initial system-environment state, in addition to developing schemes for their local detection. Recent experiments addressing the detection, quantification, and control of
Closed hierarchy of correlations in Markovian open quantum systems
International Nuclear Information System (INIS)
Žunkovič, Bojan
2014-01-01
We study the Lindblad master equation in the space of operators and provide simple criteria for closeness of the hierarchy of equations for correlations. We separately consider the time evolution of closed and open systems and show that open systems satisfying the closeness conditions are not necessarily of Gaussian type. In addition, we show that dissipation can induce the closeness of the hierarchy of correlations in interacting quantum systems. As an example we study an interacting optomechanical model, the Fermi–Hubbard model, and the Rabi model, all coupled to a fine-tuned Markovian environment and obtain exact analytic expressions for the time evolution of two-point correlations. (paper)
Fluctuation relation for heat exchange in Markovian open quantum systems
Ramezani, M.; Golshani, M.; Rezakhani, A. T.
2018-04-01
A fluctuation relation for the heat exchange of an open quantum system under a thermalizing Markovian dynamics is derived. We show that the probability that the system absorbs an amount of heat from its bath, at a given time interval, divided by the probability of the reverse process (releasing the same amount of heat to the bath) is given by an exponential factor which depends on the amount of heat and the difference between the temperatures of the system and the bath. Interestingly, this relation is akin to the standard form of the fluctuation relation (for forward-backward dynamics). We also argue that the probability of the violation of the second law of thermodynamics in the form of the Clausius statement (i.e., net heat transfer from a cold system to its hot bath) drops exponentially with both the amount of heat and the temperature differences of the baths.
Thermodynamic description of non-Markovian information flux of nonequilibrium open quantum systems
Chen, Hong-Bin; Chen, Guang-Yin; Chen, Yueh-Nan
2017-12-01
One of the fundamental issues in the field of open quantum systems is the classification and quantification of non-Markovianity. In the contest of quantity-based measures of non-Markovianity, the intuition of non-Markovianity in terms of information backflow is widely discussed. However, it is not easy to characterize the information flux for a given system state and show its connection to non-Markovianity. Here, by using the concepts from thermodynamics and information theory, we discuss a potential definition of information flux of an open quantum system, valid for static environments. We present a simple protocol to show how a system attempts to share information with its environment and how it builds up system-environment correlations. We also show that the information returned from the correlations characterizes the non-Markovianity and a hierarchy of indivisibility of the system dynamics.
Non-Markovian linear response theory for quantum open systems and its applications.
Shen, H Z; Li, D X; Yi, X X
2017-01-01
The Kubo formula is an equation that expresses the linear response of an observable due to a time-dependent perturbation. It has been extended from closed systems to open systems in recent years under the Markovian approximation, but is barely explored for open systems in non-Markovian regimes. In this paper, we derive a formula for the linear response of an open system to a time-independent external field. This response formula is available for both Markovian and non-Markovian dynamics depending on parameters in the spectral density of the environment. As an illustration of the theory, the Hall conductance of a two-band system subjected to environments is derived and discussed. With the tight-binding model, we point out the Hall conductance changes from Markovian to non-Markovian dynamics by modulating the spectral density of the environment. Our results suggest a way to the controlling of the system response, which has potential applications for quantum statistical mechanics and condensed matter physics.
Pseudothermalization in driven-dissipative non-Markovian open quantum systems
Lebreuilly, José; Chiocchetta, Alessio; Carusotto, Iacopo
2018-03-01
We investigate a pseudothermalization effect, where an open quantum system coupled to a nonequilibrated environment consisting of several non-Markovian reservoirs presents an emergent thermal behavior. This thermal behavior is visible at both static and dynamical levels and the system satisfies the fluctuation-dissipation theorem. Our analysis is focused on the exactly solvable model of a weakly interacting driven-dissipative Bose gas in presence of frequency-dependent particle pumping and losses, and is based on a quantum Langevin theory, which we derive starting from a microscopical quantum optics model. For generic non-Markovian reservoirs, we demonstrate that the emergence of thermal properties occurs in the range of frequencies corresponding to low-energy excitations. For the specific case of non-Markovian baths verifying the Kennard-Stepanov relation, we show that pseudothermalization can instead occur at all energy scales. The possible implications regarding the interpretation of thermal laws in low-temperature exciton-polariton experiments are discussed. We finally show that the presence of either a saturable pumping or a dispersive environment leads to a breakdown of the pseudothermalization effect.
Connecting two jumplike unravelings for non-Markovian open quantum systems
Energy Technology Data Exchange (ETDEWEB)
Luoma, Kimmo; Suominen, Kalle-Antti; Piilo, Jyrki [Turku Centre for Quantum Physics, Department of Physics and Astronomy, University of Turku, FI-20014 Turun Yliopisto (Finland)
2011-09-15
The development and use of Monte Carlo algorithms plays a visible role in the study of non-Markovian quantum dynamics due to the provided insight and powerful numerical methods for solving the system dynamics. In the Markovian case, the connections between the various types of methods are fairly well understood while, for the non-Markovian case, there has so far been only a few studies. We focus here on two jumplike unravelings of non-Markovian dynamics: the non-Markovian quantum jump (NMQJ) method and the property state method by Gambetta, Askerud, and Wiseman (GAW). The results for simple quantum optical systems illustrate the connections between the realizations of the two methods and also highlight how the probability currents between the system and environment, or between the property states of the total system, are associated with the decay rates of time-local master equations and, consequently, with the jump rates of the NMQJ method.
Connecting two jumplike unravelings for non-Markovian open quantum systems
International Nuclear Information System (INIS)
Luoma, Kimmo; Suominen, Kalle-Antti; Piilo, Jyrki
2011-01-01
The development and use of Monte Carlo algorithms plays a visible role in the study of non-Markovian quantum dynamics due to the provided insight and powerful numerical methods for solving the system dynamics. In the Markovian case, the connections between the various types of methods are fairly well understood while, for the non-Markovian case, there has so far been only a few studies. We focus here on two jumplike unravelings of non-Markovian dynamics: the non-Markovian quantum jump (NMQJ) method and the property state method by Gambetta, Askerud, and Wiseman (GAW). The results for simple quantum optical systems illustrate the connections between the realizations of the two methods and also highlight how the probability currents between the system and environment, or between the property states of the total system, are associated with the decay rates of time-local master equations and, consequently, with the jump rates of the NMQJ method.
Properties of quantum Markovian master equations
International Nuclear Information System (INIS)
Gorini, V.; Frigerio, A.; Verri, M.; Kossakowski, A.; Sudarshan, E.C.G.
1976-11-01
An essentially self-contained account is given of some general structural properties of the dynamics of quantum open Markovian systems. Some recent results regarding the problem of the classification of quantum Markovian master equations and the limiting conditions under which the dynamical evolution of a quantum open system obeys an exact semigroup law (weak coupling limit and singular coupling limit are reviewed). A general form of quantum detailed balance and its relation to thermal relaxation and to microreversibility is discussed
Optical signatures of non-Markovian behavior in open quantum systems
DEFF Research Database (Denmark)
McCutcheon, Dara
2016-01-01
for the correlation functions, making only a second-order expansion in the system-environment coupling strength and invoking the Born approximation at a fixed initial time. The results are used to investigate a driven semiconductor quantum dot coupled to an acoustic phonon bath, where we find the non-Markovian nature...
Quantum non-Markovianity: characterization, quantification and detection
International Nuclear Information System (INIS)
Rivas, Ángel; Huelga, Susana F; Plenio, Martin B
2014-01-01
We present a comprehensive and up-to-date review of the concept of quantum non-Markovianity, a central theme in the theory of open quantum systems. We introduce the concept of a quantum Markovian process as a generalization of the classical definition of Markovianity via the so-called divisibility property and relate this notion to the intuitive idea that links non-Markovianity with the persistence of memory effects. A detailed comparison with other definitions presented in the literature is provided. We then discuss several existing proposals to quantify the degree of non-Markovianity of quantum dynamics and to witness non-Markovian behavior, the latter providing sufficient conditions to detect deviations from strict Markovianity. Finally, we conclude by enumerating some timely open problems in the field and provide an outlook on possible research directions. (review article)
Quantum non-Markovianity: characterization, quantification and detection
Rivas, Ángel; Huelga, Susana F.; Plenio, Martin B.
2014-09-01
We present a comprehensive and up-to-date review of the concept of quantum non-Markovianity, a central theme in the theory of open quantum systems. We introduce the concept of a quantum Markovian process as a generalization of the classical definition of Markovianity via the so-called divisibility property and relate this notion to the intuitive idea that links non-Markovianity with the persistence of memory effects. A detailed comparison with other definitions presented in the literature is provided. We then discuss several existing proposals to quantify the degree of non-Markovianity of quantum dynamics and to witness non-Markovian behavior, the latter providing sufficient conditions to detect deviations from strict Markovianity. Finally, we conclude by enumerating some timely open problems in the field and provide an outlook on possible research directions.
Markovianity and non-Markovianity in quantum and classical systems
International Nuclear Information System (INIS)
Vacchini, Bassano; Smirne, Andrea; Laine, Elsi-Mari; Piilo, Jyrki; Breuer, Heinz-Peter
2011-01-01
We discuss the conceptually different definitions used for the non-Markovianity of classical and quantum processes. The well-established definition of non-Markovianity of a classical stochastic process represents a condition on the Kolmogorov hierarchy of the n-point joint probability distributions. Since this definition cannot be transferred to the quantum regime, quantum non-Markovianity has recently been defined and quantified in terms of the underlying quantum dynamical map, using either its divisibility properties or the behavior of the trace distance between pairs of initial states. Here, we investigate and compare these definitions and their relations to the classical notion of non-Markovianity by employing a large class of non-Markovian processes, known as semi-Markov processes, which admit a natural extension to the quantum case. A number of specific physical examples are constructed that allow us to study the basic features of the classical and the quantum definitions and to evaluate explicitly the measures of quantum non-Markovianity. Our results clearly demonstrate several fundamental differences between the classical and the quantum notion of non-Markovianity, as well as between the various quantum measures of non-Markovianity. In particular, we show that the divisibility property in the classical case does not coincide with Markovianity and that the non-Markovianity measure based on divisibility assigns equal infinite values to different dynamics, which can be distinguished by exploiting the trace distance measure. A simple exact expression for the latter is also obtained in a special case.
Polyakov, Evgeny A.; Rubtsov, Alexey N.
2018-02-01
When conducting the numerical simulation of quantum transport, the main obstacle is a rapid growth of the dimension of entangled Hilbert subspace. The Quantum Monte Carlo simulation techniques, while being capable of treating the problems of high dimension, are hindered by the so-called "sign problem". In the quantum transport, we have fundamental asymmetry between the processes of emission and absorption of environment excitations: the emitted excitations are rapidly and irreversibly scattered away. Whereas only a small part of these excitations is absorbed back by the open subsystem, thus exercising the non-Markovian self-action of the subsystem onto itself. We were able to devise a method for the exact simulation of the dominant quantum emission processes, while taking into account the small backaction effects in an approximate self-consistent way. Such an approach allows us to efficiently conduct simulations of real-time dynamics of small quantum subsystems immersed in non-Markovian bath for large times, reaching the quasistationary regime. As an example we calculate the spatial quench dynamics of Kondo cloud for a bozonized Kodno impurity model.
Chakraborty, Ahana; Sensarma, Rajdeep
2018-03-01
The Born-Markov approximation is widely used to study the dynamics of open quantum systems coupled to external baths. Using Keldysh formalism, we show that the dynamics of a system of bosons (fermions) linearly coupled to a noninteracting bosonic (fermionic) bath falls outside this paradigm if the bath spectral function has nonanalyticities as a function of frequency. In this case, we show that the dissipative and noise kernels governing the dynamics have distinct power-law tails. The Green's functions show a short-time "quasi"-Markovian exponential decay before crossing over to a power-law tail governed by the nonanalyticity of the spectral function. We study a system of bosons (fermions) hopping on a one-dimensional lattice, where each site is coupled linearly to an independent bath of noninteracting bosons (fermions). We obtain exact expressions for the Green's functions of this system, which show power-law decay ˜|t - t'|-3 /2 . We use these to calculate the density and current profile, as well as unequal-time current-current correlators. While the density and current profiles show interesting quantitative deviations from Markovian results, the current-current correlators show qualitatively distinct long-time power-law tails |t - t'|-3 characteristic of non-Markovian dynamics. We show that the power-law decays survive in the presence of interparticle interaction in the system, but the crossover time scale is shifted to larger values with increasing interaction strength.
Mixing-induced quantum non-Markovianity and information flow
Breuer, Heinz-Peter; Amato, Giulio; Vacchini, Bassano
2018-04-01
Mixing dynamical maps describing open quantum systems can lead from Markovian to non-Markovian processes. Being surprising and counter-intuitive, this result has been used as argument against characterization of non-Markovianity in terms of information exchange. Here, we demonstrate that, quite the contrary, mixing can be understood in a natural way which is fully consistent with existing theories of memory effects. In particular, we show how mixing-induced non-Markovianity can be interpreted in terms of the distinguishability of quantum states, system-environment correlations and the information flow between system and environment.
Adaptive resummation of Markovian quantum dynamics
International Nuclear Information System (INIS)
Lucas, Felix
2014-01-01
In this thesis we derive a highly convergent, nonperturbative expansion of Markovian open quantum dynamics. It is based on a splitting of the incoherent dynamics into periods of continuous evolution and abrupt jumps and attains its favorable convergence properties from an adaptive resummation of this so-called jump expansion. By means of the long-standing problems of spatial particle detection and Landau-Zener tunneling in the presence of dephasing, we show that this adaptive resummation technique facilitates new highly accurate analytic approximations of Markovian open systems. The open Landau-Zener model leads us to propose an efficient and robust incoherent control technique for the isomerization reaction of the visual pigment protein rhodopsin. Besides leading to approximate analytic descriptions of Markovian open quantum dynamics, the adaptive resummation of the jump expansion implies an efficient numerical simulation method. We spell out the corresponding numerical algorithm by means of Monte Carlo integration of the relevant terms in the jump expansion and demonstrate it in a set of paradigmatic open quantum systems.
Jump probabilities in the non-Markovian quantum jump method
International Nuclear Information System (INIS)
Haerkoenen, Kari
2010-01-01
The dynamics of a non-Markovian open quantum system described by a general time-local master equation is studied. The propagation of the density operator is constructed in terms of two processes: (i) deterministic evolution and (ii) evolution of a probability density functional in the projective Hilbert space. The analysis provides a derivation for the jump probabilities used in the recently developed non-Markovian quantum jump (NMQJ) method (Piilo et al 2008 Phys. Rev. Lett. 100 180402).
Exploiting Non-Markovianity for Quantum Control.
Reich, Daniel M; Katz, Nadav; Koch, Christiane P
2015-07-22
Quantum technology, exploiting entanglement and the wave nature of matter, relies on the ability to accurately control quantum systems. Quantum control is often compromised by the interaction of the system with its environment since this causes loss of amplitude and phase. However, when the dynamics of the open quantum system is non-Markovian, amplitude and phase flow not only from the system into the environment but also back. Interaction with the environment is then not necessarily detrimental. We show that the back-flow of amplitude and phase can be exploited to carry out quantum control tasks that could not be realized if the system was isolated. The control is facilitated by a few strongly coupled, sufficiently isolated environmental modes. Our paradigmatic example considers a weakly anharmonic ladder with resonant amplitude control only, restricting realizable operations to SO(N). The coupling to the environment, when harnessed with optimization techniques, allows for full SU(N) controllability.
Foundations and measures of quantum non-Markovianity
International Nuclear Information System (INIS)
Breuer, Heinz-Peter
2012-01-01
The basic features of the dynamics of open quantum systems, such as the dissipation of energy, the decay of coherences, the relaxation to an equilibrium or non-equilibrium stationary state, and the transport of excitations in complex structures are of central importance in many applications of quantum mechanics. The theoretical description, analysis and control of non-Markovian quantum processes play an important role in this context. While in a Markovian process an open system irretrievably loses information to its surroundings, non-Markovian processes feature a flow of information from the environment back to the open system, which implies the presence of memory effects and represents the key property of non-Markovian quantum behaviour. Here, we review recent ideas developing a general mathematical definition for non-Markovianity in the quantum regime and a measure for the degree of memory effects in the dynamics of open systems, which are based on the exchange of information between system and environment. We further study the dynamical effects induced by the presence of system–environment correlations in the total initial state and design suitable methods to detect such correlations through local measurements on the open system. (topical review)
Mangaud, E.; Puthumpally-Joseph, R.; Sugny, D.; Meier, C.; Atabek, O.; Desouter-Lecomte, M.
2018-04-01
Optimal control theory is implemented with fully converged hierarchical equations of motion (HEOM) describing the time evolution of an open system density matrix strongly coupled to the bath in a spin-boson model. The populations of the two-level sub-system are taken as control objectives; namely, their revivals or exchange when switching off the field. We, in parallel, analyze how the optimal electric field consequently modifies the information back flow from the environment through different non-Markovian witnesses. Although the control field has a dipole interaction with the central sub-system only, its indirect influence on the bath collective mode dynamics is probed through HEOM auxiliary matrices, revealing a strong correlation between control and dissipation during a non-Markovian process. A heterojunction is taken as an illustrative example for modeling in a realistic way the two-level sub-system parameters and its spectral density function leading to a non-perturbative strong coupling regime with the bath. Although, due to strong system-bath couplings, control performances remain rather modest, the most important result is a noticeable increase of the non-Markovian bath response induced by the optimally driven processes.
Non-Markovian decoherent quantum walks
International Nuclear Information System (INIS)
Xue Peng; Zhang Yong-Sheng
2013-01-01
Quantum walks act in obviously different ways from their classical counterparts, but decoherence will lessen and close this gap between them. To understand this process, it is necessary to investigate the evolution of quantum walks under different decoherence situations. In this article, we study a non-Markovian decoherent quantum walk on a line. In a short time regime, the behavior of the walk deviates from both ideal quantum walks and classical random walks. The position variance as a measure of the quantum walk collapses and revives for a short time, and tends to have a linear relation with time. That is, the walker's behavior shows a diffusive spread over a long time limit, which is caused by non-Markovian dephasing affecting the quantum correlations between the quantum walker and his coin. We also study both quantum discord and measurement-induced disturbance as measures of the quantum correlations, and observe both collapse and revival in the short time regime, and the tendency to be zero in the long time limit. Therefore, quantum walks with non-Markovian decoherence tend to have diffusive spreading behavior over long time limits, while in the short time regime they oscillate between ballistic and diffusive spreading behavior, and the quantum correlation collapses and revives due to the memory effect
Selected Aspects of Markovian and Non-Markovian Quantum Master Equations
Lendi, K.
A few particular marked properties of quantum dynamical equations accounting for general relaxation and dissipation are selected and summarized in brief. Most results derive from the universal concept of complete positivity. The considerations mainly regard genuinely irreversible processes as characterized by a unique asymptotically stationary final state for arbitrary initial conditions. From ordinary Markovian master equations and associated quantum dynamical semigroup time-evolution, derivations of higher order Onsager coefficients and related entropy production are discussed. For general processes including non-faithful states a regularized version of quantum relative entropy is introduced. Further considerations extend to time-dependent infinitesimal generators of time-evolution and to a possible description of propagation of initial states entangled between open system and environment. In the coherence-vector representation of the full non-Markovian equations including entangled initial states, first results are outlined towards identifying mathematical properties of a restricted class of trial integral-kernel functions suited to phenomenological applications.
Jonsson, Thorsteinn H.; Manolescu, Andrei; Goan, Hsi-Sheng; Abdullah, Nzar Rauf; Sitek, Anna; Tang, Chi-Shung; Gudmundsson, Vidar
2017-11-01
Master equations are commonly used to describe time evolution of open systems. We introduce a general computationally efficient method for calculating a Markovian solution of the Nakajima-Zwanzig generalized master equation. We do so for a time-dependent transport of interacting electrons through a complex nano scale system in a photon cavity. The central system, described by 120 many-body states in a Fock space, is weakly coupled to the external leads. The efficiency of the approach allows us to place the bias window defined by the external leads high into the many-body spectrum of the cavity photon-dressed states of the central system revealing a cascade of intermediate transitions as the system relaxes to a steady state. The very diverse relaxation times present in the open system, reflecting radiative or non-radiative transitions, require information about the time evolution through many orders of magnitude. In our approach, the generalized master equation is mapped from a many-body Fock space of states to a Liouville space of transitions. We show that this results in a linear equation which is solved exactly through an eigenvalue analysis, which supplies information on the steady state and the time evolution of the system.
Non-Markovianity hinders Quantum Darwinism
Galve, Fernando; Zambrini, Roberta; Maniscalco, Sabrina
2016-01-01
We investigate Quantum Darwinism and the emergence of a classical world from the quantum one in connection with the spectral properties of the environment. We use a microscopic model of quantum environment in which, by changing a simple system parameter, we can modify the information back flow from environment into the system, and therefore its non-Markovian character. We show that the presence of memory effects hinders the emergence of classical objective reality, linking these two apparently unrelated concepts via a unique dynamical feature related to decoherence factors.
Quantum adiabatic Markovian master equations
International Nuclear Information System (INIS)
Albash, Tameem; Zanardi, Paolo; Boixo, Sergio; Lidar, Daniel A
2012-01-01
We develop from first principles Markovian master equations suited for studying the time evolution of a system evolving adiabatically while coupled weakly to a thermal bath. We derive two sets of equations in the adiabatic limit, one using the rotating wave (secular) approximation that results in a master equation in Lindblad form, the other without the rotating wave approximation but not in Lindblad form. The two equations make markedly different predictions depending on whether or not the Lamb shift is included. Our analysis keeps track of the various time and energy scales associated with the various approximations we make, and thus allows for a systematic inclusion of higher order corrections, in particular beyond the adiabatic limit. We use our formalism to study the evolution of an Ising spin chain in a transverse field and coupled to a thermal bosonic bath, for which we identify four distinct evolution phases. While we do not expect this to be a generic feature, in one of these phases dissipation acts to increase the fidelity of the system state relative to the adiabatic ground state. (paper)
Moix, Jeremy M.; Cao, Jianshu
2013-10-01
The hierarchical equations of motion technique has found widespread success as a tool to generate the numerically exact dynamics of non-Markovian open quantum systems. However, its application to low temperature environments remains a serious challenge due to the need for a deep hierarchy that arises from the Matsubara expansion of the bath correlation function. Here we present a hybrid stochastic hierarchical equation of motion (sHEOM) approach that alleviates this bottleneck and leads to a numerical cost that is nearly independent of temperature. Additionally, the sHEOM method generally converges with fewer hierarchy tiers allowing for the treatment of larger systems. Benchmark calculations are presented on the dynamics of two level systems at both high and low temperatures to demonstrate the efficacy of the approach. Then the hybrid method is used to generate the exact dynamics of systems that are nearly impossible to treat by the standard hierarchy. First, exact energy transfer rates are calculated across a broad range of temperatures revealing the deviations from the Förster rates. This is followed by computations of the entanglement dynamics in a system of two qubits at low temperature spanning the weak to strong system-bath coupling regimes.
Non-Markovian quantum processes: Complete framework and efficient characterization
Pollock, Felix A.; Rodríguez-Rosario, César; Frauenheim, Thomas; Paternostro, Mauro; Modi, Kavan
2018-01-01
Currently, there is no systematic way to describe a quantum process with memory solely in terms of experimentally accessible quantities. However, recent technological advances mean we have control over systems at scales where memory effects are non-negligible. The lack of such an operational description has hindered advances in understanding physical, chemical, and biological processes, where often unjustified theoretical assumptions are made to render a dynamical description tractable. This has led to theories plagued with unphysical results and no consensus on what a quantum Markov (memoryless) process is. Here, we develop a universal framework to characterize arbitrary non-Markovian quantum processes. We show how a multitime non-Markovian process can be reconstructed experimentally, and that it has a natural representation as a many-body quantum state, where temporal correlations are mapped to spatial ones. Moreover, this state is expected to have an efficient matrix-product-operator form in many cases. Our framework constitutes a systematic tool for the effective description of memory-bearing open-system evolutions.
He, Zhi; Zhu, Lie-Qiang; Li, Li
2017-03-01
A non-Markovianity measure based on Brukner-Zeilinger invariant information to characterize non-Markovian effect of open systems undergoing unital dynamical maps is proposed. The method takes advantage of non-increasing property of the Brukner-Zeilinger invariant information under completely positive and trace-preserving unital maps. The simplicity of computing the Brukner-Zeilinger invariant information is the advantage of the proposed measure because of mainly depending on the purity of quantum state. The measure effectively captures the characteristics of non-Markovianity of unital dynamical maps. As some concrete application, we consider two typical non-Markovian noise channels, i.e., the phase damping channel and the random unitary channel to show the sensitivity of the proposed measure. By investigation, we find that the conditions of detecting the non-Markovianity for the phase damping channel are consistent with the results of existing measures for non-Markovianity, i.e., information flow, divisibility and quantum mutual information. However, for the random unitary channel non-Markovian conditions are same to that of the information flow, but is different from that of the divisibility and quantum mutual information. Supported by the National Natural Science Foundation of China under Grant No. 61505053, the Natural Science Foundation of Hunan Province under Grant No. 2015JJ3092, the Research Foundation of Education Bureau of Hunan Province, China under Grant No. 16B177, the School Foundation from the Hunan University of Arts and Science under Grant No. 14ZD01
International Nuclear Information System (INIS)
He Zhi; Zhu Lie-Qiang; Li Li
2017-01-01
A non-Markovianity measure based on Brukner–Zeilinger invariant information to characterize non-Markovian effect of open systems undergoing unital dynamical maps is proposed. The method takes advantage of non-increasing property of the Brukner–Zeilinger invariant information under completely positive and trace-preserving unital maps. The simplicity of computing the Brukner–Zeilinger invariant information is the advantage of the proposed measure because of mainly depending on the purity of quantum state. The measure effectively captures the characteristics of non-Markovianity of unital dynamical maps. As some concrete application, we consider two typical non-Markovian noise channels, i.e., the phase damping channel and the random unitary channel to show the sensitivity of the proposed measure. By investigation, we find that the conditions of detecting the non-Markovianity for the phase damping channel are consistent with the results of existing measures for non-Markovianity, i.e., information flow, divisibility and quantum mutual information. However, for the random unitary channel non-Markovian conditions are same to that of the information flow, but is different from that of the divisibility and quantum mutual information. (paper)
Exact non-Markovian master equations for multiple qubit systems: Quantum-trajectory approach
Chen, Yusui; You, J. Q.; Yu, Ting
2014-11-01
A wide class of exact master equations for a multiple qubit system can be explicitly constructed by using the corresponding exact non-Markovian quantum-state diffusion equations. These exact master equations arise naturally from the quantum decoherence dynamics of qubit system as a quantum memory coupled to a collective colored noisy source. The exact master equations are also important in optimal quantum control, quantum dissipation, and quantum thermodynamics. In this paper, we show that the exact non-Markovian master equation for a dissipative N -qubit system can be derived explicitly from the statistical average of the corresponding non-Markovian quantum trajectories. We illustrated our general formulation by an explicit construction of a three-qubit system coupled to a non-Markovian bosonic environment. This multiple qubit master equation offers an accurate time evolution of quantum systems in various domains, and paves the way to investigate the memory effect of an open system in a non-Markovian regime without any approximation.
Non-Markovian spontaneous emission from a single quantum dot
DEFF Research Database (Denmark)
Madsen, Kristian Høeg; Ates, Serkan; Lund-Hansen, Toke
2011-01-01
We observe non-Markovian dynamics of a single quantum dot when tuned into resonance with a cavity mode. Excellent agreement between experiment and theory is observed providing the first quantitative description of such a system.......We observe non-Markovian dynamics of a single quantum dot when tuned into resonance with a cavity mode. Excellent agreement between experiment and theory is observed providing the first quantitative description of such a system....
A classical appraisal of quantum definitions of non-Markovian dynamics
International Nuclear Information System (INIS)
Vacchini, Bassano
2012-01-01
We consider the issue of non-Markovianity of a quantum dynamics starting from a comparison with the classical definition of Markovian processes. We point to the fact that two sufficient but not necessary signatures of non-Markovianity of a classical process find their natural quantum counterpart in recently introduced measures of quantum non-Markovianity. This behaviour is analysed in detail for quantum dynamics which can be built taking as input a class of classical processes. (paper)
Non-Markovian Investigation of an Autonomous Quantum Heat Engine
Goyal, Ketan
A systematic study of a quantum heat engine is presented in this thesis. In particular, we study heat conduction through a two-two level composite system, which is then connected to a photon cavity to extract work, forming an autonomous quantum heat engine. The question as to what extent quantum effects such as quantum coherence and correlations impact thermodynamic properties of such a system is addressed. The investigated heat engine has been previously studied using the popular Born-Markovian quantum master equation under weak internal coupling approximation. However, we show that the used approach is quite limited in addressing such problems as it is incapable of correctly accounting for the quantum effects. By using a non-Markovian approach involving hierarchical equations of motion, we show that quantum coherence and correlations between system and environments play a significant role in energy transfer processes of heat conduction and work.
Counting statistics of non-markovian quantum stochastic processes
DEFF Research Database (Denmark)
Flindt, Christian; Novotny, T.; Braggio, A.
2008-01-01
We derive a general expression for the cumulant generating function (CGF) of non-Markovian quantum stochastic transport processes. The long-time limit of the CGF is determined by a single dominating pole of the resolvent of the memory kernel from which we extract the zero-frequency cumulants...
Non-Markovian dissipative quantum mechanics with stochastic trajectories
International Nuclear Information System (INIS)
Koch, Werner
2010-01-01
All fields of physics - be it nuclear, atomic and molecular, solid state, or optical - offer examples of systems which are strongly influenced by the environment of the actual system under investigation. The scope of what is called ''the environment'' may vary, i.e., how far from the system of interest an interaction between the two does persist. Typically, however, it is much larger than the open system itself. Hence, a fully quantum mechanical treatment of the combined system without approximations and without limitations of the type of system is currently out of reach. With the single assumption of the environment to consist of an internally thermalized set of infinitely many harmonic oscillators, the seminal work of Stockburger and Grabert [Chem. Phys., 268:249-256, 2001] introduced an open system description that captures the environmental influence by means of a stochastic driving of the reduced system. The resulting stochastic Liouville-von Neumann equation describes the full non-Markovian dynamics without explicit memory but instead accounts for it implicitly through the correlations of the complex-valued noise forces. The present thesis provides a first application of the Stockburger-Grabert stochastic Liouville-von Neumann equation to the computation of the dynamics of anharmonic, continuous open systems. In particular, it is demonstrated that trajectory based propagators allow for the construction of a numerically stable propagation scheme. With this approach it becomes possible to achieve the tremendous increase of the noise sample count necessary to stochastically converge the results when investigating such systems with continuous variables. After a test against available analytic results for the dissipative harmonic oscillator, the approach is subsequently applied to the analysis of two different realistic, physical systems. As a first example, the dynamics of a dissipative molecular oscillator is investigated. Long time propagation - until
Non-Markovian dissipative quantum mechanics with stochastic trajectories
Energy Technology Data Exchange (ETDEWEB)
Koch, Werner
2010-09-09
All fields of physics - be it nuclear, atomic and molecular, solid state, or optical - offer examples of systems which are strongly influenced by the environment of the actual system under investigation. The scope of what is called ''the environment'' may vary, i.e., how far from the system of interest an interaction between the two does persist. Typically, however, it is much larger than the open system itself. Hence, a fully quantum mechanical treatment of the combined system without approximations and without limitations of the type of system is currently out of reach. With the single assumption of the environment to consist of an internally thermalized set of infinitely many harmonic oscillators, the seminal work of Stockburger and Grabert [Chem. Phys., 268:249-256, 2001] introduced an open system description that captures the environmental influence by means of a stochastic driving of the reduced system. The resulting stochastic Liouville-von Neumann equation describes the full non-Markovian dynamics without explicit memory but instead accounts for it implicitly through the correlations of the complex-valued noise forces. The present thesis provides a first application of the Stockburger-Grabert stochastic Liouville-von Neumann equation to the computation of the dynamics of anharmonic, continuous open systems. In particular, it is demonstrated that trajectory based propagators allow for the construction of a numerically stable propagation scheme. With this approach it becomes possible to achieve the tremendous increase of the noise sample count necessary to stochastically converge the results when investigating such systems with continuous variables. After a test against available analytic results for the dissipative harmonic oscillator, the approach is subsequently applied to the analysis of two different realistic, physical systems. As a first example, the dynamics of a dissipative molecular oscillator is investigated. Long time
Continuous quantum error correction for non-Markovian decoherence
International Nuclear Information System (INIS)
Oreshkov, Ognyan; Brun, Todd A.
2007-01-01
We study the effect of continuous quantum error correction in the case where each qubit in a codeword is subject to a general Hamiltonian interaction with an independent bath. We first consider the scheme in the case of a trivial single-qubit code, which provides useful insights into the workings of continuous error correction and the difference between Markovian and non-Markovian decoherence. We then study the model of a bit-flip code with each qubit coupled to an independent bath qubit and subject to continuous correction, and find its solution. We show that for sufficiently large error-correction rates, the encoded state approximately follows an evolution of the type of a single decohering qubit, but with an effectively decreased coupling constant. The factor by which the coupling constant is decreased scales quadratically with the error-correction rate. This is compared to the case of Markovian noise, where the decoherence rate is effectively decreased by a factor which scales only linearly with the rate of error correction. The quadratic enhancement depends on the existence of a Zeno regime in the Hamiltonian evolution which is absent in purely Markovian dynamics. We analyze the range of validity of this result and identify two relevant time scales. Finally, we extend the result to more general codes and argue that the performance of continuous error correction will exhibit the same qualitative characteristics
Quantum measurements in spin-boson model under non-Markovian environment
Berrada, K.; Aldaghri, O.
2017-07-01
We propose a control approach of the parameter estimation for a two-level quantum system interacting with a bosonic reservoir considering non-Markovian open, dissipative quantum system. We show that the precision of the estimation significantly affected and behaves differently within the framework of the markovian and non-Markovian regimes. The influence of memory effects for an Ohmic reservoir with Lorentz-Drude regularization on the estimation-parameter precision are numerically demonstrated under the following three conditions: ω0 ≪ωc , ω0 ≈ωc or ω0 ≫ωc , where ω0 is the characteristic frequency of the two-level system, and ωc is the cut-off frequency of Ohmic reservoir. We investigate the precision rate in high temperature, intermediate temperature, and low temperature reservoirs for various values of the ratio r =ωc /ω0 considering manifold external fields. We reveal that the enhancement and preservation of the measurement precision, highly depend on the combination of the external control field, reservoir parameters, and non-Markovian effects.
Markovian Limit of a Spatio-Temporal Correlated Open Systems
Monnai, T.
Large fluctuation of Brownian particles is affected by the finiteness of the correlation length of the background noise field. Indeed a Fokker—Planck equation is derived in a Markovian limit of a spatio-temporal short correlated noise. Corresponding kinetic quantities are renormalized due to the spatio-temporal memory. We also investigate the case of open system by connecting a thermostat to the system.
Uhrig dynamical control of a three-level system via non-Markovian quantum state diffusion
International Nuclear Information System (INIS)
Shu, Wenchong; Zhao, Xinyu; Jing, Jun; Yu, Ting; Wu, Lian-Ao
2013-01-01
In this paper, we use the quantum state diffusion (QSD) equation to implement the Uhrig dynamical decoupling to a three-level quantum system coupled to a non-Markovian reservoir comprising of infinite numbers of degrees of freedom. For this purpose, we first reformulate the non-Markovian QSD to incorporate the effect of the external control fields. With this stochastic QSD approach, we demonstrate that an unknown state of the three-level quantum system can be universally protected against both coloured phase and amplitude noises when the control-pulse sequences and control operators are properly designed. The advantage of using non-Markovian QSD equations is that the control dynamics of open quantum systems can be treated exactly without using Trotter product formula and be efficiently simulated even when the environment is comprised of infinite numbers of degrees of freedom. We also show how the control efficacy depends on the environment memory time and the designed time points of applied control pulses. (paper)
Quantum Non-Markovian Langevin Equations and Transport Coefficients
International Nuclear Information System (INIS)
Sargsyan, V.V.; Antonenko, N.V.; Kanokov, Z.; Adamian, G.G.
2005-01-01
Quantum diffusion equations featuring explicitly time-dependent transport coefficients are derived from generalized non-Markovian Langevin equations. Generalized fluctuation-dissipation relations and analytic expressions for calculating the friction and diffusion coefficients in nuclear processes are obtained. The asymptotic behavior of the transport coefficients and correlation functions for a damped harmonic oscillator that is linearly coupled in momentum to a heat bath is studied. The coupling to a heat bath in momentum is responsible for the appearance of the diffusion coefficient in coordinate. The problem of regression of correlations in quantum dissipative systems is analyzed
Non-equilibrium effects upon the non-Markovian Caldeira-Leggett quantum master equation
International Nuclear Information System (INIS)
Bolivar, A.O.
2011-01-01
Highlights: → Classical Brownian motion described by a non-Markovian Fokker-Planck equation. → Quantization process. → Quantum Brownian motion described by a non-Markovian Caldeira-Leggett equation. → A non-equilibrium quantum thermal force is predicted. - Abstract: We obtain a non-Markovian quantum master equation directly from the quantization of a non-Markovian Fokker-Planck equation describing the Brownian motion of a particle immersed in a generic environment (e.g. a non-thermal fluid). As far as the especial case of a heat bath comprising of quantum harmonic oscillators is concerned, we derive a non-Markovian Caldeira-Leggett master equation on the basis of which we work out the concept of non-equilibrium quantum thermal force exerted by the harmonic heat bath upon the Brownian motion of a free particle. The classical limit (or dequantization process) of this sort of non-equilibrium quantum effect is scrutinized, as well.
Tightness Entropic Uncertainty Relation in Quantum Markovian-Davies Environment
Zhang, Jun; Liu, Liang; Han, Yan
2018-05-01
In this paper, we investigate the tightness of entropic uncertainty relation in the absence (presence) of the quantum memory which the memory particle being weakly coupled to a decohering Davies-type Markovian environment. The results show that the tightness of the quantum uncertainty relation can be controlled by the energy relaxation time F, the dephasing time G and the rescaled temperature p, the perfect tightness can be arrived by dephasing and energy relaxation satisfying F = 2G and p = 1/2. In addition, the tightness of the memory-assisted entropic uncertainty relation and the entropic uncertainty relation can be influenced mainly by the purity. While in memory-assisted model, the purity and quantum correlation can also influence the tightness actively while the quantum entanglement can influence the tightness slightly.
Non-Markovian effects on quantum-communication protocols
International Nuclear Information System (INIS)
Yeo, Ye; Oh, C. H.; An, Jun-Hong
2010-01-01
We show how, under the influence of non-Markovian environments, two different maximally entangled Bell states give rise to states that have equal classical correlations and the same capacities to violate the Bell-Clauser-Horne-Shimony-Holt inequality, but intriguingly differing usefulness for teleportation and dense coding. We elucidate how different entanglement measures like negativity and concurrence, and two different measures of quantum discord, could account for these behaviors. In particular, we explicitly show how the Ollivier-Zurek measure of discord directly accounts for one state being a better resource for dense coding compared to another. Our study leads to several important issues about these measures of discord.
Non-Markovian dynamics of charge carriers in quantum dots
International Nuclear Information System (INIS)
Vaz, E; Kyriakidis, J
2008-01-01
We have investigated the dynamics of bound particles in multilevel current-carrying quantum dots. We look specifically in the regime of resonant tunnelling transport, where several channels are available for transport. Through a non-Markovian formalism under the Born approximation, we investigate the real-time evolution of the confined particles including transport-induced decoherence and relaxation. In the case of a coherent superposition between states with different particle number, we find that a Fock-space coherence may be preserved even in the presence of tunneling into and out of the dot. Real-time results are presented for various asymmetries of tunneling rates into different orbitals
The Dynamical Invariant of Open Quantum System
Wu, S. L.; Zhang, X. Y.; Yi, X. X.
2015-01-01
The dynamical invariant, whose expectation value is constant, is generalized to open quantum system. The evolution equation of dynamical invariant (the dynamical invariant condition) is presented for Markovian dynamics. Different with the dynamical invariant for the closed quantum system, the evolution of the dynamical invariant for the open quantum system is no longer unitary, and the eigenvalues of it are time-dependent. Since any hermitian operator fulfilling dynamical invariant condition ...
Non-Markovian quantum Brownian motion in one dimension in electric fields
Shen, H. Z.; Su, S. L.; Zhou, Y. H.; Yi, X. X.
2018-04-01
Quantum Brownian motion is the random motion of quantum particles suspended in a field (or an effective field) resulting from their collision with fast-moving modes in the field. It provides us with a fundamental model to understand various physical features concerning open systems in chemistry, condensed-matter physics, biophysics, and optomechanics. In this paper, without either the Born-Markovian or rotating-wave approximation, we derive a master equation for a charged-Brownian particle in one dimension coupled with a thermal reservoir in electric fields. The effect of the reservoir and the electric fields is manifested as time-dependent coefficients and coherent terms, respectively, in the master equation. The two-photon correlation between the Brownian particle and the reservoir can induce nontrivial squeezing dynamics to the particle. We derive a current equation including the source from the driving fields, transient current from the system flowing into the environment, and the two-photon current caused by the non-rotating-wave term. The presented results then are compared with that given by the rotating-wave approximation in the weak-coupling limit, and these results are extended to a more general quantum network involving an arbitrary number of coupled-Brownian particles. The presented formalism might open a way to better understand exactly the non-Markovian quantum network.
Non-Markovian dynamics of quantum systems: formalism, transport coefficients
International Nuclear Information System (INIS)
Kanokov, Z.; Palchikov, Yu.V.; Antonenko, N.V.; Adamian, G.G.; Kanokov, Z.; Adamian, G.G.; Scheid, W.
2004-01-01
Full text: The generalized Linbland equations with non-stationary transport coefficients are derived from the Langevin equations for the case of nonlinear non-Markovian noise [1]. The equations of motion for the collective coordinates are consistent with the generalized quantum fluctuation dissipation relations. The microscopic justification of the Linbland axiomatic approach is performed. Explicit expressions for the time-dependent transport coefficients are presented for the case of FC- and RWA-oscillators and a general linear coupling in coordinate and in momentum between the collective subsystem and heat bath. The explicit equations for the correlation functions show that the Onsanger's regression hypothesis does not hold exactly for the non-Markovian equations of motion. However, under some conditions the regression of fluctuations goes to zero in the same manner as the average values. In the low and high temperature regimes we found that the dissipation leads to long-time tails in correlation functions in the RWA-oscillator. In the case of the FC-oscillator a non-exponential power-like decay of the correlation function in coordinate is only obtained only at the low temperature limit. The calculated results depend rather weakly on the memory time in many applications. The found transient times for diffusion coefficients D pp (t), D qp (t) and D qq (t) are quite short. The value of classical diffusion coefficients in momentum underestimates the asymptotic value of quantum one D pp (t), but the asymptotic values of classical σ qq c and quantum σ qq second moments are close due to the negativity of quantum mixed diffusion coefficient D qp (t)
International Nuclear Information System (INIS)
Hoerhammer, C.
2007-01-01
In this thesis, non-Markovian dynamics, decoherence and entanglement in dissipative quantum systems are studied. In particular, applications to quantum information theory of continuous variable systems are considered. The non-Markovian dynamics are described by the Hu-Paz-Zhang master equation of quantum Brownian motion. In this context the focus is on non-Markovian effects on decoherence and separability time scales of various single- mode and two-mode continuous variable states. It is verified that moderate non-Markovian influences slow down the decay of interference fringes and quantum correlations, while strong non-Markovian effects resulting from an out-of-resonance bath can even accelerate the loss of coherence, compared to predictions of Markovian approximations. Qualitatively different scenarios including exponential, Gaussian or algebraic decay of the decoherence function are analyzed. It is shown that partial recurrence of coherence can occur in case of non-Lindblad-type dynamics. The time evolution of quantum correlations of entangled two-mode continuous variable states is examined in single-reservoir and two-reservoir models, representing noisy correlated or uncorrelated non-Markovian quantum channels. For this purpose the model of quantum Brownian motion is extended. Various separability criteria for Gaussian and non-Gaussian continuous variable systems are applied. In both types of reservoir models moderate non-Markovian effects prolong the separability time scales. However, in these models the properties of the stationary state may differ. In the two-reservoir model the initial entanglement is completely lost and both modes are finally uncorrelated. In a common reservoir both modes interact indirectly via the coupling to the same bath variables. Therefore, new quantum correlations may emerge between the two modes. Below a critical bath temperature entanglement is preserved even in the steady state. A separability criterion is derived, which depends
International Nuclear Information System (INIS)
Afsaneh, E.; Yavari, H.
2014-01-01
The superconducting reservoir effect on the current carrying transport of a double quantum dot in Markovian regime is investigated. For this purpose, a quantum master equation at finite temperature is derived for the many-body density matrix of an open quantum system. The dynamics and the steady-state properties of the double quantum dot system for arbitrary bias are studied. We will show that how the populations and coherencies of the system states are affected by superconducting leads. The energy parameter of system contains essentially four contributions due to dots system-electrodes coupling, intra dot coupling, two quantum dots inter coupling and superconducting gap. The coupling effect of each energy contribution is applied to currents and coherencies results. In addition, the effect of energy gap is studied by considering the amplitude and lifetime of coherencies to get more current through the system. (author)
Entanglement in open quantum systems
International Nuclear Information System (INIS)
Isar, A.
2007-01-01
In the framework of the theory of open systems based on quantum dynamical semigroups, we solve the master equation for two independent bosonic oscillators interacting with an environment in the asymptotic long-time regime. We give a description of the continuous-variable entanglement in terms of the covariance matrix of the quantum states of the considered system for an arbitrary Gaussian input state. Using the Peres-Simon necessary and sufficient condition for separability of two-mode Gaussian states, we show that the two non-interacting systems immersed in a common environment and evolving under a Markovian, completely positive dynamics become asymptotically entangled for certain environments, so that their non-local quantum correlations exist in the long-time regime. (author) Key words: quantum information theory, open systems, quantum entanglement, inseparable states
Quantum operation for a one-qubit system under a non-Markovian environment
International Nuclear Information System (INIS)
Xue Shibei; Zhang Jing; Wu Rebing; Li Chunwen; Tarn, Tzyh-Jong
2011-01-01
This paper introduces a simple alternating-current (AC) control strategy to perform quantum state manipulations under non-Markovian noise. A genetic algorithm is adopted to optimize the parameters of the AC control, which can be further used to fulfil one-qubit quantum operations at a given final time. Theoretical analysis and simulations show that our method works almost equally well for 1/f noise, ohmic, sub-ohmic and super-ohmic noise, which demonstrates the robustness of our strategy for noise with various spectra. In comparison with the Markovian cases, our method is more suitable to be used to suppress non-Markovian noise.
Study on the security of discrete-variable quantum key distribution over non-Markovian channels
International Nuclear Information System (INIS)
Huang Peng; Zhu Jun; He Guangqiang; Zeng Guihua
2012-01-01
The dynamic of the secret key rate of the discrete-variable quantum key distribution (QKD) protocol over the non-Markovian quantum channel is investigated. In particular, we calculate the secret key rate for the six-state protocol over non-Markovian depolarizing channels with coloured noise and Markovian depolarizing channels with Gaussian white noise, respectively. We find that the secure secret key rate for the non-Markovian depolarizing channel will be larger than the Markovian one under the same conditions even when their upper bounds of tolerable quantum bit error rate are equal. This indicates that this coloured noise in the non-Markovian depolarizing channel can enhance the security of communication. Moreover, we show that the secret key rate fluctuates near the secure point when the coupling strength of the system with the environment is high. The results demonstrate that the non-Markovian effects of the transmission channel can have a positive impact on the security of discrete-variable QKD. (paper)
Delineating incoherent non-Markovian dynamics using quantum coherence
Energy Technology Data Exchange (ETDEWEB)
Chanda, Titas, E-mail: titaschanda@hri.res.in; Bhattacharya, Samyadeb, E-mail: samyadebbhattacharya@hri.res.in
2016-03-15
We introduce a method of characterization of non-Markovianity using coherence of a system interacting with the environment. We show that under the allowed incoherent operations, monotonicity of a valid coherence measure is affected due to non-Markovian features of the system–environment evolution. We also define a measure to quantify non-Markovianity of the underlying dynamics based on the non-monotonic behavior of the coherence measure. We investigate our proposed non-Markovianity marker in the behavior of dephasing and dissipative dynamics for one and two qubit cases. We also show that our proposed measure captures the back-flow of information from the environment to the system and compatible with well known distinguishability criteria of non-Markovianity.
Decoherence in open quantum systems
International Nuclear Information System (INIS)
Isar, A.
2005-01-01
In the framework of the Lindblad theory for open quantum systems we determine the degree of quantum decoherence of a harmonic oscillator interacting with a thermal bath. In the present paper we have studied QD with the Markovian equation of Lindblad in order to understand the quantum to classical transition for a system consisting of an one-dimensional harmonic oscillator in interaction with a thermal bath in the framework of the theory of open quantum systems based on quantum dynamical semigroups. The role of QD became relevant in many interesting physical problems from field theory, atomic physics, quantum optics and quantum information processing, to which we can add material science, heavy ion collisions, quantum gravity and cosmology, condensed matter physics. Just to mention only a few of them: to understand the way in which QD enhances the quantum to classical transition of density fluctuations; to study systems of trapped and cold atoms (or ions) which may offer the possibility of engineering the environment, like trapped atoms inside cavities, relation between decoherence and other cavity QED effects (such as Casimir effect); on mesoscopic scale, decoherence in the context of Bose-Einstein condensation. In many cases physicists are interested in understanding the specific causes of QD just because they want to prevent decoherence from damaging quantum states and to protect the information stored in quantum states from the degrading effect of the interaction with the environment. Thus, decoherence is responsible for washing out the quantum interference effects which are desirable to be seen as signals in some experiments. QD has a negative influence on many areas relying upon quantum coherence effects, such as quantum computation and quantum control of atomic and molecular processes. The physics of information and computation is such a case, where decoherence is an obvious major obstacle in the implementation of information-processing hardware that takes
Enhancement of Quantum Correlations in Qubit-Qutrit Systems under the non-Markovian Environment
Institute of Scientific and Technical Information of China (English)
Abdul Basit; Hamad Ali; Fazal Badshah; Guo-Qin Ge
2017-01-01
We investigate the time evolution of quantum correlations of a hybrid qubit-qutrit system under the classical Ornstein-Uhlenbeck (OU) noise.Here we consider two different one-parameter families of qubit-qutrit states which independently interact with the non-Markovian reservoirs.A comparison with the Markovian dynamics reveals that for the same set of initial condition parameters,the non-Markovian behavior of the environment plays an important role in the enhancement of the survival time of quantum correlations.In addition,it is observed that the non-Markovian strength (γ/F) has a positive impact on the correlations time.For the initial separable states it is found that there is a finite time interval in which the geometric quantum discord is frozen despite the presence of a noisy environment and that interval can be further prolonged by using the non-Markovian property.Moreover,its decay can be significantly delayed.
Iotti, Rita Claudia; Rossi, Fausto
2017-12-01
Microscopic modeling of electronic phase coherence versus energy dissipation plays a crucial role in the design and optimization of new-generation electronic quantum nanodevices, like quantum-cascade light sources and quantum logic gates; in this context, non-Markovian density-matrix approaches are widely used simulation strategies. Here we show that such methods, along with valuable virtues, in some circumstances may exhibit potential limitations that need to be taken into account for a reliable description of quantum materials and related devices. More specifically, extending the analysis recently proposed in [EPL 112, 67005 (2015)] to high temperatures and degenerate conditions, we show that the usual mean-field treatment - employed to derive quantum-kinetic equations - in some cases may lead to anomalous results, characterized by decoherence suppression and positivity violations. By means of a simple two-level model, we show that such unexpected behaviors may affect zero-dimensional electronic systems coupled to dispersionless phonon modes, while such anomalies are expected to play a negligible role in nanosystems with higher dimensionality; these limitations are found to be significant in the low-density and low-temperature limit, while in the degenerate and/or finite-temperature regime - typical of many state-of-the-art quantum devices - their impact is strongly reduced.
Exact solution for a non-Markovian dissipative quantum dynamics.
Ferialdi, Luca; Bassi, Angelo
2012-04-27
We provide the exact analytic solution of the stochastic Schrödinger equation describing a harmonic oscillator interacting with a non-Markovian and dissipative environment. This result represents an arrival point in the study of non-Markovian dynamics via stochastic differential equations. It is also one of the few exactly solvable models for infinite-dimensional systems. We compute the Green's function; in the case of a free particle and with an exponentially correlated noise, we discuss the evolution of Gaussian wave functions.
Open quantum generalisation of Hopfield neural networks
Rotondo, P.; Marcuzzi, M.; Garrahan, J. P.; Lesanovsky, I.; Müller, M.
2018-03-01
We propose a new framework to understand how quantum effects may impact on the dynamics of neural networks. We implement the dynamics of neural networks in terms of Markovian open quantum systems, which allows us to treat thermal and quantum coherent effects on the same footing. In particular, we propose an open quantum generalisation of the Hopfield neural network, the simplest toy model of associative memory. We determine its phase diagram and show that quantum fluctuations give rise to a qualitatively new non-equilibrium phase. This novel phase is characterised by limit cycles corresponding to high-dimensional stationary manifolds that may be regarded as a generalisation of storage patterns to the quantum domain.
Fault-tolerant quantum computation for local non-Markovian noise
International Nuclear Information System (INIS)
Terhal, Barbara M.; Burkard, Guido
2005-01-01
We derive a threshold result for fault-tolerant quantum computation for local non-Markovian noise models. The role of error amplitude in our analysis is played by the product of the elementary gate time t 0 and the spectral width of the interaction Hamiltonian between system and bath. We discuss extensions of our model and the applicability of our analysis
Controlling quantum memory-assisted entropic uncertainty in non-Markovian environments
Zhang, Yanliang; Fang, Maofa; Kang, Guodong; Zhou, Qingping
2018-03-01
Quantum memory-assisted entropic uncertainty relation (QMA EUR) addresses that the lower bound of Maassen and Uffink's entropic uncertainty relation (without quantum memory) can be broken. In this paper, we investigated the dynamical features of QMA EUR in the Markovian and non-Markovian dissipative environments. It is found that dynamical process of QMA EUR is oscillation in non-Markovian environment, and the strong interaction is favorable for suppressing the amount of entropic uncertainty. Furthermore, we presented two schemes by means of prior weak measurement and posterior weak measurement reversal to control the amount of entropic uncertainty of Pauli observables in dissipative environments. The numerical results show that the prior weak measurement can effectively reduce the wave peak values of the QMA-EUA dynamic process in non-Markovian environment for long periods of time, but it is ineffectual on the wave minima of dynamic process. However, the posterior weak measurement reversal has an opposite effects on the dynamic process. Moreover, the success probability entirely depends on the quantum measurement strength. We hope that our proposal could be verified experimentally and might possibly have future applications in quantum information processing.
Energy Technology Data Exchange (ETDEWEB)
Hoerhammer, C.
2007-11-26
In this thesis, non-Markovian dynamics, decoherence and entanglement in dissipative quantum systems are studied. In particular, applications to quantum information theory of continuous variable systems are considered. The non-Markovian dynamics are described by the Hu-Paz-Zhang master equation of quantum Brownian motion. In this context the focus is on non-Markovian effects on decoherence and separability time scales of various single- mode and two-mode continuous variable states. It is verified that moderate non-Markovian influences slow down the decay of interference fringes and quantum correlations, while strong non-Markovian effects resulting from an out-of-resonance bath can even accelerate the loss of coherence, compared to predictions of Markovian approximations. Qualitatively different scenarios including exponential, Gaussian or algebraic decay of the decoherence function are analyzed. It is shown that partial recurrence of coherence can occur in case of non-Lindblad-type dynamics. The time evolution of quantum correlations of entangled two-mode continuous variable states is examined in single-reservoir and two-reservoir models, representing noisy correlated or uncorrelated non-Markovian quantum channels. For this purpose the model of quantum Brownian motion is extended. Various separability criteria for Gaussian and non-Gaussian continuous variable systems are applied. In both types of reservoir models moderate non-Markovian effects prolong the separability time scales. However, in these models the properties of the stationary state may differ. In the two-reservoir model the initial entanglement is completely lost and both modes are finally uncorrelated. In a common reservoir both modes interact indirectly via the coupling to the same bath variables. Therefore, new quantum correlations may emerge between the two modes. Below a critical bath temperature entanglement is preserved even in the steady state. A separability criterion is derived, which depends
Directory of Open Access Journals (Sweden)
Pengqin Shi
2016-09-01
Full Text Available Based on the time-nonlocal particle number-resolved master equation, we investigate the sequential electron transport through the interacting double quantum dots. Our calculations show that there exists the effect of energy renormalization in the dispersion of the bath interaction spectrum and it is sensitive to the the bandwidth of the bath. This effect would strongly affect the stationary current and its zero-frequency shot noise for weak inter-dot coherent coupling strength, but for strong inter-dot coupling regime, it is negligible due to the strong intrinsic Rabi coherent dynamics. Moreover, the possible observable effects of the energy renormalization in the noise spectrum are also investigated through the Rabi coherence signal. Finally, the non-Markovian effect is manifested in the finite-frequency noise spectrum with the appearance of quasisteps, and the magnitude of these quasisteps are modified by the dispersion function.
Noninvasive Quantum Measurement of Arbitrary Operator Order by Engineered Non-Markovian Detectors
Bülte, Johannes; Bednorz, Adam; Bruder, Christoph; Belzig, Wolfgang
2018-04-01
The development of solid-state quantum technologies requires the understanding of quantum measurements in interacting, nonisolated quantum systems. In general, a permanent coupling of detectors to a quantum system leads to memory effects that have to be taken into account in interpreting the measurement results. We analyze a generic setup of two detectors coupled to a quantum system and derive a compact formula in the weak-measurement limit that interpolates between an instantaneous (text-book type) and almost continuous—detector dynamics-dependent—measurement. A quantum memory effect that we term "system-mediated detector-detector interaction" is crucial to observe noncommuting observables simultaneously. Finally, we propose a mesoscopic double-dot detector setup in which the memory effect is tunable and that can be used to explore the transition to non-Markovian quantum measurements experimentally.
International Nuclear Information System (INIS)
Deb, Prasenjit; Banik, Manik
2015-01-01
Quantum correlation lies at the very heart of almost all of the non-classical phenomena exhibited by quantum systems composed of two or more subsystems. In recent times it has been pointed out that there is a kind of quantum correlation, namely discord, which is more general than entanglement. Some authors have investigated the phenomenon that for certain initial states the quantum correlations as well as the classical correlations exhibit sudden change under simple Markovian noise. We show that this dynamical behavior of the correlations of both types can be explained using the idea of complementary correlations. We also show that though a certain class of mixed entangled states can resist the monotonic decay of quantum correlations, this is not true for all mixed states. Moreover, pure entangled states of two qubits will never exhibit such sudden change. (paper)
Non-Markovian entanglement dynamics of noisy continuous-variable quantum channels
International Nuclear Information System (INIS)
An, J.-H.; Zhang, W.-M.
2007-01-01
We investigate the entanglement dynamics of continuous-variable quantum channels in terms of an entangled squeezed state of two cavity fields in a general non-Markovian environment. Using the Feynman-Vernon influence functional theory in the coherent-state representation, we derive an exact master equation with time-dependent coefficients reflecting the non-Markovian influence of the environment. The influence of environments with different spectral densities, e.g., Ohmic, sub-Ohmic, and super-Ohmic, is numerically studied. The non-Markovian process shows its remarkable influence on the entanglement dynamics due to the sensitive time dependence of the dissipation and noise functions within the typical time scale of the environment. The Ohmic environment shows a weak dissipation-noise effect on the entanglement dynamics, while the sub-Ohmic and super-Ohmic environments induce much more severe noise. In particular, the memory of the system interacting with the environment contributes a strong decoherence effect to the entanglement dynamics in the super-Ohmic case
Open quantum systems and error correction
Shabani Barzegar, Alireza
Quantum effects can be harnessed to manipulate information in a desired way. Quantum systems which are designed for this purpose are suffering from harming interaction with their surrounding environment or inaccuracy in control forces. Engineering different methods to combat errors in quantum devices are highly demanding. In this thesis, I focus on realistic formulations of quantum error correction methods. A realistic formulation is the one that incorporates experimental challenges. This thesis is presented in two sections of open quantum system and quantum error correction. Chapters 2 and 3 cover the material on open quantum system theory. It is essential to first study a noise process then to contemplate methods to cancel its effect. In the second chapter, I present the non-completely positive formulation of quantum maps. Most of these results are published in [Shabani and Lidar, 2009b,a], except a subsection on geometric characterization of positivity domain of a quantum map. The real-time formulation of the dynamics is the topic of the third chapter. After introducing the concept of Markovian regime, A new post-Markovian quantum master equation is derived, published in [Shabani and Lidar, 2005a]. The section of quantum error correction is presented in three chapters of 4, 5, 6 and 7. In chapter 4, we introduce a generalized theory of decoherence-free subspaces and subsystems (DFSs), which do not require accurate initialization (published in [Shabani and Lidar, 2005b]). In Chapter 5, we present a semidefinite program optimization approach to quantum error correction that yields codes and recovery procedures that are robust against significant variations in the noise channel. Our approach allows us to optimize the encoding, recovery, or both, and is amenable to approximations that significantly improve computational cost while retaining fidelity (see [Kosut et al., 2008] for a published version). Chapter 6 is devoted to a theory of quantum error correction (QEC
Deterministic quantum controlled-PHASE gates based on non-Markovian environments
Zhang, Rui; Chen, Tian; Wang, Xiang-Bin
2017-12-01
We study the realization of the quantum controlled-PHASE gate in an atom-cavity system beyond the Markovian approximation. The general description of the dynamics for the atom-cavity system without any approximation is presented. When the spectral density of the reservoir has the Lorentz form, by making use of the memory backflow from the reservoir, we can always construct the deterministic quantum controlled-PHASE gate between a photon and an atom, no matter the atom-cavity coupling strength is weak or strong. While, the phase shift in the output pulse hinders the implementation of quantum controlled-PHASE gates in the sub-Ohmic, Ohmic or super-Ohmic reservoirs.
International Nuclear Information System (INIS)
Zhao Xinyu; Jing Jun; Corn, Brittany; Yu Ting
2011-01-01
Non-Markovian dynamics is studied for two interacting qubits strongly coupled to a dissipative bosonic environment. We derive a non-Markovian quantum-state-diffusion (QSD) equation for the coupled two-qubit system without any approximations, and in particular, without the Markov approximation. As an application and illustration of our derived time-local QSD equation, we investigate the temporal behavior of quantum coherence dynamics. In particular, we find a strongly non-Markovian regime where entanglement generation is significantly modulated by the environmental memory. Additionally, we study residual entanglement in the steady state by analyzing the steady-state solution of the QSD equation. Finally, we discuss an approximate QSD equation.
Quantum theory of multiple-input-multiple-output Markovian feedback with diffusive measurements
International Nuclear Information System (INIS)
Chia, A.; Wiseman, H. M.
2011-01-01
Feedback control engineers have been interested in multiple-input-multiple-output (MIMO) extensions of single-input-single-output (SISO) results of various kinds due to its rich mathematical structure and practical applications. An outstanding problem in quantum feedback control is the extension of the SISO theory of Markovian feedback by Wiseman and Milburn [Phys. Rev. Lett. 70, 548 (1993)] to multiple inputs and multiple outputs. Here we generalize the SISO homodyne-mediated feedback theory to allow for multiple inputs, multiple outputs, and arbitrary diffusive quantum measurements. We thus obtain a MIMO framework which resembles the SISO theory and whose additional mathematical structure is highlighted by the extensive use of vector-operator algebra.
Quantum metrology subject to spatially correlated Markovian noise: restoring the Heisenberg limit
International Nuclear Information System (INIS)
Jeske, Jan; Cole, Jared H; Huelga, Susana F
2014-01-01
Environmental noise can hinder the metrological capabilities of entangled states. While the use of entanglement allows for Heisenberg-limited resolution, the largest permitted by quantum mechanics, deviations from strictly unitary dynamics quickly restore the standard scaling dictated by the central limit theorem. Product and maximally entangled states become asymptotically equivalent when the noisy evolution is both local and strictly Markovian. However, temporal correlations in the noise have been shown to lift this equivalence while fully (spatially) correlated noise allows for the identification of decoherence-free subspaces. Here we analyze precision limits in the presence of noise with finite correlation length and show that there exist robust entangled state preparations which display persistent Heisenberg scaling despite the environmental decoherence, even for small correlation length. Our results emphasize the relevance of noise correlations in the study of quantum advantage and could be relevant beyond metrological applications. (paper)
International Nuclear Information System (INIS)
Gambetta, Jay; Wiseman, H.M.
2002-01-01
Do stochastic Schroedinger equations, also known as unravelings, have a physical interpretation? In the Markovian limit, where the system on average obeys a master equation, the answer is yes. Markovian stochastic Schroedinger equations generate quantum trajectories for the system state conditioned on continuously monitoring the bath. For a given master equation, there are many different unravelings, corresponding to different sorts of measurement on the bath. In this paper we address the non-Markovian case, and in particular the sort of stochastic Schroedinger equation introduced by Strunz, Diosi, and Gisin [Phys. Rev. Lett. 82, 1801 (1999)]. Using a quantum-measurement theory approach, we rederive their unraveling that involves complex-valued Gaussian noise. We also derive an unraveling involving real-valued Gaussian noise. We show that in the Markovian limit, these two unravelings correspond to heterodyne and homodyne detection, respectively. Although we use quantum-measurement theory to define these unravelings, we conclude that the stochastic evolution of the system state is not a true quantum trajectory, as the identity of the state through time is a fiction
Giorgi, Gian Luca; Galve, Fernando; Zambrini, Roberta
2015-08-01
Quantum Darwinism explains the emergence of a classical description of objects in terms of the creation of many redundant registers in an environment containing their classical information. This amplification phenomenon, where only classical information reaches the macroscopic observer and through which different observers can agree on the objective existence of such object, has been revived lately for several types of situations, successfully explaining classicality. We explore quantum Darwinism in the setting of an environment made of two level systems which are initially prepared in the ground state of the XX model, which exhibits different phases; we find that the different phases have different abilities to redundantly acquire classical information about the system, the "ferromagnetic phase" being the only one able to complete quantum Darwinism. At the same time we relate this ability to how non-Markovian the system dynamics is, based on the interpretation that non-Markovian dynamics is associated with backflow of information from environment to system, thus spoiling the information transfer needed for Darwinism. Finally, we explore mixing of bath registers by allowing a small interaction among them, finding that this spoils the stored information as previously found in the literature.
International Nuclear Information System (INIS)
Zou, Hong-Mei; Fang, Mao-Fa; Yang, Bai-Yuan; Guo, You-Neng; He, Wei; Zhang, Shi-Yang
2014-01-01
The quantum entropic uncertainty relation and entanglement witness in the two-atom system coupling with the non-Markovian environments are studied using the time-convolutionless master-equation approach. The influence of the non-Markovian effect and detuning on the lower bound of the quantum entropic uncertainty relation and entanglement witness is discussed in detail. The results show that, only if the two non-Markovian reservoirs are identical, increasing detuning and non-Markovian effect can reduce the lower bound of the entropic uncertainty relation, lengthen the time region during which the entanglement can be witnessed, and effectively protect the entanglement region witnessed by the lower bound of the entropic uncertainty relation. The results can be applied in quantum measurement, quantum cryptography tasks and quantum information processing. (paper)
Quantum algorithm for simulating the dynamics of an open quantum system
International Nuclear Information System (INIS)
Wang Hefeng; Ashhab, S.; Nori, Franco
2011-01-01
In the study of open quantum systems, one typically obtains the decoherence dynamics by solving a master equation. The master equation is derived using knowledge of some basic properties of the system, the environment, and their interaction: One basically needs to know the operators through which the system couples to the environment and the spectral density of the environment. For a large system, it could become prohibitively difficult to even write down the appropriate master equation, let alone solve it on a classical computer. In this paper, we present a quantum algorithm for simulating the dynamics of an open quantum system. On a quantum computer, the environment can be simulated using ancilla qubits with properly chosen single-qubit frequencies and with properly designed coupling to the system qubits. The parameters used in the simulation are easily derived from the parameters of the system + environment Hamiltonian. The algorithm is designed to simulate Markovian dynamics, but it can also be used to simulate non-Markovian dynamics provided that this dynamics can be obtained by embedding the system of interest into a larger system that obeys Markovian dynamics. We estimate the resource requirements for the algorithm. In particular, we show that for sufficiently slow decoherence a single ancilla qubit could be sufficient to represent the entire environment, in principle.
Perturbation expansions of stochastic wavefunctions for open quantum systems
Ke, Yaling; Zhao, Yi
2017-11-01
Based on the stochastic unravelling of the reduced density operator in the Feynman path integral formalism for an open quantum system in touch with harmonic environments, a new non-Markovian stochastic Schrödinger equation (NMSSE) has been established that allows for the systematic perturbation expansion in the system-bath coupling to arbitrary order. This NMSSE can be transformed in a facile manner into the other two NMSSEs, i.e., non-Markovian quantum state diffusion and time-dependent wavepacket diffusion method. Benchmarked by numerically exact results, we have conducted a comparative study of the proposed method in its lowest order approximation, with perturbative quantum master equations in the symmetric spin-boson model and the realistic Fenna-Matthews-Olson complex. It is found that our method outperforms the second-order time-convolutionless quantum master equation in the whole parameter regime and even far better than the fourth-order in the slow bath and high temperature cases. Besides, the method is applicable on an equal footing for any kind of spectral density function and is expected to be a powerful tool to explore the quantum dynamics of large-scale systems, benefiting from the wavefunction framework and the time-local appearance within a single stochastic trajectory.
Non-Markovian dynamics of quantum systems: decay rate, capture and pure states
International Nuclear Information System (INIS)
Kanokov, Z.; Palchikov, Yu.V.; Antonenko, N.V.; Adamian, G.G.; Kanokov, Z.; Adamian, G.G.; Scheid, W.
2004-01-01
Full text: With the exact numerical solution of the equation for the reduced density matrix we found a minor role of the time dependence of the friction and diffusion coefficients in the escape rate from a potential well [1]. Since the used friction and diffusion coefficients were self- consistently under certain approximations derived, they preserve the positivity of the density matrix at any time. The mixed diffusion coefficient leads to a decrease of the escape rate. Since the used value of quantum diffusion coefficient in momentum is larger than the one following from a 'classic' treatment, the obtained escape rate is close to the rate calculated with the 'classic' set of diffusion coefficients. If the regime of motion is close to the under damped case or the temperature is small, the quasi-stationary escape rate can increase with friction. This is explained by the larger role of the increasing diffusion in the decay process. The agreement of the escape rate obtained with the analytical expressions in comparison to numerically calculated data depends on the characteristics of the considered system. The agreement is better in the overdamped regime. However, for any regime the deviations are not larger than in the case of the classical Kramers formula. Therefore, the analytical expressions can be applied in a large range of parameters for the potential and diffusion coefficients. We demonstrated that the uncertainty function is related to the linear entropy. The diffusion coefficients supplying the purity of states were elaborated for the non-Markovian dynamics. The obtained dependences of the capture probability on the friction proves that the quantum nature of this process should be taken into consideration when one calculates the capture cross section in nucleus-nucleus collisions
Fractal-Markovian scaling of turbulent bursting process in open channel flow
International Nuclear Information System (INIS)
Keshavarzi, Ali Reza; Ziaei, Ali Naghi; Homayoun, Emdad; Shirvani, Amin
2005-01-01
The turbulent coherent structure of flow in open channel is a chaotic and stochastic process in nature. The coherence structure of the flow or bursting process consists of a series of eddies with a variety of different length scales and it is very important for the entrainment of sediment particles from the bed. In this study, a fractal-Markovian process is applied to the measured turbulent data in open channel. The turbulent data was measured in an experimental flume using three-dimensional acoustic Doppler velocity meter (ADV). A fractal interpolation function (FIF) algorithm was used to simulate more than 500,000 time series data of measured instantaneous velocity fluctuations and Reynolds shear stress. The fractal interpolation functions (FIF) enables to simulate and construct time series of u', v', and u'v' for any particular movement and state in the Markov process. The fractal dimension of the bursting events is calculated for 16 particular movements with the transition probability of the events based on 1st order Markov process. It was found that the average fractal dimensions of the streamwise flow velocity (u') are; 1.73, 1.74, 1.71 and 1.74 with the transition probability of 60.82%, 63.77%, 59.23% and 62.09% for the 1-1, 2-2, 3-3 and 4-4 movements, respectively. It was also found that the fractal dimensions of Reynold stress u'v' for quadrants 1, 2, 3 and 4 are 1.623, 1.623, 1.625 and 1.618, respectively
Open quantum dynamics via environmental monitoring
Energy Technology Data Exchange (ETDEWEB)
Hornberger, Klaus [Arnold Sommerfeld Center for Theoretical Physics, Ludwig-Maximilians-Universitaet Muenchen, Theresienstrasse 37, 80333 Munich (Germany)
2007-05-15
A general method is discussed to obtain Markovian master equations which describe the interaction with the environment in a microscopic and non-perturbative fashion. It is based on combining time-dependent scattering theory with the concept of continuous quantum measurements. The applications to the case of a Brownian point particle and to the case of a complex molecule, both in the presence of a gaseous environment, are outlined.
The open quantum Brownian motions
International Nuclear Information System (INIS)
Bauer, Michel; Bernard, Denis; Tilloy, Antoine
2014-01-01
Using quantum parallelism on random walks as the original seed, we introduce new quantum stochastic processes, the open quantum Brownian motions. They describe the behaviors of quantum walkers—with internal degrees of freedom which serve as random gyroscopes—interacting with a series of probes which serve as quantum coins. These processes may also be viewed as the scaling limit of open quantum random walks and we develop this approach along three different lines: the quantum trajectory, the quantum dynamical map and the quantum stochastic differential equation. We also present a study of the simplest case, with a two level system as an internal gyroscope, illustrating the interplay between the ballistic and diffusive behaviors at work in these processes. Notation H z : orbital (walker) Hilbert space, C Z in the discrete, L 2 (R) in the continuum H c : internal spin (or gyroscope) Hilbert space H sys =H z ⊗H c : system Hilbert space H p : probe (or quantum coin) Hilbert space, H p =C 2 ρ t tot : density matrix for the total system (walker + internal spin + quantum coins) ρ-bar t : reduced density matrix on H sys : ρ-bar t =∫dxdy ρ-bar t (x,y)⊗|x〉 z 〈y| ρ-hat t : system density matrix in a quantum trajectory: ρ-hat t =∫dxdy ρ-hat t (x,y)⊗|x〉 z 〈y|. If diagonal and localized in position: ρ-hat t =ρ t ⊗|X t 〉 z 〈X t | ρ t : internal density matrix in a simple quantum trajectory X t : walker position in a simple quantum trajectory B t : normalized Brownian motion ξ t , ξ t † : quantum noises (paper)
Non-Markovianity-assisted high-fidelity Deutsch-Jozsa algorithm in diamond
Dong, Yang; Zheng, Yu; Li, Shen; Li, Cong-Cong; Chen, Xiang-Dong; Guo, Guang-Can; Sun, Fang-Wen
2018-01-01
The memory effects in non-Markovian quantum dynamics can induce the revival of quantum coherence, which is believed to provide important physical resources for quantum information processing (QIP). However, no real quantum algorithms have been demonstrated with the help of such memory effects. Here, we experimentally implemented a non-Markovianity-assisted high-fidelity refined Deutsch-Jozsa algorithm (RDJA) with a solid spin in diamond. The memory effects can induce pronounced non-monotonic variations in the RDJA results, which were confirmed to follow a non-Markovian quantum process by measuring the non-Markovianity of the spin system. By applying the memory effects as physical resources with the assistance of dynamical decoupling, the probability of success of RDJA was elevated above 97% in the open quantum system. This study not only demonstrates that the non-Markovianity is an important physical resource but also presents a feasible way to employ this physical resource. It will stimulate the application of the memory effects in non-Markovian quantum dynamics to improve the performance of practical QIP.
Interpretation of non-Markovian stochastic Schroedinger equations as a hidden-variable theory
International Nuclear Information System (INIS)
Gambetta, Jay; Wiseman, H.M.
2003-01-01
Do diffusive non-Markovian stochastic Schroedinger equations (SSEs) for open quantum systems have a physical interpretation? In a recent paper [Phys. Rev. A 66, 012108 (2002)] we investigated this question using the orthodox interpretation of quantum mechanics. We found that the solution of a non-Markovian SSE represents the state the system would be in at that time if a measurement was performed on the environment at that time, and yielded a particular result. However, the linking of solutions at different times to make a trajectory is, we concluded, a fiction. In this paper we investigate this question using the modal (hidden variable) interpretation of quantum mechanics. We find that the noise function z(t) appearing in the non-Markovian SSE can be interpreted as a hidden variable for the environment. That is, some chosen property (beable) of the environment has a definite value z(t) even in the absence of measurement on the environment. The non-Markovian SSE gives the evolution of the state of the system 'conditioned' on this environment hidden variable. We present the theory for diffusive non-Markovian SSEs that have as their Markovian limit SSEs corresponding to homodyne and heterodyne detection, as well as one which has no Markovian limit
Asymptotically open quantum systems
International Nuclear Information System (INIS)
Westrich, M.
2008-04-01
In the present thesis we investigate the structure of time-dependent equations of motion in quantum mechanics.We start from two coupled systems with an autonomous equation of motion. A limit, in which the dynamics of one of the two systems has a decoupled evolution and imposes a non-autonomous evolution for the second system is identified. A result due to K. Hepp that provides a classical limit for dynamics turns out to be part and parcel for this limit and is generalized in our work. The method introduced by J.S. Howland for the solution of the time-dependent Schroedinger equation is interpreted as such a limit. Moreover, we associate our limit with the modern theory of quantization. (orig.)
Revealing electronic open quantum systems with subsystem TDDFT
Krishtal, Alisa; Pavanello, Michele
2016-03-01
Open quantum systems (OQSs) are perhaps the most realistic systems one can approach through simulations. In recent years, describing OQSs with Density Functional Theory (DFT) has been a prominent avenue of research with most approaches based on a density matrix partitioning in conjunction with an ad-hoc description of system-bath interactions. We propose a different theoretical approach to OQSs based on partitioning of the electron density. Employing the machinery of subsystem DFT (and its time-dependent extension), we provide a novel way of isolating and analyzing the various terms contributing to the coupling between the system and the surrounding bath. To illustrate the theory, we provide numerical simulations on a toy system (a molecular dimer) and on a condensed phase system (solvated excimer). The simulations show that non-Markovian dynamics in the electronic system-bath interactions are important in chemical applications. For instance, we show that the superexchange mechanism of transport in donor-bridge-acceptor systems is a non-Markovian interaction between the donor-acceptor (OQS) with the bridge (bath) which is fully characterized by real-time subsystem time-dependent DFT.
Revealing electronic open quantum systems with subsystem TDDFT.
Krishtal, Alisa; Pavanello, Michele
2016-03-28
Open quantum systems (OQSs) are perhaps the most realistic systems one can approach through simulations. In recent years, describing OQSs with Density Functional Theory (DFT) has been a prominent avenue of research with most approaches based on a density matrix partitioning in conjunction with an ad-hoc description of system-bath interactions. We propose a different theoretical approach to OQSs based on partitioning of the electron density. Employing the machinery of subsystem DFT (and its time-dependent extension), we provide a novel way of isolating and analyzing the various terms contributing to the coupling between the system and the surrounding bath. To illustrate the theory, we provide numerical simulations on a toy system (a molecular dimer) and on a condensed phase system (solvated excimer). The simulations show that non-Markovian dynamics in the electronic system-bath interactions are important in chemical applications. For instance, we show that the superexchange mechanism of transport in donor-bridge-acceptor systems is a non-Markovian interaction between the donor-acceptor (OQS) with the bridge (bath) which is fully characterized by real-time subsystem time-dependent DFT.
Non-Markovianity in the collision model with environmental block
Jin, Jiasen; Yu, Chang-shui
2018-05-01
We present an extended collision model to simulate the dynamics of an open quantum system. In our model, the unit to represent the environment is, instead of a single particle, a block which consists of a number of environment particles. The introduced blocks enable us to study the effects of different strategies of system–environment interactions and states of the blocks on the non-Markovianities. We demonstrate our idea in the Gaussian channels of an all-optical system and derive a necessary and sufficient condition of non-Markovianity for such channels. Moreover, we show the equivalence of our criterion to the non-Markovian quantum jump in the simulation of the pure damping process of a single-mode field. We also show that the non-Markovianity of the channel working in the strategy that the system collides with environmental particles in each block in a certain order will be affected by the size of the block and the embedded entanglement and the effects of heating and squeezing the vacuum environmental state will quantitatively enhance the non-Markovianity.
Nonlinear Quantum Metrology of Many-Body Open Systems
Beau, M.; del Campo, A.
2017-07-01
We introduce general bounds for the parameter estimation error in nonlinear quantum metrology of many-body open systems in the Markovian limit. Given a k -body Hamiltonian and p -body Lindblad operators, the estimation error of a Hamiltonian parameter using a Greenberger-Horne-Zeilinger state as a probe is shown to scale as N-[k -(p /2 )], surpassing the shot-noise limit for 2 k >p +1 . Metrology equivalence between initial product states and maximally entangled states is established for p ≥1 . We further show that one can estimate the system-environment coupling parameter with precision N-(p /2 ), while many-body decoherence enhances the precision to N-k in the noise-amplitude estimation of a fluctuating k -body Hamiltonian. For the long-range Ising model, we show that the precision of this parameter beats the shot-noise limit when the range of interactions is below a threshold value.
Non-Markovianity and memory of the initial state
Hinarejos, Margarida; Bañuls, Mari-Carmen; Pérez, Armando; de Vega, Inés
2017-08-01
We explore in a rigorous manner the intuitive connection between the non-Markovianity of the evolution of an open quantum system and the performance of the system as a quantum memory. Using the paradigmatic case of a two-level open quantum system coupled to a bosonic bath, we compute the recovery fidelity, which measures the best possible performance of the system to store a qubit of information. We deduce that this quantity is connected, but not uniquely determined, by the non-Markovianity, for which we adopt the Breuer-Laine-Piilo measure proposed in Breuer et al (2009 Phys. Rev. Lett. 103 210401). We illustrate our findings with explicit calculations for the case of a structured environment.
A Dynamical Theory of Markovian Diffusion
Davidson, Mark
2001-01-01
A dynamical treatment of Markovian diffusion is presented and several applications discussed. The stochastic interpretation of quantum mechanics is considered within this framework. A model for Brownian movement which includes second order quantum effects is derived.
Qubit models of weak continuous measurements: markovian conditional and open-system dynamics
Gross, Jonathan A.; Caves, Carlton M.; Milburn, Gerard J.; Combes, Joshua
2018-04-01
In this paper we approach the theory of continuous measurements and the associated unconditional and conditional (stochastic) master equations from the perspective of quantum information and quantum computing. We do so by showing how the continuous-time evolution of these master equations arises from discretizing in time the interaction between a system and a probe field and by formulating quantum-circuit diagrams for the discretized evolution. We then reformulate this interaction by replacing the probe field with a bath of qubits, one for each discretized time segment, reproducing all of the standard quantum-optical master equations. This provides an economical formulation of the theory, highlighting its fundamental underlying assumptions.
Quantum speed limits in open system dynamics
del Campo, A.; Egusquiza, I. L.; Plenio, M. B.; Huelga, S. F.
2012-01-01
Bounds to the speed of evolution of a quantum system are of fundamental interest in quantum metrology, quantum chemical dynamics and quantum computation. We derive a time-energy uncertainty relation for open quantum systems undergoing a general, completely positive and trace preserving (CPT) evolution which provides a bound to the quantum speed limit. When the evolution is of the Lindblad form, the bound is analogous to the Mandelstam-Tamm relation which applies in the unitary case, with the ...
Controllable Subspaces of Open Quantum Dynamical Systems
International Nuclear Information System (INIS)
Zhang Ming; Gong Erling; Xie Hongwei; Hu Dewen; Dai Hongyi
2008-01-01
This paper discusses the concept of controllable subspace for open quantum dynamical systems. It is constructively demonstrated that combining structural features of decoherence-free subspaces with the ability to perform open-loop coherent control on open quantum systems will allow decoherence-free subspaces to be controllable. This is in contrast to the observation that open quantum dynamical systems are not open-loop controllable. To a certain extent, this paper gives an alternative control theoretical interpretation on why decoherence-free subspaces can be useful for quantum computation.
Memory Effects and Nonequilibrium Correlations in the Dynamics of Open Quantum Systems
Morozov, V. G.
2018-01-01
We propose a systematic approach to the dynamics of open quantum systems in the framework of Zubarev's nonequilibrium statistical operator method. The approach is based on the relation between ensemble means of the Hubbard operators and the matrix elements of the reduced statistical operator of an open quantum system. This key relation allows deriving master equations for open systems following a scheme conceptually identical to the scheme used to derive kinetic equations for distribution functions. The advantage of the proposed formalism is that some relevant dynamical correlations between an open system and its environment can be taken into account. To illustrate the method, we derive a non-Markovian master equation containing the contribution of nonequilibrium correlations associated with energy conservation.
Kraus map for non-Markovian quantum dynamics driven by a thermal reservoir
van Wonderen, A.J.; Suttorp, L.G.
2013-01-01
Starting from unitary dynamics we study the evolution in time of a non-relativistic quantum system that exchanges energy with a thermal reservoir of harmonic oscillators. System and reservoir are assumed to be initially decorrelated. Reservoir correlation functions are factorized by means of a Kraus
Time-dependent density functional theory for open quantum systems with unitary propagation.
Yuen-Zhou, Joel; Tempel, David G; Rodríguez-Rosario, César A; Aspuru-Guzik, Alán
2010-01-29
We extend the Runge-Gross theorem for a very general class of open quantum systems under weak assumptions about the nature of the bath and its coupling to the system. We show that for Kohn-Sham (KS) time-dependent density functional theory, it is possible to rigorously include the effects of the environment within a bath functional in the KS potential. A Markovian bath functional inspired by the theory of nonlinear Schrödinger equations is suggested, which can be readily implemented in currently existing real-time codes. Finally, calculations on a helium model system are presented.
Duality quantum algorithm efficiently simulates open quantum systems
Wei, Shi-Jie; Ruan, Dong; Long, Gui-Lu
2016-01-01
Because of inevitable coupling with the environment, nearly all practical quantum systems are open system, where the evolution is not necessarily unitary. In this paper, we propose a duality quantum algorithm for simulating Hamiltonian evolution of an open quantum system. In contrast to unitary evolution in a usual quantum computer, the evolution operator in a duality quantum computer is a linear combination of unitary operators. In this duality quantum algorithm, the time evolution of the open quantum system is realized by using Kraus operators which is naturally implemented in duality quantum computer. This duality quantum algorithm has two distinct advantages compared to existing quantum simulation algorithms with unitary evolution operations. Firstly, the query complexity of the algorithm is O(d3) in contrast to O(d4) in existing unitary simulation algorithm, where d is the dimension of the open quantum system. Secondly, By using a truncated Taylor series of the evolution operators, this duality quantum algorithm provides an exponential improvement in precision compared with previous unitary simulation algorithm. PMID:27464855
Linear response theory for quantum open systems
Wei, J. H.; Yan, YiJing
2011-01-01
Basing on the theory of Feynman's influence functional and its hierarchical equations of motion, we develop a linear response theory for quantum open systems. Our theory provides an effective way to calculate dynamical observables of a quantum open system at its steady-state, which can be applied to various fields of non-equilibrium condensed matter physics.
Repeated interactions in open quantum systems
Energy Technology Data Exchange (ETDEWEB)
Bruneau, Laurent, E-mail: laurent.bruneau@u-cergy.fr [Laboratoire AGM, Université de Cergy-Pontoise, Site Saint-Martin, BP 222, 95302 Cergy-Pontoise (France); Joye, Alain, E-mail: Alain.Joye@ujf-grenoble.fr [Institut Fourier, UMR 5582, CNRS-Université Grenoble I, BP 74, 38402 Saint-Martin d’Hères (France); Merkli, Marco, E-mail: merkli@mun.ca [Department of Mathematics and Statistics Memorial University of Newfoundland, St. John' s, NL Canada A1C 5S7 (Canada)
2014-07-15
Analyzing the dynamics of open quantum systems has a long history in mathematics and physics. Depending on the system at hand, basic physical phenomena that one would like to explain are, for example, convergence to equilibrium, the dynamics of quantum coherences (decoherence) and quantum correlations (entanglement), or the emergence of heat and particle fluxes in non-equilibrium situations. From the mathematical physics perspective, one of the main challenges is to derive the irreversible dynamics of the open system, starting from a unitary dynamics of the system and its environment. The repeated interactions systems considered in these notes are models of non-equilibrium quantum statistical mechanics. They are relevant in quantum optics, and more generally, serve as a relatively well treatable approximation of a more difficult quantum dynamics. In particular, the repeated interaction models allow to determine the large time (stationary) asymptotics of quantum systems out of equilibrium.
Ishizaki, Akihito; Tanimura, Yoshitaka
2008-05-01
Based on the influence functional formalism, we have derived a nonperturbative equation of motion for a reduced system coupled to a harmonic bath with colored noise in which the system-bath coupling operator does not necessarily commute with the system Hamiltonian. The resultant expression coincides with the time-convolutionless quantum master equation derived from the second-order perturbative approximation, which is also equivalent to a generalized Redfield equation. This agreement occurs because, in the nonperturbative case, the relaxation operators arise from the higher-order system-bath interaction that can be incorporated into the reduced density matrix as the influence operator; while the second-order interaction remains as a relaxation operator in the equation of motion. While the equation describes the exact dynamics of the density matrix beyond weak system-bath interactions, it does not have the capability to calculate nonlinear response functions appropriately. This is because the equation cannot describe memory effects which straddle the external system interactions due to the reduced description of the bath. To illustrate this point, we have calculated the third-order two-dimensional (2D) spectra for a two-level system from the present approach and the hierarchically coupled equations approach that can handle quantal system-bath coherence thanks to its hierarchical formalism. The numerical demonstration clearly indicates the lack of the system-bath correlation in the present formalism as fast dephasing profiles of the 2D spectra.
Directory of Open Access Journals (Sweden)
V.V.Ignatyuk
2004-01-01
Full Text Available Non-Markovian kinetic equations in the second Born approximation are derived for a two-zone semiconductor excited by a short laser pulse. Both collision dynamics and running nonequilibrium correlations are taken into consideration. The energy balance and relaxation of the system to equilibrium are discussed. Results of numerical solution of the kinetic equations for carriers and phonons are presented.
Quantum dynamics in open quantum-classical systems.
Kapral, Raymond
2015-02-25
Often quantum systems are not isolated and interactions with their environments must be taken into account. In such open quantum systems these environmental interactions can lead to decoherence and dissipation, which have a marked influence on the properties of the quantum system. In many instances the environment is well-approximated by classical mechanics, so that one is led to consider the dynamics of open quantum-classical systems. Since a full quantum dynamical description of large many-body systems is not currently feasible, mixed quantum-classical methods can provide accurate and computationally tractable ways to follow the dynamics of both the system and its environment. This review focuses on quantum-classical Liouville dynamics, one of several quantum-classical descriptions, and discusses the problems that arise when one attempts to combine quantum and classical mechanics, coherence and decoherence in quantum-classical systems, nonadiabatic dynamics, surface-hopping and mean-field theories and their relation to quantum-classical Liouville dynamics, as well as methods for simulating the dynamics.
International Nuclear Information System (INIS)
Goan, Hsi-Sheng; Jian, Chung-Chin; Chen, Po-Wen
2010-01-01
We evaluate the non-Markovian finite-temperature two-time correlation functions (CF's) of system operators of a pure-dephasing spin-boson model in two different ways, one by the direct exact operator technique and the other by the recently derived evolution equations, valid to second order in the system-environment interaction Hamiltonian. This pure-dephasing spin-boson model that is exactly solvable has been extensively studied as a simple decoherence model. However, its exact non-Markovian finite-temperature two-time system operator CF's, to our knowledge, have not been presented in the literature. This may be mainly due to the fact, illustrated in this article, that in contrast to the Markovian case, the time evolution of the reduced density matrix of the system (or the reduced quantum master equation) alone is not sufficient to calculate the two-time system operator CF's of non-Markovian open systems. The two-time CF's obtained using the recently derived evolution equations in the weak system-environment coupling case for this non-Markovian pure-dephasing model happen to be the same as those obtained from the exact evaluation. However, these results significantly differ from the non-Markovian two-time CF's obtained by wrongly directly applying the quantum regression theorem (QRT), a useful procedure to calculate the two-time CF's for weak-coupling Markovian open systems. This demonstrates clearly that the recently derived evolution equations generalize correctly the QRT to non-Markovian finite-temperature cases. It is believed that these evolution equations will have applications in many different branches of physics.
Quantum open system theory: bipartite aspects.
Yu, T; Eberly, J H
2006-10-06
We demonstrate in straightforward calculations that even under ideally weak noise the relaxation of bipartite open quantum systems contains elements not previously encountered in quantum noise physics. While additivity of decay rates is known to be generic for decoherence of a single system, we demonstrate that it breaks down for bipartite coherence of even the simplest composite systems.
Quantum speed limits in open system dynamics.
del Campo, A; Egusquiza, I L; Plenio, M B; Huelga, S F
2013-02-01
Bounds to the speed of evolution of a quantum system are of fundamental interest in quantum metrology, quantum chemical dynamics, and quantum computation. We derive a time-energy uncertainty relation for open quantum systems undergoing a general, completely positive, and trace preserving evolution which provides a bound to the quantum speed limit. When the evolution is of the Lindblad form, the bound is analogous to the Mandelstam-Tamm relation which applies in the unitary case, with the role of the Hamiltonian being played by the adjoint of the generator of the dynamical semigroup. The utility of the new bound is exemplified in different scenarios, ranging from the estimation of the passage time to the determination of precision limits for quantum metrology in the presence of dephasing noise.
Evolution of entropy in different types of non-Markovian three-level ...
Indian Academy of Sciences (India)
ference between Markovian and non-Markovian systems lies in the memory ... In recent years, research on quantum entanglement has attracted a lot of attention, which .... Hamiltonians for three types of atoms in the interaction picture are.
Entanglement, non-Markovianity, and causal non-separability
Milz, Simon; Pollock, Felix A.; Le, Thao P.; Chiribella, Giulio; Modi, Kavan
2018-03-01
Quantum mechanics, in principle, allows for processes with indefinite causal order. However, most of these causal anomalies have not yet been detected experimentally. We show that every such process can be simulated experimentally by means of non-Markovian dynamics with a measurement on additional degrees of freedom. In detail, we provide an explicit construction to implement arbitrary a causal processes. Furthermore, we give necessary and sufficient conditions for open system dynamics with measurement to yield processes that respect causality locally, and find that tripartite entanglement and nonlocal unitary transformations are crucial requirements for the simulation of causally indefinite processes. These results show a direct connection between three counter-intuitive concepts: entanglement, non-Markovianity, and causal non-separability.
International Nuclear Information System (INIS)
Fulinski, A.
1994-01-01
The properties of non-Markovian noises with exponentially correlated memory are discussed. Considered are dichotomic noise, white shot noise, Gaussian white noise, and Gaussian colored noise. The stationary correlation functions of the non-Markovian versions of these noises are given by linear combinations of two or three exponential functions (colored noises) or of the δ function and exponential function (white noises). The non-Markovian white noises are well defined only when the kernel of the non-Markovian master equation contains a nonzero admixture of a Markovian term. Approximate equations governing the probability densities for processes driven by such non-Markovian noises are derived, including non-Markovian versions of the Fokker-Planck equation and the telegrapher's equation. As an example, it is shown how the non-Markovian nature changes the behavior of the driven linear process
Basic mechanisms in the laser control of non-Markovian dynamics
Puthumpally-Joseph, R.; Mangaud, E.; Chevet, V.; Desouter-Lecomte, M.; Sugny, D.; Atabek, O.
2018-03-01
Referring to a Fano-type model qualitative analogy we develop a comprehensive basic mechanism for the laser control of the non-Markovian bath response and fully implement it in a realistic control scheme, in strongly coupled open quantum systems. Converged hierarchical equations of motion are worked out to numerically solve the master equation of a spin-boson Hamiltonian to reach the reduced electronic density matrix of a heterojunction in the presence of strong terahertz laser pulses. Robust and efficient control is achieved increasing by a factor of 2 the non-Markovianity measured by the time evolution of the volume of accessible states. The consequences of such fields on the central system populations and coherence are examined, putting the emphasis on the relation between the increase of non-Markovianity and the slowing down of decoherence processes.
QUANTUM AND CLASSICAL CORRELATIONS IN GAUSSIAN OPEN QUANTUM SYSTEMS
Directory of Open Access Journals (Sweden)
Aurelian ISAR
2015-01-01
Full Text Available In the framework of the theory of open systems based on completely positive quantum dynamical semigroups, we give a description of the continuous-variable quantum correlations (quantum entanglement and quantum discord for a system consisting of two noninteracting bosonic modes embedded in a thermal environment. We solve the Kossakowski-Lindblad master equation for the time evolution of the considered system and describe the entanglement and discord in terms of the covariance matrix for Gaussian input states. For all values of the temperature of the thermal reservoir, an initial separable Gaussian state remains separable for all times. We study the time evolution of logarithmic negativity, which characterizes the degree of entanglement, and show that in the case of an entangled initial squeezed thermal state, entanglement suppression takes place for all temperatures of the environment, including zero temperature. We analyze the time evolution of the Gaussian quantum discord, which is a measure of all quantum correlations in the bipartite state, including entanglement, and show that it decays asymptotically in time under the effect of the thermal bath. This is in contrast with the sudden death of entanglement. Before the suppression of the entanglement, the qualitative evolution of quantum discord is very similar to that of the entanglement. We describe also the time evolution of the degree of classical correlations and of quantum mutual information, which measures the total correlations of the quantum system.
Tunneling with dissipation in open quantum systems
International Nuclear Information System (INIS)
Adamyan, G.G.; Antonenko, N.V.; Scheid, W.
1997-01-01
Based on the general form of the master equation for open quantum systems the tunneling is considered. Using the path integral technique a simple closed form expression for the tunneling rate through a parabolic barrier is obtained. The tunneling in the open quantum systems strongly depends on the coupling with environment. We found the cases when the dissipation prohibits tunneling through the barrier but decreases the crossing of the barrier for the energies above the barrier. As a particular application, the case of decay from the metastable state is considered
Scattering theory for open quantum systems
International Nuclear Information System (INIS)
Behrndt, Jussi
2006-01-01
Quantum systems which interact with their environment are often modeled by maximal dissipative operators or so-called Pseudo-Hamiltonians. In this paper the scattering theory for such open systems is considered. First it is assumed that a single maximal dissipative operator A D in a Hilbert space H is used to describe an open quantum system. In this case the minimal self-adjoint dilation K of A D can be regarded as the Hamiltonian of a closed system which contains the open system {A D ,h}, but since K is necessarily not semibounded from below, this model is difficult to interpret from a physical point of view. In the second part of the paper an open quantum system is modeled with a family {A(μ)} of maximal dissipative operators depending on energy μ, and it is shown that the open system can be embedded into a closed system where the Hamiltonian is semibounded. Surprisingly it turns out that the corresponding scattering matrix can be completely recovered from scattering matrices of single Pseudo-Hamiltonians as in the first part of the paper. The general results are applied to a class of Sturm-Liouville operators arising in dissipative and quantum transmitting Schroedinger-Poisson systems. (orig.)
Scattering theory for open quantum systems
Energy Technology Data Exchange (ETDEWEB)
Behrndt, Jussi [Technische Univ. Berlin (Germany). Inst. fuer Mathematik; Malamud, Mark M. [Donetsk National University (Ukraine). Dept. of Mathematics; Neidhardt, Hagen [Weierstrass-Institut fuer Angewandte Analysis und Stochastik (WIAS) im Forschungsverbund Berlin e.V. (Germany)
2006-07-01
Quantum systems which interact with their environment are often modeled by maximal dissipative operators or so-called Pseudo-Hamiltonians. In this paper the scattering theory for such open systems is considered. First it is assumed that a single maximal dissipative operator A{sub D} in a Hilbert space H is used to describe an open quantum system. In this case the minimal self-adjoint dilation K of A{sub D} can be regarded as the Hamiltonian of a closed system which contains the open system {l_brace}A{sub D},h{r_brace}, but since K is necessarily not semibounded from below, this model is difficult to interpret from a physical point of view. In the second part of the paper an open quantum system is modeled with a family {l_brace}A({mu}){r_brace} of maximal dissipative operators depending on energy {mu}, and it is shown that the open system can be embedded into a closed system where the Hamiltonian is semibounded. Surprisingly it turns out that the corresponding scattering matrix can be completely recovered from scattering matrices of single Pseudo-Hamiltonians as in the first part of the paper. The general results are applied to a class of Sturm-Liouville operators arising in dissipative and quantum transmitting Schroedinger-Poisson systems. (orig.)
Quantum state engineering in hybrid open quantum systems
Joshi, Chaitanya; Larson, Jonas; Spiller, Timothy P.
2016-04-01
We investigate a possibility to generate nonclassical states in light-matter coupled noisy quantum systems, namely, the anisotropic Rabi and Dicke models. In these hybrid quantum systems, a competing influence of coherent internal dynamics and environment-induced dissipation drives the system into nonequilibrium steady states (NESSs). Explicitly, for the anisotropic Rabi model, the steady state is given by an incoherent mixture of two states of opposite parities, but as each parity state displays light-matter entanglement, we also find that the full state is entangled. Furthermore, as a natural extension of the anisotropic Rabi model to an infinite spin subsystem, we next explored the NESS of the anisotropic Dicke model. The NESS of this linearized Dicke model is also an inseparable state of light and matter. With an aim to enrich the dynamics beyond the sustainable entanglement found for the NESS of these hybrid quantum systems, we also propose to combine an all-optical feedback strategy for quantum state protection and for establishing quantum control in these systems. Our present work further elucidates the relevance of such hybrid open quantum systems for potential applications in quantum architectures.
Epidemic Dynamics in Open Quantum Spin Systems
Pérez-Espigares, Carlos; Marcuzzi, Matteo; Gutiérrez, Ricardo; Lesanovsky, Igor
2017-10-01
We explore the nonequilibrium evolution and stationary states of an open many-body system that displays epidemic spreading dynamics in a classical and a quantum regime. Our study is motivated by recent experiments conducted in strongly interacting gases of highly excited Rydberg atoms where the facilitated excitation of Rydberg states competes with radiative decay. These systems approximately implement open quantum versions of models for population dynamics or disease spreading where species can be in a healthy, infected or immune state. We show that in a two-dimensional lattice, depending on the dominance of either classical or quantum effects, the system may display a different kind of nonequilibrium phase transition. We moreover discuss the observability of our findings in laser driven Rydberg gases with particular focus on the role of long-range interactions.
Exceptional points in open quantum systems
International Nuclear Information System (INIS)
Mueller, Markus; Rotter, Ingrid
2008-01-01
Open quantum systems are embedded in the continuum of scattering wavefunctions and are naturally described by non-Hermitian Hamilton operators. In the complex energy plane, exceptional points appear at which two (or more) eigenvalues of the Hamilton operator coalesce. Although they are a countable set of single points in the complex energy plane and therefore of measure zero, they determine decisively the dynamics of open quantum systems. A powerful method for the description of open quantum systems is the Feshbach projection operator formalism. It is used in the present paper as a basic tool for the study of exceptional points and of the role they play for the dynamics of open quantum systems. Among others, the topological structure of the exceptional points, the rigidity of the phases of the eigenfunctions in their vicinity, the enhancement of observable values due to the reduced phase rigidity and the appearance of phase transitions are considered. The results are compared with existing experimental data on microwave cavities. In the last section, some questions being still unsolved, are considered
Time-dependent current-density functional theory for generalized open quantum systems.
Yuen-Zhou, Joel; Rodríguez-Rosario, César; Aspuru-Guzik, Alán
2009-06-14
In this article, we prove the one-to-one correspondence between vector potentials and particle and current densities in the context of master equations with arbitrary memory kernels, therefore extending time-dependent current-density functional theory (TD-CDFT) to the domain of generalized many-body open quantum systems (OQS). We also analyse the issue of A-representability for the Kohn-Sham (KS) scheme proposed by D'Agosta and Di Ventra for Markovian OQS [Phys. Rev. Lett. 2007, 98, 226403] and discuss its domain of validity. We suggest ways to expand their scheme, but also propose a novel KS scheme where the auxiliary system is both closed and non-interacting. This scheme is tested numerically with a model system, and several considerations for the future development of functionals are indicated. Our results formalize the possibility of practising TD-CDFT in OQS, hence expanding the applicability of the theory to non-Hamiltonian evolutions.
Mappings of open quantum systems onto chain representations and Markovian embeddings
Energy Technology Data Exchange (ETDEWEB)
Woods, M. P., E-mail: mischa.woods05@imperial.ac.uk [QOLS, Blackett Laboratory, Imperial College London, London SW7 2BW (United Kingdom); Institute für Theoretische Physik, Universität Ulm, D-89069 Ulm (Germany); Groux, R. [Lycée Polyvalent Rouvière, Rue Sainte Claire Deville. BP 1205, 83070 Toulon (France); Chin, A. W.; Huelga, S. F.; Plenio, M. B. [Institute für Theoretische Physik, Universität Ulm, D-89069 Ulm (Germany)
2014-03-15
We study systems coupled linearly to a bath of oscillators. In an iterative process, the bath is transformed into a chain of oscillators with nearest neighbour interactions. A systematic procedure is provided to obtain the spectral density of the residual bath in each step, and it is shown that under general conditions these data converge. That is, the asymptotic part of the chain is universal, translation invariant with semicircular spectral density. The methods are based on orthogonal polynomials, in which we also solve the outstanding so-called “sequence of secondary measures problem” and give them a physical interpretation.
System–environment correlations and non-Markovian dynamics
International Nuclear Information System (INIS)
Pernice, A; Helm, J; Strunz, W T
2012-01-01
We determine the total state dynamics of a dephasing open quantum system using the standard environment of harmonic oscillators. Of particular interest are random unitary approaches to the same reduced dynamics and system–environment correlations in the full model. Concentrating on a model with an at times negative dephasing rate, the issue of ‘non-Markovianity’ will also be addressed. Crucially, given the quantum environment, the appearance of non-Markovian dynamics turns out to be accompanied by a loss of system–environment correlations. Depending on the initial purity of the qubit state, these system–environment correlations may be purely classical over the whole relevant time scale, or there may be intervals of genuine system–environment entanglement. In the latter case, we see no obvious relation between the build-up or decay of these quantum correlations and ‘non-Markovianity’. (paper)
The brachistochrone problem in open quantum systems
International Nuclear Information System (INIS)
Rotter, Ingrid
2007-01-01
Recently, the quantum brachistochrone problem has been discussed in the literature by using non-Hermitian Hamilton operators of different types. Here, it is demonstrated that the passage time is tunable in realistic open quantum systems due to the biorthogonality of the eigenfunctions of the non-Hermitian Hamilton operator. As an example, the numerical results obtained by Bulgakov et al for the transmission through microwave cavities of different shapes are analyzed from the point of view of the brachistochrone problem. The passage time is shortened in the crossover from the weak-coupling to the strong-coupling regime where the resonance states overlap and many branch points (exceptional points) in the complex plane exist. The effect can not be described in the framework of the standard quantum mechanics with the Hermitian Hamilton operator and consideration of S matrix poles
Noise suppression via generalized-Markovian processes
Marshall, Jeffrey; Campos Venuti, Lorenzo; Zanardi, Paolo
2017-11-01
It is by now well established that noise itself can be useful for performing quantum information processing tasks. We present results which show how one can effectively reduce the error rate associated with a noisy quantum channel by counteracting its detrimental effects with another form of noise. In particular, we consider the effect of adding on top of a purely Markovian (Lindblad) dynamics, a more general form of dissipation, which we refer to as generalized-Markovian noise. This noise has an associated memory kernel and the resulting dynamics are described by an integrodifferential equation. The overall dynamics are characterized by decay rates which depend not only on the original dissipative time scales but also on the new integral kernel. We find that one can engineer this kernel such that the overall rate of decay is lowered by the addition of this noise term. We illustrate this technique for the case where the bare noise is described by a dephasing Pauli channel. We analytically solve this model and show that one can effectively double (or even triple) the length of the channel, while achieving the same fidelity, entanglement, and error threshold. We numerically verify this scheme can also be used to protect against thermal Markovian noise (at nonzero temperature), which models spontaneous emission and excitation processes. A physical interpretation of this scheme is discussed, whereby the added generalized-Markovian noise causes the system to become periodically decoupled from the background Markovian noise.
Symmetry and stability of open quantum systems
International Nuclear Information System (INIS)
Scutaru, H.
1979-01-01
The presentation of the thesis involves an introduction and six chapters. Chapter 1 presents notions and results used in the other chpaters. Chapters 2-6 present our results which are focused on two notions: generalized observable and dynamic semigroup. These notions characterize a specific research domain (set up during the last 10 years) which is currently called quantum mechanics of open systems. The two notions (generalized observable and dynamic semigroup) are mathematically correlated. They belong to the set of completely positive linear applications among observable algebras. This fact, associated with that formulation of quantum mechanics according to which it is a special case of quantum mechanics namely, that for which the observable algebra is commutative, help to understand the similar essence of the results presented in chapter 2-6. Thus, the natural mathematical background has been achieved for our results; it is represented by that category whose objects are the observable algebras and whose morphisms are completely positive linear contractions generating unity within unity. These ideas are extensively presented in the introduction. The fact that the relations between classical mechanics and quantum mechanics can be rigorously treated as positive linear applications between classical observable algebras commutative and quantum observable algebras non-commutative, which are automatically fully positive, has been initially shown in our paper. (author)
Gao, Fang; Rey-de-Castro, Roberto; Wang, Yaoxiong; Rabitz, Herschel; Shuang, Feng
2016-05-01
Many systems under control with an applied field also interact with the surrounding environment. Understanding the control mechanisms has remained a challenge, especially the role played by the interaction between the field and the environment. In order to address this need, here we expand the scope of the Hamiltonian-encoding and observable-decoding (HE-OD) technique. HE-OD was originally introduced as a theoretical and experimental tool for revealing the mechanism induced by control fields in closed quantum systems. The results of open-system HE-OD analysis presented here provide quantitative mechanistic insights into the roles played by a Markovian environment. Two model open quantum systems are considered for illustration. In these systems, transitions are induced by either an applied field linked to a dipole operator or Lindblad operators coupled to the system. For modest control yields, the HE-OD results clearly show distinct cooperation between the dynamics induced by the optimal field and the environment. Although the HE-OD methodology introduced here is considered in simulations, it has an analogous direct experimental formulation, which we suggest may be applied to open systems in the laboratory to reveal mechanistic insights.
Conductance Peaks in Open Quantum Dots
International Nuclear Information System (INIS)
Ramos, J. G. G. S.; Bazeia, D.; Hussein, M. S.; Lewenkopf, C. H.
2011-01-01
We present a simple measure of the conductance fluctuations in open ballistic chaotic quantum dots, extending the number of maxima method originally proposed for the statistical analysis of compound nuclear reactions. The average number of extreme points (maxima and minima) in the dimensionless conductance T as a function of an arbitrary external parameter Z is directly related to the autocorrelation function of T(Z). The parameter Z can be associated with an applied gate voltage causing shape deformation in quantum dot, an external magnetic field, the Fermi energy, etc. The average density of maxima is found to be Z >=α Z /Z c , where α Z is a universal constant and Z c is the conductance autocorrelation length, which is system specific. The analysis of Z > does not require large statistic samples, providing a quite amenable way to access information about parametric correlations, such as Z c .
Quantum games in open systems using biophysical Hamiltonians
International Nuclear Information System (INIS)
Faber, Jean; Portugal, Renato; Rosa, Luiz Pinguelli
2006-01-01
We analyze the necessary physical conditions to model an open quantum system as a quantum game. By applying the formalism of quantum operations on a particular system, we use Kraus operators as quantum strategies. The physical interpretation is a conflict among different configurations of the environment. The resolution of the conflict displays regimes of minimum loss of information
Quantum games in open systems using biophysical Hamiltonians
Energy Technology Data Exchange (ETDEWEB)
Faber, Jean [National Laboratory of Scientific Computing (LNCC), Av. Getulio Vargas 333, Quitandinha 25651-075, Petropolis, RJ (Brazil)]. E-mail: faber@lncc.br; Portugal, Renato [National Laboratory of Scientific Computing (LNCC), Av. Getulio Vargas 333, Quitandinha 25651-075, Petropolis, RJ (Brazil)]. E-mail: portugal@lncc.br; Rosa, Luiz Pinguelli [Federal University of Rio de Janeiro, COPPE-UFRJ, RJ (Brazil)]. E-mail: lpr@adc.coppe.ufrj.br
2006-09-25
We analyze the necessary physical conditions to model an open quantum system as a quantum game. By applying the formalism of quantum operations on a particular system, we use Kraus operators as quantum strategies. The physical interpretation is a conflict among different configurations of the environment. The resolution of the conflict displays regimes of minimum loss of information.
Non-Markovian dynamics of a qubit due to single-photon scattering in a waveguide
Fang, Yao-Lung L.; Ciccarello, Francesco; Baranger, Harold U.
2018-04-01
We investigate the open dynamics of a qubit due to scattering of a single photon in an infinite or semi-infinite waveguide. Through an exact solution of the time-dependent multi-photon scattering problem, we find the qubit's dynamical map. Tools of open quantum systems theory allow us then to show the general features of this map, find the corresponding non-Linbladian master equation, and assess in a rigorous way its non-Markovian nature. The qubit dynamics has distinctive features that, in particular, do not occur in emission processes. Two fundamental sources of non-Markovianity are present: the finite width of the photon wavepacket and the time delay for propagation between the qubit and the end of the semi-infinite waveguide.
Thermodynamic fingerprints of non-Markovianity in a system of coupled superconducting qubits
Hamedani Raja, Sina; Borrelli, Massimo; Schmidt, Rebecca; Pekola, Jukka P.; Maniscalco, Sabrina
2018-03-01
The exploitation and characterization of memory effects arising from the interaction between system and environment is a key prerequisite for quantum reservoir engineering beyond the standard Markovian limit. In this paper we investigate a prototype of non-Markovian dynamics experimentally implementable with superconducting qubits. We rigorously quantify non-Markovianity, highlighting the effects of the environmental temperature on the Markovian to non-Markovian crossover. We investigate how memory effects influence, and specifically suppress, the ability to perform work on the driven qubit. We show that the average work performed on the qubit can be used as a diagnostic tool to detect the presence or absence of memory effects.
Effective operator formalism for open quantum systems
DEFF Research Database (Denmark)
Reiter, Florentin; Sørensen, Anders Søndberg
2012-01-01
We present an effective operator formalism for open quantum systems. Employing perturbation theory and adiabatic elimination of excited states for a weakly driven system, we derive an effective master equation which reduces the evolution to the ground-state dynamics. The effective evolution...... involves a single effective Hamiltonian and one effective Lindblad operator for each naturally occurring decay process. Simple expressions are derived for the effective operators which can be directly applied to reach effective equations of motion for the ground states. We compare our method...
Stationary states of two-level open quantum systems
International Nuclear Information System (INIS)
Gardas, Bartlomiej; Puchala, Zbigniew
2011-01-01
A problem of finding stationary states of open quantum systems is addressed. We focus our attention on a generic type of open system: a qubit coupled to its environment. We apply the theory of block operator matrices and find stationary states of two-level open quantum systems under certain conditions applied on both the qubit and the surrounding.
Description of an open quantum mechanical system
International Nuclear Information System (INIS)
Rotter, I.; Forschungszentrum Rossendorf e.V.
1994-05-01
A model for the description of an open quantum mechanical many-particle system is formulated. It starts from the shell model and treats the continuous states by a coupled channels method. The mixing of the discrete shell model states via the continuum of decay channels results in the genuine decaying states of the system. These states are eigenstates of a non-Hermitean Hamilton operator the eigenvalues of which give both the energies and the widths of the states. All correlations between two particles which are caused by the two-particle residual interaction, are taken into account including those via the continuum. In the formalism describing the open quantum mechanical system, the coupling between the system and its environment appears nonlinearly. If the resonance states start to overlap, a redistribution of the spectroscopic values ('trapping effect') takes place. As a result, the complexity of the system is reduced at high level density, structures in space and time are formed. This redistribution describes, on the one hand, the transition from the well-known nuclear properties at low level density to those at high level density and fits, on the other hand, into the concept of selforganization. (orig.)
Adiabatically steered open quantum systems: Master equation and optimal phase
International Nuclear Information System (INIS)
Salmilehto, J.; Solinas, P.; Ankerhold, J.; Moettoenen, M.
2010-01-01
We introduce an alternative way to derive the generalized form of the master equation recently presented by J. P. Pekola et al. [Phys. Rev. Lett. 105, 030401 (2010)] for an adiabatically steered two-level quantum system interacting with a Markovian environment. The original derivation employed the effective Hamiltonian in the adiabatic basis with the standard interaction picture approach but without the usual secular approximation. Our approach is based on utilizing a master equation for a nonsteered system in the first superadiabatic basis. It is potentially efficient in obtaining higher-order equations. Furthermore, we show how to select the phases of the adiabatic eigenstates to minimize the local adiabatic parameter and how this selection leads to states which are invariant under a local gauge change. We also discuss the effects of the adiabatic noncyclic geometric phase on the master equation.
Tracking an open quantum system using a finite state machine: Stability analysis
International Nuclear Information System (INIS)
Karasik, R. I.; Wiseman, H. M.
2011-01-01
A finite-dimensional Markovian open quantum system will undergo quantum jumps between pure states, if we can monitor the bath to which it is coupled with sufficient precision. In general these jumps, plus the between-jump evolution, create a trajectory which passes through infinitely many different pure states, even for ergodic systems. However, as shown recently by us [Phys. Rev. Lett. 106, 020406 (2011)], it is possible to construct adaptive monitorings which restrict the system to jumping between a finite number of states. That is, it is possible to track the system using a finite state machine as the apparatus. In this paper we consider the question of the stability of these monitoring schemes. Restricting to cyclic jumps for a qubit, we give a strong analytical argument that these schemes are always stable and supporting analytical and numerical evidence for the example of resonance fluorescence. This example also enables us to explore a range of behaviors in the evolution of individual trajectories, for several different monitoring schemes.
Unstable particles as open quantum systems
International Nuclear Information System (INIS)
Caban, Pawel; Rembielinski, Jakub; Smolinski, Kordian A.; Walczak, Zbigniew
2005-01-01
We present the probability-preserving description of the decaying particle within the framework of quantum mechanics of open systems, taking into account the superselection rule prohibiting the superposition of the particle and vacuum. In our approach the evolution of the system is given by a family of completely positive trace-preserving maps forming a one-parameter dynamical semigroup. We give the Kraus representation for the general evolution of such systems, which allows one to write the evolution for systems with two or more particles. Moreover, we show that the decay of the particle can be regarded as a Markov process by finding explicitly the master equation in the Lindblad form. We also show that there are remarkable restrictions on the possible strength of decoherence
A quantum causal discovery algorithm
Giarmatzi, Christina; Costa, Fabio
2018-03-01
Finding a causal model for a set of classical variables is now a well-established task—but what about the quantum equivalent? Even the notion of a quantum causal model is controversial. Here, we present a causal discovery algorithm for quantum systems. The input to the algorithm is a process matrix describing correlations between quantum events. Its output consists of different levels of information about the underlying causal model. Our algorithm determines whether the process is causally ordered by grouping the events into causally ordered non-signaling sets. It detects if all relevant common causes are included in the process, which we label Markovian, or alternatively if some causal relations are mediated through some external memory. For a Markovian process, it outputs a causal model, namely the causal relations and the corresponding mechanisms, represented as quantum states and channels. Our algorithm opens the route to more general quantum causal discovery methods.
Bayesian feedback versus Markovian feedback in a two-level atom
International Nuclear Information System (INIS)
Wiseman, H.M.; Mancini, Stefano; Wang Jin
2002-01-01
We compare two different approaches to the control of the dynamics of a continuously monitored open quantum system. The first is Markovian feedback, as introduced in quantum optics by Wiseman and Milburn [Phys. Rev. Lett. 70, 548 (1993)]. The second is feedback based on an estimate of the system state, developed recently by Doherty and Jacobs [Phys. Rev. A 60, 2700 (1999)]. Here we choose to call it, for brevity, Bayesian feedback. For systems with nonlinear dynamics, we expect these two methods of feedback control to give markedly different results. The simplest possible nonlinear system is a driven and damped two-level atom, so we choose this as our model system. The monitoring is taken to be homodyne detection of the atomic fluorescence, and the control is by modulating the driving. The aim of the feedback in both cases is to stabilize the internal state of the atom as close as possible to an arbitrarily chosen pure state, in the presence of inefficient detection and other forms of decoherence. Our results (obtained without recourse to stochastic simulations) prove that Bayesian feedback is never inferior, and is usually superior, to Markovian feedback. However, it would be far more difficult to implement than Markovian feedback and it loses its superiority when obvious simplifying approximations are made. It is thus not clear which form of feedback would be better in the face of inevitable experimental imperfections
Non-Markovianity of Gaussian Channels.
Torre, G; Roga, W; Illuminati, F
2015-08-14
We introduce a necessary and sufficient criterion for the non-Markovianity of Gaussian quantum dynamical maps based on the violation of divisibility. The criterion is derived by defining a general vectorial representation of the covariance matrix which is then exploited to determine the condition for the complete positivity of partial maps associated with arbitrary time intervals. Such construction does not rely on the Choi-Jamiolkowski representation and does not require optimization over states.
High frequency response of open quantum dots
International Nuclear Information System (INIS)
Brunner, R.; Meisels, R.; Kuchar, F.; Ferry, D.; Elhassan, M.; Ishibashi, K.
2002-01-01
Full text: We investigate the response of the transport through open quantum dots to millimeterwave radiation (up to 55 GHz). In the low-field region ( 11 cm -2 and a mobility of 1.2 10 6 cm 2 /Vs. By applying a sufficiently negative voltage to the gates the 2DES is split into two regions connected only by a dot-like region (about 350 nm diameter) between them. The DC data exhibit backscattering peaks at fields of a few tenth of a Tesla. Shubnikovde- Haas (SdH) oscillations appear above 0.5 T. While the SdH oscillations show the usual temperature dependence, the backscattering peaks are temperature independent up to 2.5 K. The backscattering peak shows a reduction of 10 percent due to the millimeterwave irradiation. However, due to the temperature independence of this peak, this reduction cannot simply be attributed to electron heating. This conclusion is supported by the observation of a strong frequency dependence of the reduction of the peak height. (author)
Simple non-Markovian microscopic models for the depolarizing channel of a single qubit
International Nuclear Information System (INIS)
Fonseca Romero, K M; Lo Franco, R
2012-01-01
The archetypal one-qubit noisy channels - depolarizing, phase-damping and amplitude-damping channels - describe both Markovian and non-Markovian evolution. Simple microscopic models for the depolarizing channel, both classical and quantum, are considered. Microscopic models that describe phase-damping and amplitude-damping channels are briefly reviewed.
Controlling open quantum systems: Tools, achievements, and limitations
Koch, Christiane P.
2016-01-01
The advent of quantum devices, which exploit the two essential elements of quantum physics, coherence and entanglement, has sparked renewed interest in the control of open quantum systems. Successful implementations face the challenge to preserve the relevant nonclassical features at the level of device operation. A major obstacle is decoherence which is caused by interaction with the environment. Optimal control theory is a tool that can be used to identify control strategies in the presence...
Comment on "Modified quantum-speed-limit bounds for open quantum dynamics in quantum channels"
Mirkin, Nicolás; Toscano, Fabricio; Wisniacki, Diego A.
2018-04-01
In a recent paper [Phys. Rev. A 95, 052118 (2017), 10.1103/PhysRevA.95.052118], the authors claim that our criticism, in Phys. Rev. A 94, 052125 (2016), 10.1103/PhysRevA.94.052125, to some quantum speed limit bounds for open quantum dynamics that appeared recently in literature are invalid. According to the authors, the problem with our analysis would be generated by an artifact of the finite-precision numerical calculations. We analytically show here that it is not possible to have any inconsistency associated with the numerical precision of calculations. Therefore, our criticism of the quantum speed limit bounds continues to be valid.
Collision models in quantum optics
Ciccarello, Francesco
2017-12-01
Quantum collision models (CMs) provide advantageous case studies for investigating major issues in open quantum systems theory, and especially quantum non-Markovianity. After reviewing their general definition and distinctive features, we illustrate the emergence of a CM in a familiar quantum optics scenario. This task is carried out by highlighting the close connection between the well-known input-output formalism and CMs. Within this quantum optics framework, usual assumptions in the CMs' literature - such as considering a bath of noninteracting yet initially correlated ancillas - have a clear physical origin.
Microscopic derivation of open quantum Brownian motion: a particular example
International Nuclear Information System (INIS)
Sinayskiy, Ilya; Petruccione, Francesco
2015-01-01
The microscopic derivation of a new type of Brownian motion, namely open quantum Brownian motion (OQBM) is presented. The quantum master equation for OQBM is derived for a weakly driven system interacting with a decoherent environment. Examples of the dynamics for initial Gaussian and non-Gaussian distributions are presented. Both examples demonstrate convergence of the OQBM dynamics to Gaussian distributions. (topical article)
Quantum A∞-structures for open-closed topological strings
International Nuclear Information System (INIS)
Herbst, M.
2006-02-01
We study factorizations of topological string amplitudes on higher genus Riemann surfaces with multiple boundary components and find quantum A ∞ -relations, which are the higher genus analog of the (classical) A ∞ -relations on the disk. For topological strings with c=3 the quantum A ∞ -relations are trivially satisfied on a single D-brane, whereas in a multiple D-brane configuration they may be used to compute open higher genus amplitudes recursively from disk amplitudes. This can be helpful in open Gromov-Witten theory in order to determine open string higher genus instanton corrections. Finally, we find that the quantum A ∞ -structure cannot quite be recast into a quantum master equation on the open string moduli space. (orig.)
Quantum Oscillator in the Thermostat as a Model in the Thermodynamics of Open Quantum Systems
Sukhanov, Aleksander
2005-01-01
The quantum oscillator in the thermostat is considered as the model of an open quantum system. Our analysis will be heavily founded on the use of the Schroedinger generalized uncertainties relations (SUR). Our first aim is to demonstrate that for the quantum oscillator the state of thermal equilibrium belongs to the correlated coherent states (CCS), which imply the saturation of SUR at any temperature. The obtained results open the perspective for the search of some statistical theory, which ...
Magneto-conductance fingerprints of purely quantum states in the open quantum dot limit
Mendoza, Michel; Ujevic, Sebastian
2012-06-01
We present quantum magneto-conductance simulations, at the quantum low energy condition, to study the open quantum dot limit. The longitudinal conductance G(E,B) of spinless and non-interacting electrons is mapped as a function of the magnetic field B and the energy E of the electrons. The quantum dot linked to the semi-infinite leads is tuned by quantum point contacts of variable width w. We analyze the transition from a quantum wire to an open quantum dot and then to an effective closed system. The transition, as a function of w, occurs in the following sequence: evolution of quasi-Landau levels to Fano resonances and quasi-bound states between the quasi-Landau levels, followed by the formation of crossings that evolve to anti-crossings inside the quasi-Landau level region. After that, Fano resonances are created between the quasi-Landau states with the final generation of resonant tunneling peaks. By comparing the G(E,B) maps, we identify the closed and open-like limits of the system as a function of the applied magnetic field. These results were used to build quantum openness diagrams G(w,B). Also, these maps allow us to determine the w-limit value from which we can qualitatively relate the closed system properties to the open one. The above analysis can be used to identify single spinless particle effects in experimental measurements of the open quantum dot limit.
Magneto-conductance fingerprints of purely quantum states in the open quantum dot limit
International Nuclear Information System (INIS)
Mendoza, Michel; Ujevic, Sebastian
2012-01-01
We present quantum magneto-conductance simulations, at the quantum low energy condition, to study the open quantum dot limit. The longitudinal conductance G(E,B) of spinless and non-interacting electrons is mapped as a function of the magnetic field B and the energy E of the electrons. The quantum dot linked to the semi-infinite leads is tuned by quantum point contacts of variable width w. We analyze the transition from a quantum wire to an open quantum dot and then to an effective closed system. The transition, as a function of w, occurs in the following sequence: evolution of quasi-Landau levels to Fano resonances and quasi-bound states between the quasi-Landau levels, followed by the formation of crossings that evolve to anti-crossings inside the quasi-Landau level region. After that, Fano resonances are created between the quasi-Landau states with the final generation of resonant tunneling peaks. By comparing the G(E,B) maps, we identify the closed and open-like limits of the system as a function of the applied magnetic field. These results were used to build quantum openness diagrams G(w,B). Also, these maps allow us to determine the w-limit value from which we can qualitatively relate the closed system properties to the open one. The above analysis can be used to identify single spinless particle effects in experimental measurements of the open quantum dot limit. (paper)
Open quantum maps from complex scaling of kicked scattering systems
Mertig, Normann; Shudo, Akira
2018-04-01
We derive open quantum maps from periodically kicked scattering systems and discuss the computation of their resonance spectra in terms of theoretically grounded methods, such as complex scaling and sufficiently weak absorbing potentials. In contrast, we also show that current implementations of open quantum maps, based on strong absorptive or even projective openings, fail to produce the resonance spectra of kicked scattering systems. This comparison pinpoints flaws in current implementations of open quantum maps, namely, the inability to separate resonance eigenvalues from the continuum as well as the presence of diffraction effects due to strong absorption. The reported deviations from the true resonance spectra appear, even if the openings do not affect the classical trapped set, and become appreciable for shorter-lived resonances, e.g., those associated with chaotic orbits. This makes the open quantum maps, which we derive in this paper, a valuable alternative for future explorations of quantum-chaotic scattering systems, for example, in the context of the fractal Weyl law. The results are illustrated for a quantum map model whose classical dynamics exhibits key features of ionization and a trapped set which is organized by a topological horseshoe.
Quantum state engineering in hybrid open quantum systems
Joshi, Chaitanya; Larson, Jonas; Spiller, Timothy P.
2015-01-01
We investigate a possibility to generate nonclassical states in light-matter coupled noisy quantum systems, namely, the anisotropic Rabi and Dicke models. In these hybrid quantum systems, a competing influence of coherent internal dynamics and environment-induced dissipation drives the system into nonequilibrium steady states (NESSs). Explicitly, for the anisotropic Rabi model, the steady state is given by an incoherent mixture of two states of opposite parities, but as each parity state disp...
Head-Marsden, Kade; Mazziotti, David A
2015-02-07
For an open, time-dependent quantum system, Lindblad derived the most general modification of the quantum Liouville equation in the Markovian approximation that models environmental effects while preserving the non-negativity of the system's density matrix. While Lindblad's modification is correct for N-electron density matrices, solution of the Liouville equation with a Lindblad operator causes the one-electron reduced density matrix (1-RDM) to violate the Pauli exclusion principle. Consequently, after a short time, the 1-RDM is not representable by an ensemble N-electron density matrix (not ensemble N-representable). In this communication, we derive the necessary and sufficient constraints on the Lindbladian matrix within the Lindblad operator to ensure that the 1-RDM remains N-representable for all time. The theory is illustrated by considering the relaxation of an excitation in several molecules F2, N2, CO, and BeH2 subject to environmental noise.
Quantum Information Biology: From Theory of Open Quantum Systems to Adaptive Dynamics
Asano, Masanari; Basieva, Irina; Khrennikov, Andrei; Ohya, Masanori; Tanaka, Yoshiharu; Yamato, Ichiro
This chapter reviews quantum(-like) information biology (QIB). Here biology is treated widely as even covering cognition and its derivatives: psychology and decision making, sociology, and behavioral economics and finances. QIB provides an integrative description of information processing by bio-systems at all scales of life: from proteins and cells to cognition, ecological and social systems. Mathematically QIB is based on the theory of adaptive quantum systems (which covers also open quantum systems). Ideologically QIB is based on the quantum-like (QL) paradigm: complex bio-systems process information in accordance with the laws of quantum information and probability. This paradigm is supported by plenty of statistical bio-data collected at all bio-scales. QIB re ects the two fundamental principles: a) adaptivity; and, b) openness (bio-systems are fundamentally open). In addition, quantum adaptive dynamics provides the most generally possible mathematical representation of these principles.
Mortezapour, Ali; Ahmadi Borji, Mahdi; Lo Franco, Rosario
2017-05-01
Efficient entanglement preservation in open quantum systems is a crucial scope towards a reliable exploitation of quantum resources. We address this issue by studying how two-qubit entanglement dynamically behaves when two atom qubits move inside two separated identical cavities. The moving qubits independently interact with their respective cavity. As a main general result, we find that under resonant qubit-cavity interaction the initial entanglement between two moving qubits remains closer to its initial value as time passes compared to the case of stationary qubits. In particular, we show that the initial entanglement can be strongly protected from decay by suitably adjusting the velocities of the qubits according to the non-Markovian features of the cavities. Our results supply a further way of preserving quantum correlations against noise with a natural implementation in cavity-QED scenarios and are straightforwardly extendable to many qubits for scalability.
QuantumOptics.jl: A Julia framework for simulating open quantum systems
Krämer, Sebastian; Plankensteiner, David; Ostermann, Laurin; Ritsch, Helmut
2018-06-01
We present an open source computational framework geared towards the efficient numerical investigation of open quantum systems written in the Julia programming language. Built exclusively in Julia and based on standard quantum optics notation, the toolbox offers speed comparable to low-level statically typed languages, without compromising on the accessibility and code readability found in dynamic languages. After introducing the framework, we highlight its features and showcase implementations of generic quantum models. Finally, we compare its usability and performance to two well-established and widely used numerical quantum libraries.
Kramer, Tobias; Noack, Matthias; Reinefeld, Alexander; Rodríguez, Mirta; Zelinskyy, Yaroslav
2018-06-11
Time- and frequency-resolved optical signals provide insights into the properties of light-harvesting molecular complexes, including excitation energies, dipole strengths and orientations, as well as in the exciton energy flow through the complex. The hierarchical equations of motion (HEOM) provide a unifying theory, which allows one to study the combined effects of system-environment dissipation and non-Markovian memory without making restrictive assumptions about weak or strong couplings or separability of vibrational and electronic degrees of freedom. With increasing system size the exact solution of the open quantum system dynamics requires memory and compute resources beyond a single compute node. To overcome this barrier, we developed a scalable variant of HEOM. Our distributed memory HEOM, DM-HEOM, is a universal tool for open quantum system dynamics. It is used to accurately compute all experimentally accessible time- and frequency-resolved processes in light-harvesting molecular complexes with arbitrary system-environment couplings for a wide range of temperatures and complex sizes. © 2018 Wiley Periodicals, Inc. © 2018 Wiley Periodicals, Inc.
Decohering histories and open quantum systems
International Nuclear Information System (INIS)
Chisolm, Eric D
2009-01-01
I briefly review the 'decohering histories' or 'consistent histories' formulation of quantum theory, due to Griffiths, Omnes, and Gell-Mann and Hartle (and the subject of my graduate work with George Sudarshan). I also sift through the many meanings that have been attached to decohering histories, with an emphasis on the most basic one: Decoherence of appropriate histories is needed to establish that quantum mechanics has the correct classical limit. Then I will describe efforts to find physical mechanisms that do this. Since most work has focused on density matrix versions of decoherence, I'll consider the relation between the two formulations, which historically has not been straightforward. Finally, I'll suggest a line of research that would use recent results by Sudarshan to illuminate this aspect of the classical limit of quantum theory.
Decohering histories and open quantum systems
Energy Technology Data Exchange (ETDEWEB)
Chisolm, Eric D, E-mail: echisolm@lanl.go [Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87545 (United States)
2009-11-01
I briefly review the 'decohering histories' or 'consistent histories' formulation of quantum theory, due to Griffiths, Omnes, and Gell-Mann and Hartle (and the subject of my graduate work with George Sudarshan). I also sift through the many meanings that have been attached to decohering histories, with an emphasis on the most basic one: Decoherence of appropriate histories is needed to establish that quantum mechanics has the correct classical limit. Then I will describe efforts to find physical mechanisms that do this. Since most work has focused on density matrix versions of decoherence, I'll consider the relation between the two formulations, which historically has not been straightforward. Finally, I'll suggest a line of research that would use recent results by Sudarshan to illuminate this aspect of the classical limit of quantum theory.
Quantum consistency of open string theories
International Nuclear Information System (INIS)
Govaerts, J.
1989-01-01
We discuss how Virasoro anomalies in open string theories uniquely select the gauge group SO(2 D/2 ) independently of any regularisation, although the cancellation of these anomalies does not occur in tachyonic theories, and regulators can always be chosen to make these theories (one-loop) finite for any SO(n) and USp(n) gauge group. The discussion is mainly restricted to open bosonic strings. These results open new perspectives for the recent suggestion made by Sagnotti, the generalisations of which allow for the construction of new open string theories in less than ten dimensions. (orig.)
Controlling open quantum systems: tools, achievements, and limitations
International Nuclear Information System (INIS)
Koch, Christiane P
2016-01-01
The advent of quantum devices, which exploit the two essential elements of quantum physics, coherence and entanglement, has sparked renewed interest in the control of open quantum systems. Successful implementations face the challenge of preserving relevant nonclassical features at the level of device operation. A major obstacle is decoherence, which is caused by interaction with the environment. Optimal control theory is a tool that can be used to identify control strategies in the presence of decoherence. Here we review recent advances in optimal control methodology that allow typical tasks in device operation for open quantum systems to be tackled and discuss examples of relaxation-optimized dynamics. Optimal control theory is also a useful tool to exploit the environment for control. We discuss examples and point out possible future extensions. (topical review)
Periodic Scarred States in Open Quantum Dots as Evidence of Quantum Darwinism
Burke, A. M.; Akis, R.; Day, T. E.; Speyer, Gil; Ferry, D. K.; Bennett, B. R.
2010-04-01
Scanning gate microscopy (SGM) is used to image scar structures in an open quantum dot, which is created in an InAs quantum well by electron-beam lithography and wet etching. The scanned images demonstrate periodicities in magnetic field that correlate to those found in the conductance fluctuations. Simulations have shown that these magnetic transform images bear a strong resemblance to actual scars found in the dot that replicate through the modes in direct agreement with quantum Darwinism.
Bohmian mechanics, open quantum systems and continuous measurements
Nassar, Antonio B
2017-01-01
This book shows how Bohmian mechanics overcomes the need for a measurement postulate involving wave function collapse. The measuring process plays a very important role in quantum mechanics. It has been widely analyzed within the Copenhagen approach through the Born and von Neumann postulates, with later extension due to Lüders. In contrast, much less effort has been invested in the measurement theory within the Bohmian mechanics framework. The continuous measurement (sharp and fuzzy, or strong and weak) problem is considered here in this framework. The authors begin by generalizing the so-called Mensky approach, which is based on restricted path integral through quantum corridors. The measuring system is then considered to be an open quantum system following a stochastic Schrödinger equation. Quantum stochastic trajectories (in the Bohmian sense) and their role in basic quantum processes are discussed in detail. The decoherence process is thereby described in terms of classical trajectories issuing from th...
Murashita, Yûto; Gong, Zongping; Ashida, Yuto; Ueda, Masahito
2017-10-01
The thermodynamics of quantum coherence has attracted growing attention recently, where the thermodynamic advantage of quantum superposition is characterized in terms of quantum thermodynamics. We investigate the thermodynamic effects of quantum coherent driving in the context of the fluctuation theorem. We adopt a quantum-trajectory approach to investigate open quantum systems under feedback control. In these systems, the measurement backaction in the forward process plays a key role, and therefore the corresponding time-reversed quantum measurement and postselection must be considered in the backward process, in sharp contrast to the classical case. The state reduction associated with quantum measurement, in general, creates a zero-probability region in the space of quantum trajectories of the forward process, which causes singularly strong irreversibility with divergent entropy production (i.e., absolute irreversibility) and hence makes the ordinary fluctuation theorem break down. In the classical case, the error-free measurement ordinarily leads to absolute irreversibility, because the measurement restricts classical paths to the region compatible with the measurement outcome. In contrast, in open quantum systems, absolute irreversibility is suppressed even in the presence of the projective measurement due to those quantum rare events that go through the classically forbidden region with the aid of quantum coherent driving. This suppression of absolute irreversibility exemplifies the thermodynamic advantage of quantum coherent driving. Absolute irreversibility is shown to emerge in the absence of coherent driving after the measurement, especially in systems under time-delayed feedback control. We show that absolute irreversibility is mitigated by increasing the duration of quantum coherent driving or decreasing the delay time of feedback control.
Non-Markovian reservoir-dependent squeezing
International Nuclear Information System (INIS)
Paavola, J
2010-01-01
The squeezing dynamics of a damped harmonic oscillator are studied for different types of environment without making the Markovian approximation. The squeezing dynamics of a coherent state depend on the reservoir spectrum in a unique way that can, in the weak coupling approximation, be analysed analytically. Comparison of squeezing dynamics for ohmic, sub-ohmic and super-ohmic environments is done, showing a clear connection between the squeezing-non-squeezing oscillations and reservoir structure. Understanding the effects occurring due to structured reservoirs is important both from a purely theoretical point of view and in connection with evolving experimental techniques and future quantum computing applications.
Perturbation Theory for Open Two-Level Nonlinear Quantum Systems
International Nuclear Information System (INIS)
Zhang Zhijie; Jiang Dongguang; Wang Wei
2011-01-01
Perturbation theory is an important tool in quantum mechanics. In this paper, we extend the traditional perturbation theory to open nonlinear two-level systems, treating decoherence parameter γ as a perturbation. By this virtue, we give a perturbative solution to the master equation, which describes a nonlinear open quantum system. The results show that for small decoherence rate γ, the ratio of the nonlinear rate C to the tunneling coefficient V (i.e., r = C/V) determines the validity of the perturbation theory. For small ratio r, the perturbation theory is valid, otherwise it yields wrong results. (general)
Scattering Theory for Open Quantum Systems with Finite Rank Coupling
International Nuclear Information System (INIS)
Behrndt, Jussi; Malamud, Mark M.; Neidhardt, Hagen
2007-01-01
Quantum systems which interact with their environment are often modeled by maximal dissipative operators or so-called Pseudo-Hamiltonians. In this paper the scattering theory for such open systems is considered. First it is assumed that a single maximal dissipative operator A D in a Hilbert space is used to describe an open quantum system. In this case the minimal self-adjoint dilation of A D can be regarded as the Hamiltonian of a closed system which contains the open system, but since K-tilde is necessarily not semibounded from below, this model is difficult to interpret from a physical point of view. In the second part of the paper an open quantum system is modeled with a family {A(μ)} of maximal dissipative operators depending on energy μ, and it is shown that the open system can be embedded into a closed system where the Hamiltonian is semibounded. Surprisingly it turns out that the corresponding scattering matrix can be completely recovered from scattering matrices of single pseudo-Hamiltonians as in the first part of the paper. The general results are applied to a class of Sturm-Liouville operators arising in dissipative and quantum transmitting Schroedinger-Poisson systems
Asymptotically open quantum systems; Asymptotisch offene Quantensysteme
Energy Technology Data Exchange (ETDEWEB)
Westrich, M.
2008-04-15
In the present thesis we investigate the structure of time-dependent equations of motion in quantum mechanics.We start from two coupled systems with an autonomous equation of motion. A limit, in which the dynamics of one of the two systems has a decoupled evolution and imposes a non-autonomous evolution for the second system is identified. A result due to K. Hepp that provides a classical limit for dynamics turns out to be part and parcel for this limit and is generalized in our work. The method introduced by J.S. Howland for the solution of the time-dependent Schroedinger equation is interpreted as such a limit. Moreover, we associate our limit with the modern theory of quantization. (orig.)
DEFF Research Database (Denmark)
Nielsen, Per Kær; Lodahl, Peter; Jauho, Antti-Pekka
2013-01-01
We study the fundamental limit on single-photon indistinguishability imposed by decoherence due to phonon interactions in semiconductor quantum dot-cavity quantum electrodynamics systems. Employing an exact diagonalization approach we find large differences compared to standard methods...
Bose-Hubbard lattice as a controllable environment for open quantum systems
Cosco, Francesco; Borrelli, Massimo; Mendoza-Arenas, Juan José; Plastina, Francesco; Jaksch, Dieter; Maniscalco, Sabrina
2018-04-01
We investigate the open dynamics of an atomic impurity embedded in a one-dimensional Bose-Hubbard lattice. We derive the reduced evolution equation for the impurity and show that the Bose-Hubbard lattice behaves as a tunable engineered environment allowing one to simulate both Markovian and non-Markovian dynamics in a controlled and experimentally realizable way. We demonstrate that the presence or absence of memory effects is a signature of the nature of the excitations induced by the impurity, being delocalized or localized in the two limiting cases of a superfluid and Mott insulator, respectively. Furthermore, our findings show how the excitations supported in the two phases can be characterized as information carriers.
Multistate and multihypothesis discrimination with open quantum systems
Kiilerich, Alexander Holm; Mølmer, Klaus
2018-05-01
We show how an upper bound for the ability to discriminate any number N of candidates for the Hamiltonian governing the evolution of an open quantum system may be calculated by numerically efficient means. Our method applies an effective master-equation analysis to evaluate the pairwise overlaps between candidate full states of the system and its environment pertaining to the Hamiltonians. These overlaps are then used to construct an N -dimensional representation of the states. The optimal positive-operator valued measure (POVM) and the corresponding probability of assigning a false hypothesis may subsequently be evaluated by phrasing optimal discrimination of multiple nonorthogonal quantum states as a semidefinite programming problem. We provide three realistic examples of multihypothesis testing with open quantum systems.
Averaging in SU(2) open quantum random walk
International Nuclear Information System (INIS)
Ampadu Clement
2014-01-01
We study the average position and the symmetry of the distribution in the SU(2) open quantum random walk (OQRW). We show that the average position in the central limit theorem (CLT) is non-uniform compared with the average position in the non-CLT. The symmetry of distribution is shown to be even in the CLT
Averaging in SU(2) open quantum random walk
Clement, Ampadu
2014-03-01
We study the average position and the symmetry of the distribution in the SU(2) open quantum random walk (OQRW). We show that the average position in the central limit theorem (CLT) is non-uniform compared with the average position in the non-CLT. The symmetry of distribution is shown to be even in the CLT.
Stochastic representation of a class of non-Markovian completely positive evolutions
International Nuclear Information System (INIS)
Budini, Adrian A.
2004-01-01
By modeling the interaction of an open quantum system with its environment through a natural generalization of the classical concept of continuous time random walk, we derive and characterize a class of non-Markovian master equations whose solution is a completely positive map. The structure of these master equations is associated with a random renewal process where each event consist in the application of a superoperator over a density matrix. Strong nonexponential decay arise by choosing different statistics of the renewal process. As examples we analyze the stochastic and averaged dynamics of simple systems that admit an analytical solution. The problem of positivity in quantum master equations induced by memory effects [S. M. Barnett and S. Stenholm, Phys. Rev. A 64, 033808 (2001)] is clarified in this context
Quantum Control of Open Systems and Dense Atomic Ensembles
DiLoreto, Christopher
Controlling the dynamics of open quantum systems; i.e. quantum systems that decohere because of interactions with the environment, is an active area of research with many applications in quantum optics and quantum computation. My thesis expands the scope of this inquiry by seeking to control open systems in proximity to an additional system. The latter could be a classical system such as metal nanoparticles, or a quantum system such as a cluster of similar atoms. By modelling the interactions between the systems, we are able to expand the accessible state space of the quantum system in question. For a single, three-level quantum system, I examine isolated systems that have only normal spontaneous emission. I then show that intensity-intensity correlation spectra, which depend directly on the density matrix of the system, can be used detect whether transitions share a common energy level. This detection is possible due to the presence of quantum interference effects between two transitions if they are connected. This effect allows one to asses energy level structure diagrams in complex atoms/molecules. By placing an open quantum system near a nanoparticle dimer, I show that the spontaneous emission rate of the system can be changed "on demand" by changing the polarization of an incident, driving field. In a three-level, Lambda system, this allows a qubit to both retain high qubit fidelity when it is operating, and to be rapidly initialized to a pure state once it is rendered unusable by decoherence. This type of behaviour is not possible in a single open quantum system; therefore adding a classical system nearby extends the overall control space of the quantum system. An open quantum system near identical neighbours in a dense ensemble is another example of how the accessible state space can be expanded. I show that a dense ensemble of atoms rapidly becomes disordered with states that are not directly excited by an incident field becoming significantly populated
DEFF Research Database (Denmark)
Mardare, Radu Iulian; Cardelli, Luca; Larsen, Kim Guldstrand
2012-01-01
Continuous Markovian Logic (CML) is a multimodal logic that expresses quantitative and qualitative properties of continuous-time labelled Markov processes with arbitrary (analytic) state-spaces, henceforth called continuous Markov processes (CMPs). The modalities of CML evaluate the rates...... of the exponentially distributed random variables that characterize the duration of the labeled transitions of a CMP. In this paper we present weak and strong complete axiomatizations for CML and prove a series of metaproperties, including the finite model property and the construction of canonical models. CML...... characterizes stochastic bisimilarity and it supports the definition of a quantified extension of the satisfiability relation that measures the "compatibility" between a model and a property. In this context, the metaproperties allows us to prove two robustness theorems for the logic stating that one can...
Approaches to open quantum systems: Decoherence, localisation and all that
International Nuclear Information System (INIS)
Yu Ting
1998-01-01
This thesis is mainly concerned with issues in quantum open systems and the foundations of quantum theory. Chapter I introduces the aim, background and main results which take place in the following chapters. Chapters II and III are used to study and compare the decoherent histories approach, the environment-induced decoherence and the localisation properties of the solutions to the stochastic Schrodinger equation in quantum jump simulation and quantum state diffusion approaches, for a quantum two-level system model. We show, in particular, that there is a close connection between the decoherent histories and the quantum jump simulation, complementing a connection with the quantum state diffusion approach noted earlier by Diosi, Gisin, Halliwell and Percival. In the case of the decoherent histories analysis, the degree of approximate decoherence is discussed in detail. As by-product, by using the von Neumann entropy, we also discuss the predictability and its relation to the upper bounds of degree of decoherence. In Chapter IV, we give an alternative and elementary derivation of the Hu-Paz-Ghang master equation for quantum Brownian motion in a general environment, which involves tracing the evolution equation for the Wigner function. We also discuss the master equation in some special cases. This master equation provides a very useful tool to study the decoherence of a quantum system due to the interaction with its environment. In Chapter V, a derivation of the parameter-based uncertainty relation between position and momentum is given. This uncertainty relation can be regarded as an exact counterpart of the time-energy uncertainty relation. The final chapter is a rather brief summary of the thesis. (author)
Keldysh field theory for driven open quantum systems.
Sieberer, L M; Buchhold, M; Diehl, S
2016-09-01
Recent experimental developments in diverse areas-ranging from cold atomic gases to light-driven semiconductors to microcavity arrays-move systems into the focus which are located on the interface of quantum optics, many-body physics and statistical mechanics. They share in common that coherent and driven-dissipative quantum dynamics occur on an equal footing, creating genuine non-equilibrium scenarios without immediate counterpart in equilibrium condensed matter physics. This concerns both their non-thermal stationary states and their many-body time evolution. It is a challenge to theory to identify novel instances of universal emergent macroscopic phenomena, which are tied unambiguously and in an observable way to the microscopic drive conditions. In this review, we discuss some recent results in this direction. Moreover, we provide a systematic introduction to the open system Keldysh functional integral approach, which is the proper technical tool to accomplish a merger of quantum optics and many-body physics, and leverages the power of modern quantum field theory to driven open quantum systems.
Eigenvectors of Open Bazhanov-Stroganov Quantum Chain
Directory of Open Access Journals (Sweden)
Nikolai Iorgov
2006-02-01
Full Text Available In this contribution we give an explicit formula for the eigenvectors of Hamiltonians of open Bazhanov-Stroganov quantum chain. The Hamiltonians of this quantum chain is defined by the generation polynomial $A_n(lambda$ which is upper-left matrix element of monodromy matrix built from the Bazhanov-Stroganov $L$-operators. The formulas for the eigenvectors are derived using iterative procedure by Kharchev and Lebedev and given in terms of $w_p(s$-function which is a root of unity analogue of $Gamma_q$-function.
Decoherence control in open quantum systems via classical feedback
International Nuclear Information System (INIS)
Ganesan, Narayan; Tarn, Tzyh-Jong
2007-01-01
In this work we propose a strategy using techniques from systems theory to completely eliminate decoherence and also provide conditions under which it can be done. A construction employing an auxiliary system, the bait, which is instrumental to decoupling the system from the environment is presented. Our approach to decoherence control in contrast to other approaches in the literature involves the bilinear input affine model of quantum control system which lends itself to various techniques from classical control theory, but with nontrivial modifications to the quantum regime. The elegance of this approach yields interesting results on open loop decouplability and decoherence free subspaces. Additionally, the feedback control of decoherence may be related to disturbance decoupling for classical input affine systems, which entails careful application of the methods by avoiding all the quantum mechanical pitfalls. In the process of calculating a suitable feedback the system must be restructured due to its tensorial nature of interaction with the environment, which is unique to quantum systems. In the subsequent section we discuss a general information extraction scheme to gain knowledge of the state and the amount of decoherence based on indirect continuous measurement. The analysis of continuous measurement on a decohering quantum system has not been extensively studied before. Finally, a methodology to synthesize feedback parameters itself is given, that technology permitting, could be implemented for practical 2-qubit systems to perform decoherence free quantum computing. The results obtained are qualitatively different and superior to the ones obtained via master equations
DEFF Research Database (Denmark)
Nielsen, Per Kær; Nielsen, Torben Roland; Lodahl, Peter
2010-01-01
treatments. A pronounced consequence is the emergence of a phonon induced spectral asymmetry when detuning the cavity from the quantum-dot resonance. The asymmetry can only be explained when considering the polaritonic quasiparticle nature of the quantum-dot-cavity system. Furthermore, a temperature induced...
An information theory model for dissipation in open quantum systems
Rogers, David M.
2017-08-01
This work presents a general model for open quantum systems using an information game along the lines of Jaynes’ original work. It is shown how an energy based reweighting of propagators provides a novel moment generating function at each time point in the process. Derivatives of the generating function give moments of the time derivatives of observables. Aside from the mathematically helpful properties, the ansatz reproduces key physics of stochastic quantum processes. At high temperature, the average density matrix follows the Caldeira-Leggett equation. Its associated Langevin equation clearly demonstrates the emergence of dissipation and decoherence time scales, as well as an additional diffusion due to quantum confinement. A consistent interpretation of these results is that decoherence and wavefunction collapse during measurement are directly related to the degree of environmental noise, and thus occur because of subjective uncertainty of an observer.
Understanding Hawking radiation in the framework of open quantum systems
International Nuclear Information System (INIS)
Yu Hongwei; Zhang Jialin
2008-01-01
We study the Hawking radiation in the framework of open quantum systems by examining the time evolution of a detector (modeled by a two-level atom) interacting with vacuum massless scalar fields. The dynamics of the detector is governed by a master equation obtained by tracing over the field degrees of freedom from the complete system. The nonunitary effects are studied by analyzing the time behavior of a particular observable of the detector, i.e., its admissible state, in the Unruh, Hartle-Hawking, as well as Boulware vacua outside a Schwarzschild black hole. We find that the detector in both the Unruh and Hartle-Hawking vacua would spontaneously excite with a nonvanishing probability the same as what one would obtain if there is thermal radiation at the Hawking temperature from the black hole, thus reproducing the basic results concerning the Hawking effect in the framework of open quantum systems
Shot-noise at a Fermi-edge singularity: Non-Markovian dynamics
Energy Technology Data Exchange (ETDEWEB)
Ubbelohde, N.; Maire, N.; Haug, R. J. [Institut für Festkörperphysik, Leibniz Universität Hannover, Appelstraße 2, D-30167 Hannover (Germany); Roszak, K. [Institute of Physics, Wrocław University of Technology, PL-50370 Wrocław (Poland); Hohls, F. [Physikalisch-Technische Bundesanstalt, D-38116 Braunschweig (Germany); Novotný, T. [Department of Condensed Matter Physics, Faculty of Mathematics and Physics, Charles University, CZ-12116 Prague (Czech Republic)
2013-12-04
For an InAs quantum dot we study the current shot noise at a Fermi-edge singularity in low temperature cross-correlation measurements. In the regime of the interaction effect the strong suppression of noise observed at zero magnetic field and the sequence of enhancement and suppression in magnetic field go beyond a Markovian master equation model. Qualitative and quantitative agreement can however be achieved by a generalized master equation model taking non-Markovian dynamics into account.
Sun, Wen-Yang; Wang, Dong; Fang, Bao-Long; Ye, Liu
2018-03-01
In this letter, the dynamics characteristics of quantum entanglement (negativity) and distinguishability (trace distance), and the flow of information for an open quantum system under relativistic motion are investigated. Explicitly, we propose a scenario that a particle A held by Alice suffers from an amplitude damping (AD) noise in a flat space-time and another particle B by Bob entangled with A travels with a fixed acceleration under a non-inertial frame. The results show that quantum distinguishability and entanglement are very vulnerable and fragile under the collective influence of AD noise and Unruh effect. Both of them will decrease with the growing intensity of the Unruh effect and the AD thermal bath. It means that the abilities of quantum distinguishability and entanglement to suppress the collective decoherence (AD noise and Unruh effect) are very weak. Furthermore, it turns out that the reduced quantum distinguishability of Alice’s system and Bob in the physically accessible region is distributed to another quantum distinguishability for Alice’s environment and Bob in the physically inaccessible region. That is, the information regarding the scenario is that the lost quantum distinguishability, as a fixed information, flows from the systems to the collective decoherence environment.
Control landscapes for observable preparation with open quantum systems
International Nuclear Information System (INIS)
Wu Rebing; Pechen, Alexander; Rabitz, Herschel; Hsieh, Michael; Tsou, Benjamin
2008-01-01
A quantum control landscape is defined as the observable as a function(al) of the system control variables. Such landscapes were introduced to provide a basis to understand the increasing number of successful experiments controlling quantum dynamics phenomena. This paper extends the concept to encompass the broader context of the environment having an influence. For the case that the open system dynamics are fully controllable, it is shown that the control landscape for open systems can be lifted to the analysis of an equivalent auxiliary landscape of a closed composite system that contains the environmental interactions. This inherent connection can be analyzed to provide relevant information about the topology of the original open system landscape. Application to the optimization of an observable expectation value reveals the same landscape simplicity observed in former studies on closed systems. In particular, no false suboptimal traps exist in the system control landscape when seeking to optimize an observable, even in the presence of complex environments. Moreover, a quantitative study of the control landscape of a system interacting with a thermal environment shows that the enhanced controllability attainable with open dynamics significantly broadens the range of the achievable observable values over the control landscape
Semiclassical evolution of dissipative Markovian systems
International Nuclear Information System (INIS)
Ozorio de Almeida, A M; Rios, P de M; Brodier, O
2009-01-01
A semiclassical approximation for an evolving density operator, driven by a 'closed' Hamiltonian operator and 'open' Markovian Lindblad operators, is obtained. The theory is based on the chord function, i.e. the Fourier transform of the Wigner function. It reduces to an exact solution of the Lindblad master equation if the Hamiltonian operator is a quadratic function and the Lindblad operators are linear functions of positions and momenta. Initially, the semiclassical formulae for the case of Hermitian Lindblad operators are reinterpreted in terms of a (real) double phase space, generated by an appropriate classical double Hamiltonian. An extra 'open' term is added to the double Hamiltonian by the non-Hermitian part of the Lindblad operators in the general case of dissipative Markovian evolution. The particular case of generic Hamiltonian operators, but linear dissipative Lindblad operators, is studied in more detail. A Liouville-type equivariance still holds for the corresponding classical evolution in double phase space, but the centre subspace, which supports the Wigner function, is compressed, along with expansion of its conjugate subspace, which supports the chord function. Decoherence narrows the relevant region of double phase space to the neighbourhood of a caustic for both the Wigner function and the chord function. This difficulty is avoided by a propagator in a mixed representation, so that a further 'small-chord' approximation leads to a simple generalization of the quadratic theory for evolving Wigner functions
Open quantum spin systems in semiconductor quantum dots and atoms in optical lattices
Energy Technology Data Exchange (ETDEWEB)
Schwager, Heike
2012-07-04
In this Thesis, we study open quantum spin systems from different perspectives. The first part is motivated by technological challenges of quantum computation. An important building block for quantum computation and quantum communication networks is an interface between material qubits for storage and data processing and travelling photonic qubits for communication. We propose the realisation of a quantum interface between a travelling-wave light field and the nuclear spins in a quantum dot strongly coupled to a cavity. Our scheme is robust against cavity decay as it uses the decay of the cavity to achieve the coupling between nuclear spins and the travelling-wave light fields. A prerequiste for such a quantum interface is a highly polarized ensemble of nuclear spins. High polarization of the nuclear spin ensemble is moreover highly desirable as it protects the potential electron spin qubit from decoherence. Here we present the theoretical description of an experiment in which highly asymmetric dynamic nuclear spin pumping is observed in a single self-assembled InGaAs quantum dot. The second part of this Thesis is devoted to fundamental studies of dissipative spin systems. We study general one-dimensional spin chains under dissipation and propose a scheme to realize a quantum spin system using ultracold atoms in an optical lattice in which both coherent interaction and dissipation can be engineered and controlled. This system enables the study of non-equilibrium and steady state physics of open and driven spin systems. We find, that the steady state expectation values of different spin models exhibit discontinuous behaviour at degeneracy points of the Hamiltonian in the limit of weak dissipation. This effect can be used to dissipatively probe the spectrum of the Hamiltonian. We moreover study spin models under the aspect of state preparation and show that dissipation drives certain spin models into highly entangled state. Finally, we study a spin chain with
Open quantum spin systems in semiconductor quantum dots and atoms in optical lattices
International Nuclear Information System (INIS)
Schwager, Heike
2012-01-01
In this Thesis, we study open quantum spin systems from different perspectives. The first part is motivated by technological challenges of quantum computation. An important building block for quantum computation and quantum communication networks is an interface between material qubits for storage and data processing and travelling photonic qubits for communication. We propose the realisation of a quantum interface between a travelling-wave light field and the nuclear spins in a quantum dot strongly coupled to a cavity. Our scheme is robust against cavity decay as it uses the decay of the cavity to achieve the coupling between nuclear spins and the travelling-wave light fields. A prerequiste for such a quantum interface is a highly polarized ensemble of nuclear spins. High polarization of the nuclear spin ensemble is moreover highly desirable as it protects the potential electron spin qubit from decoherence. Here we present the theoretical description of an experiment in which highly asymmetric dynamic nuclear spin pumping is observed in a single self-assembled InGaAs quantum dot. The second part of this Thesis is devoted to fundamental studies of dissipative spin systems. We study general one-dimensional spin chains under dissipation and propose a scheme to realize a quantum spin system using ultracold atoms in an optical lattice in which both coherent interaction and dissipation can be engineered and controlled. This system enables the study of non-equilibrium and steady state physics of open and driven spin systems. We find, that the steady state expectation values of different spin models exhibit discontinuous behaviour at degeneracy points of the Hamiltonian in the limit of weak dissipation. This effect can be used to dissipatively probe the spectrum of the Hamiltonian. We moreover study spin models under the aspect of state preparation and show that dissipation drives certain spin models into highly entangled state. Finally, we study a spin chain with
Non-Markovian electron dynamics in nanostructures coupled to dissipative contacts
Novakovic, B.; Knezevic, I.
2013-02-01
In quasiballistic semiconductor nanostructures, carrier exchange between the active region and dissipative contacts is the mechanism that governs relaxation. In this paper, we present a theoretical treatment of transient quantum transport in quasiballistic semiconductor nanostructures, which is based on the open system theory and valid on timescales much longer than the characteristic relaxation time in the contacts. The approach relies on a model interaction between the current-limiting active region and the contacts, given in the scattering-state basis. We derive a non-Markovian master equation for the irreversible evolution of the active region's many-body statistical operator by coarse-graining the exact dynamical map over the contact relaxation time. In order to obtain the response quantities of a nanostructure under bias, such as the potential and the charge and current densities, the non-Markovian master equation must be solved numerically together with the Schr\\"{o}dinger, Poisson, and continuity equations. We discuss how to numerically solve this coupled system of equations and illustrate the approach on the example of a silicon nin diode.
Surveying the quantum group symmetries of integrable open spin chains
Nepomechie, Rafael I.; Retore, Ana L.
2018-05-01
Using anisotropic R-matrices associated with affine Lie algebras g ˆ (specifically, A2n(2), A2n-1 (2) , Bn(1), Cn(1), Dn(1)) and suitable corresponding K-matrices, we construct families of integrable open quantum spin chains of finite length, whose transfer matrices are invariant under the quantum group corresponding to removing one node from the Dynkin diagram of g ˆ . We show that these transfer matrices also have a duality symmetry (for the cases Cn(1) and Dn(1)) and additional Z2 symmetries that map complex representations to their conjugates (for the cases A2n-1 (2) , Bn(1) and Dn(1)). A key simplification is achieved by working in a certain "unitary" gauge, in which only the unbroken symmetry generators appear. The proofs of these symmetries rely on some new properties of the R-matrices. We use these symmetries to explain the degeneracies of the transfer matrices.
Exact master equations for the non-Markovian decay of a qubit
International Nuclear Information System (INIS)
Vacchini, Bassano; Breuer, Heinz-Peter
2010-01-01
Exact master equations describing the decay of a two-state system into a structured reservoir are constructed. By employing the exact solution for the model, analytical expressions are determined for the memory kernel of the Nakajima-Zwanzig master equation and for the generator of the corresponding time-convolutionless master equation. This approach allows an explicit comparison of the convergence behavior of the corresponding perturbation expansions. Moreover, the structure of widely used phenomenological master equations with a memory kernel may be incompatible with a nonperturbative treatment of the underlying microscopic model. Several physical implications of the results on the microscopic analysis and the phenomenological modeling of non-Markovian quantum dynamics of open systems are discussed.
Trautmann, N.; Hauke, P.
2018-02-01
The transport of excitations governs fundamental properties of matter. Particularly rich physics emerges in the interplay between disorder and environmental noise, even in small systems such as photosynthetic biomolecules. Counterintuitively, noise can enhance coherent quantum transport, which has been proposed as a mechanism behind the high transport efficiencies observed in photosynthetic complexes. This effect has been called "environment-assisted quantum transport". Here, we propose a quantum simulation of the excitation transport in an open quantum network, taking advantage of the high controllability of current trapped-ion experiments. Our scheme allows for the controlled study of various different aspects of the excitation transfer, ranging from the influence of static disorder and interaction range, over the effect of Markovian and non-Markovian dephasing, to the impact of a continuous insertion of excitations. Our paper discusses experimental error sources and realistic parameters, showing that it can be implemented in state-of-the-art ion-chain experiments.
Statistical quasi-particle theory for open quantum systems
Zhang, Hou-Dao; Xu, Rui-Xue; Zheng, Xiao; Yan, YiJing
2018-04-01
This paper presents a comprehensive account on the recently developed dissipaton-equation-of-motion (DEOM) theory. This is a statistical quasi-particle theory for quantum dissipative dynamics. It accurately describes the influence of bulk environments, with a few number of quasi-particles, the dissipatons. The novel dissipaton algebra is then followed, which readily bridges the Schrödinger equation to the DEOM theory. As a fundamental theory of quantum mechanics in open systems, DEOM characterizes both the stationary and dynamic properties of system-and-bath interferences. It treats not only the quantum dissipative systems of primary interest, but also the hybrid environment dynamics that could be experimentally measurable. Examples are the linear or nonlinear Fano interferences and the Herzberg-Teller vibronic couplings in optical spectroscopies. This review covers the DEOM construction, the underlying dissipaton algebra and theorems, the physical meanings of dynamical variables, the possible identifications of dissipatons, and some recent advancements in efficient DEOM evaluations on various problems. The relations of the present theory to other nonperturbative methods are also critically presented.
Tanimura, Y; Steffen, T
2000-01-01
The relaxation processes in a quantum system nonlinearly coupled to a harmonic Gaussian-Markovian heat bath are investigated by the quantum Fokker-Planck equation in the hierarchy form. This model describes frequency fluctuations in the quantum system with an arbitrary correlation time and thus
QUANTUM ESPRESSO: a modular and open-source software project for quantum simulations of materials.
Giannozzi, Paolo; Baroni, Stefano; Bonini, Nicola; Calandra, Matteo; Car, Roberto; Cavazzoni, Carlo; Ceresoli, Davide; Chiarotti, Guido L; Cococcioni, Matteo; Dabo, Ismaila; Dal Corso, Andrea; de Gironcoli, Stefano; Fabris, Stefano; Fratesi, Guido; Gebauer, Ralph; Gerstmann, Uwe; Gougoussis, Christos; Kokalj, Anton; Lazzeri, Michele; Martin-Samos, Layla; Marzari, Nicola; Mauri, Francesco; Mazzarello, Riccardo; Paolini, Stefano; Pasquarello, Alfredo; Paulatto, Lorenzo; Sbraccia, Carlo; Scandolo, Sandro; Sclauzero, Gabriele; Seitsonen, Ari P; Smogunov, Alexander; Umari, Paolo; Wentzcovitch, Renata M
2009-09-30
QUANTUM ESPRESSO is an integrated suite of computer codes for electronic-structure calculations and materials modeling, based on density-functional theory, plane waves, and pseudopotentials (norm-conserving, ultrasoft, and projector-augmented wave). The acronym ESPRESSO stands for opEn Source Package for Research in Electronic Structure, Simulation, and Optimization. It is freely available to researchers around the world under the terms of the GNU General Public License. QUANTUM ESPRESSO builds upon newly-restructured electronic-structure codes that have been developed and tested by some of the original authors of novel electronic-structure algorithms and applied in the last twenty years by some of the leading materials modeling groups worldwide. Innovation and efficiency are still its main focus, with special attention paid to massively parallel architectures, and a great effort being devoted to user friendliness. QUANTUM ESPRESSO is evolving towards a distribution of independent and interoperable codes in the spirit of an open-source project, where researchers active in the field of electronic-structure calculations are encouraged to participate in the project by contributing their own codes or by implementing their own ideas into existing codes.
Hong, Changki; Park, Jinhong; Chung, Yunchul; Choi, Hyungkook; Umansky, Vladimir
2017-11-01
Transmission through a quantum point contact (QPC) in the quantum Hall regime usually exhibits multiple resonances as a function of gate voltage and high nonlinearity in bias. Such behavior is unpredictable and changes sample by sample. Here, we report the observation of a sharp transition of the transmission through an open QPC at finite bias, which was observed consistently for all the tested QPCs. It is found that the bias dependence of the transition can be fitted to the Fermi-Dirac distribution function through universal scaling. The fitted temperature matches quite nicely to the electron temperature measured via shot-noise thermometry. While the origin of the transition is unclear, we propose a phenomenological model based on our experimental results that may help to understand such a sharp transition. Similar transitions are observed in the fractional quantum Hall regime, and it is found that the temperature of the system can be measured by rescaling the quasiparticle energy with the effective charge (e*=e /3 ). We believe that the observed phenomena can be exploited as a tool for measuring the electron temperature of the system and for studying the quasiparticle charges of the fractional quantum Hall states.
Model for calorimetric measurements in an open quantum system
Donvil, Brecht; Muratore-Ginanneschi, Paolo; Pekola, Jukka P.; Schwieger, Kay
2018-05-01
We investigate the experimental setup proposed in New J. Phys. 15, 115006 (2013), 10.1088/1367-2630/15/11/115006 for calorimetric measurements of thermodynamic indicators in an open quantum system. As a theoretical model we consider a periodically driven qubit coupled with a large yet finite electron reservoir, the calorimeter. The calorimeter is initially at equilibrium with an infinite phonon bath. As time elapses, the temperature of the calorimeter varies in consequence of energy exchanges with the qubit and the phonon bath. We show how under weak-coupling assumptions, the evolution of the qubit-calorimeter system can be described by a generalized quantum jump process including as dynamical variable the temperature of the calorimeter. We study the jump process by numeric and analytic methods. Asymptotically with the duration of the drive, the qubit-calorimeter attains a steady state. In this same limit, we use multiscale perturbation theory to derive a Fokker-Planck equation governing the calorimeter temperature distribution. We inquire the properties of the temperature probability distribution close and at the steady state. In particular, we predict the behavior of measurable statistical indicators versus the qubit-calorimeter coupling constant.
Information dynamics and open systems classical and quantum approach
Ingarden, R S; Ohya, M
1997-01-01
This book aims to present an information-theoretical approach to thermodynamics and its generalisations On the one hand, it generalises the concept of `information thermodynamics' to that of `information dynamics' in order to stress applications outside thermal phenomena On the other hand, it is a synthesis of the dynamics of state change and the theory of complexity, which provide a common framework to treat both physical and nonphysical systems together Both classical and quantum systems are discussed, and two appendices are included to explain principal definitions and some important aspects of the theory of Hilbert spaces and operator algebras The concept of higher-order temperatures is explained and applied to biological and linguistic systems The theory of open systems is presented in a new, much more general form Audience This volume is intended mainly for theoretical and mathematical physicists, but also for mathematicians, experimental physicists, physical chemists, theoretical biologists, communicat...
Composite quantum collision models
Lorenzo, Salvatore; Ciccarello, Francesco; Palma, G. Massimo
2017-09-01
A collision model (CM) is a framework to describe open quantum dynamics. In its memoryless version, it models the reservoir R as consisting of a large collection of elementary ancillas: the dynamics of the open system S results from successive collisions of S with the ancillas of R . Here, we present a general formulation of memoryless composite CMs, where S is partitioned into the very open system under study S coupled to one or more auxiliary systems {Si} . Their composite dynamics occurs through internal S -{Si} collisions interspersed with external ones involving {Si} and the reservoir R . We show that important known instances of quantum non-Markovian dynamics of S —such as the emission of an atom into a reservoir featuring a Lorentzian, or multi-Lorentzian, spectral density or a qubit subject to random telegraph noise—can be mapped on to such memoryless composite CMs.
Correlation Functions in Open Quantum-Classical Systems
Hsieh, Chang-Yu; Kapral, Raymond
2013-01-01
Quantum time correlation functions are often the principal objects of interest in experimental investigations of the dynamics of quantum systems. For instance, transport properties, such as diffusion and reaction rate coefficients, can be obtained by integrating these functions. The evaluation of such correlation functions entails sampling from quantum equilibrium density operators and quantum time evolution of operators. For condensed phase and complex systems, where quantum dynamics is diff...
Markovian Dynamics of Josephson Parametric Amplification
Directory of Open Access Journals (Sweden)
W. Kaiser
2017-09-01
Full Text Available In this work, we derive the dynamics of the lossy DC pumped non-degenerate Josephson parametric amplifier (DCPJPA. The main element in a DCPJPA is the superconducting Josephson junction. The DC bias generates the AC Josephson current varying the nonlinear inductance of the junction. By this way the Josephson junction acts as the pump oscillator as well as the time varying reactance of the parametric amplifier. In quantum-limited amplification, losses and noise have an increased impact on the characteristics of an amplifier. We outline the classical model of the lossy DCPJPA and derive the available noise power spectral densities. A classical treatment is not capable of including properties like spontaneous emission which is mandatory in case of amplification at the quantum limit. Thus, we derive a quantum mechanical model of the lossy DCPJPA. Thermal losses are modeled by the quantum Langevin approach, by coupling the quantized system to a photon heat bath in thermodynamic equilibrium. The mode occupation in the bath follows the Bose-Einstein statistics. Based on the second quantization formalism, we derive the Heisenberg equations of motion of both resonator modes. We assume the dynamics of the system to follow the Markovian approximation, i.e. the system only depends on its actual state and is memory-free. We explicitly compute the time evolution of the contributions to the signal mode energy and give numeric examples based on different damping and coupling constants. Our analytic results show, that this model is capable of including thermal noise into the description of the DC pumped non-degenerate Josephson parametric amplifier.
Markovian Dynamics of Josephson Parametric Amplification
Kaiser, Waldemar; Haider, Michael; Russer, Johannes A.; Russer, Peter; Jirauschek, Christian
2017-09-01
In this work, we derive the dynamics of the lossy DC pumped non-degenerate Josephson parametric amplifier (DCPJPA). The main element in a DCPJPA is the superconducting Josephson junction. The DC bias generates the AC Josephson current varying the nonlinear inductance of the junction. By this way the Josephson junction acts as the pump oscillator as well as the time varying reactance of the parametric amplifier. In quantum-limited amplification, losses and noise have an increased impact on the characteristics of an amplifier. We outline the classical model of the lossy DCPJPA and derive the available noise power spectral densities. A classical treatment is not capable of including properties like spontaneous emission which is mandatory in case of amplification at the quantum limit. Thus, we derive a quantum mechanical model of the lossy DCPJPA. Thermal losses are modeled by the quantum Langevin approach, by coupling the quantized system to a photon heat bath in thermodynamic equilibrium. The mode occupation in the bath follows the Bose-Einstein statistics. Based on the second quantization formalism, we derive the Heisenberg equations of motion of both resonator modes. We assume the dynamics of the system to follow the Markovian approximation, i.e. the system only depends on its actual state and is memory-free. We explicitly compute the time evolution of the contributions to the signal mode energy and give numeric examples based on different damping and coupling constants. Our analytic results show, that this model is capable of including thermal noise into the description of the DC pumped non-degenerate Josephson parametric amplifier.
Quantum Brownian motion model for the stock market
Meng, Xiangyi; Zhang, Jian-Wei; Guo, Hong
2016-06-01
It is believed by the majority today that the efficient market hypothesis is imperfect because of market irrationality. Using the physical concepts and mathematical structures of quantum mechanics, we construct an econophysical framework for the stock market, based on which we analogously map massive numbers of single stocks into a reservoir consisting of many quantum harmonic oscillators and their stock index into a typical quantum open system-a quantum Brownian particle. In particular, the irrationality of stock transactions is quantitatively considered as the Planck constant within Heisenberg's uncertainty relationship of quantum mechanics in an analogous manner. We analyze real stock data of Shanghai Stock Exchange of China and investigate fat-tail phenomena and non-Markovian behaviors of the stock index with the assistance of the quantum Brownian motion model, thereby interpreting and studying the limitations of the classical Brownian motion model for the efficient market hypothesis from a new perspective of quantum open system dynamics.
Symmetry-protected coherent relaxation of open quantum systems
van Caspel, Moos; Gritsev, Vladimir
2018-05-01
We compute the effect of Markovian bulk dephasing noise on the staggered magnetization of the spin-1/2 XXZ Heisenberg chain, as the system evolves after a Néel quench. For sufficiently weak system-bath coupling, the unitary dynamics are found to be preserved up to a single exponential damping factor. This is a consequence of the interplay between PT symmetry and weak symmetries, which strengthens previous predictions for PT -symmetric Liouvillian dynamics. Requirements are a nondegenerate PT -symmetric generator of time evolution L ̂, a weak parity symmetry, and an observable that is antisymmetric under this parity transformation. The spectrum of L ̂ then splits up into symmetry sectors, yielding the same decay rate for all modes that contribute to the observable's time evolution. This phenomenon may be realized in trapped ion experiments and has possible implications for the control of decoherence in out-of-equilibrium many-body systems.
Operational Markov Condition for Quantum Processes
Pollock, Felix A.; Rodríguez-Rosario, César; Frauenheim, Thomas; Paternostro, Mauro; Modi, Kavan
2018-01-01
We derive a necessary and sufficient condition for a quantum process to be Markovian which coincides with the classical one in the relevant limit. Our condition unifies all previously known definitions for quantum Markov processes by accounting for all potentially detectable memory effects. We then derive a family of measures of non-Markovianity with clear operational interpretations, such as the size of the memory required to simulate a process or the experimental falsifiability of a Markovian hypothesis.
Applicability of transfer tensor method for open quantum system dynamics.
Gelzinis, Andrius; Rybakovas, Edvardas; Valkunas, Leonas
2017-12-21
Accurate simulations of open quantum system dynamics is a long standing issue in the field of chemical physics. Exact methods exist, but are costly, while perturbative methods are limited in their applicability. Recently a new black-box type method, called transfer tensor method (TTM), was proposed [J. Cerrillo and J. Cao, Phys. Rev. Lett. 112, 110401 (2014)]. It allows one to accurately simulate long time dynamics with a numerical cost of solving a time-convolution master equation, provided many initial system evolution trajectories are obtained from some exact method beforehand. The possible time-savings thus strongly depend on the ratio of total versus initial evolution lengths. In this work, we investigate the parameter regimes where an application of TTM would be most beneficial in terms of computational time. We identify several promising parameter regimes. Although some of them correspond to cases when perturbative theories could be expected to perform well, we find that the accuracy of such approaches depends on system parameters in a more complex way than it is commonly thought. We propose that the TTM should be applied whenever system evolution is expected to be long and accuracy of perturbative methods cannot be ensured or in cases when the system under consideration does not correspond to any single perturbative regime.
Simulation of Quantum Tunnelling in an Open System
Fernández, Julio F.
2003-04-01
Magnetic clusters, such as Fe8 and Mn12, within large organic molecules, behave at low temperature T as large single spins S, that is, as single molecule magnets (SMM's). In crystals, magnetic anisotropy gives rise to energy barriers U, and quantum tunnelling is then the only available path for magnetic relaxation at vanishingly small temperatures. Even this path, however, would seem to be nearly closed by energy conservation requirements, given the existence of magnetic dipolar interactions among all SMM's in the crystal. Nevertheless, magnetic relaxation that is temperature independent has lately been observed for temperatures under 0.1 U/kBS for Fe8 and Mn12 (U ≈ 30 K and U ≈ 60 K, for Fe8 and Mn12, respectively, and S = 10 for both of them). Prokof'ev and Stamp (PS) were able to explain it by taking into account hyperfine interactions between the tunnelling electronic spins and nuclear spins. In the PS theory, the system of nuclear spins acts much as a heat bath providing a somewhat random magnetic field h(t) that acts on the otherwise closed system of interacting magnetic dipoles. Thus, the open nature of these systems plays an essential role in bringing tunnelling about. Their numerical simulations are explained, results that follow from the simulations are discussed, and a simple derivation of the tunnelling rate is given.
Entropy balance in pure interactions of open quantum systems
International Nuclear Information System (INIS)
Urigu, R.
1989-01-01
Processes are considered in which a statistical ensemble w of quantum systems is split into ensembles, or channels (w i ), conditional to the occurrence, with respective probabilities (p i w ), of associated macroscopic effects. These processes are described here by a family of operations T i : w → p i w w iT , which remarkably generalize the usual state reductions of the nondestructive measurements. In a previous work it was proved that the microscopic entropy of the given open system decreases or at most remains constant if all the T i are pure operations, i.e., they transform pure states into pure states; it is proved here that the increase in entropy of the external world, computed as S Tm (w) = - Σ i p i w lg p i w , is sufficient to compensate for such an entropy decrease whenever the T i are all pure operations of the first kind, whereas whenever some T i is pure of the second kind (or nonpure, too), the total entropy, computed as above, may decrease
Dynamics of quantum tomography in an open system
Uchiyama, Chikako
2015-06-01
In this study, we provide a way to describe the dynamics of quantum tomography in an open system with a generalized master equation, considering a case where the relevant system under tomographic measurement is influenced by the environment. We apply this to spin tomography because such situations typically occur in μSR (muon spin rotation/relaxation/resonance) experiments where microscopic features of the material are investigated by injecting muons as probes. As a typical example to describe the interaction between muons and a sample material, we use a spin-boson model where the relevant spin interacts with a bosonic environment. We describe the dynamics of a spin tomogram using a time-convolutionless type of generalized master equation that enables us to describe short time scales and/or low-temperature regions. Through numerical evaluation for the case of Ohmic spectral density with an exponential cutoff, a clear interdependency is found between the time evolution of elements of the density operator and a spin tomogram. The formulation in this paper may provide important fundamental information for the analysis of results from, for example, μSR experiments on short time scales and/or in low-temperature regions using spin tomography.
Correlation Functions in Open Quantum-Classical Systems
Directory of Open Access Journals (Sweden)
Chang-Yu Hsieh
2013-12-01
Full Text Available Quantum time correlation functions are often the principal objects of interest in experimental investigations of the dynamics of quantum systems. For instance, transport properties, such as diffusion and reaction rate coefficients, can be obtained by integrating these functions. The evaluation of such correlation functions entails sampling from quantum equilibrium density operators and quantum time evolution of operators. For condensed phase and complex systems, where quantum dynamics is difficult to carry out, approximations must often be made to compute these functions. We present a general scheme for the computation of correlation functions, which preserves the full quantum equilibrium structure of the system and approximates the time evolution with quantum-classical Liouville dynamics. Several aspects of the scheme are discussed, including a practical and general approach to sample the quantum equilibrium density, the properties of the quantum-classical Liouville equation in the context of correlation function computations, simulation schemes for the approximate dynamics and their interpretation and connections to other approximate quantum dynamical methods.
Non-Markovian nuclear dynamics
International Nuclear Information System (INIS)
Kolomietz, V.M.
2011-01-01
A prove of equations of motion for the nuclear shape variables which establish a direct connection of the memory effects with the dynamic distortion of the Fermi surface is suggested. The equations of motion for the nuclear Fermi liquid drop are derived from the collisional kinetic equation. In general, the corresponding equations are non-Markovian. The memory effects appear due to the Fermi surface distortions and depend on the relaxation time. The main purpose of the present work is to apply the non-Markovian dynamics to the description of the nuclear giant multipole resonances (GMR) and the large amplitude motion. We take also into consideration the random forces and concentrate on the formation of both the conservative and the friction forces to make more clear the memory effect on the nuclear dynamics. In this respect, the given approach represents an extension of the traditional liquid drop model (LDM) to the case of the nuclear Fermi liquid drop. In practical application, we pay close attention to the description of the descent of the nucleus from the fission barrier to the scission point.
open-quotes Interaction-freeclose quotes measurements of quantum objects?
International Nuclear Information System (INIS)
White, A.G.; Kwiat, P.G.; James, D.F.
1999-01-01
It is now well established that the presence of an opaque classical object can be unambiguously determined by an open-quotes interaction-freeclose quotes measurement (IFM), where the object and the probe never directly interact. For quantum objects, we examine open-quotes interaction-freeclose quotes measurement (the object wavefunction is unchanged) and open-quotes interaction-freeclose quotes preparation (the object wavefunction is changed without physical interaction) and find that in general, neither is possible. We propose using high efficiency IFM close-quote s as a quantum information bus to connect disjoint quantum systems. copyright 1999 American Institute of Physics
Open-System Quantum Annealing in Mean-Field Models with Exponential Degeneracy*
Directory of Open Access Journals (Sweden)
Kostyantyn Kechedzhi
2016-05-01
Full Text Available Real-life quantum computers are inevitably affected by intrinsic noise resulting in dissipative nonunitary dynamics realized by these devices. We consider an open-system quantum annealing algorithm optimized for such a realistic analog quantum device which takes advantage of noise-induced thermalization and relies on incoherent quantum tunneling at finite temperature. We theoretically analyze the performance of this algorithm considering a p-spin model that allows for a mean-field quasiclassical solution and, at the same time, demonstrates the first-order phase transition and exponential degeneracy of states, typical characteristics of spin glasses. We demonstrate that finite-temperature effects introduced by the noise are particularly important for the dynamics in the presence of the exponential degeneracy of metastable states. We determine the optimal regime of the open-system quantum annealing algorithm for this model and find that it can outperform simulated annealing in a range of parameters. Large-scale multiqubit quantum tunneling is instrumental for the quantum speedup in this model, which is possible because of the unusual nonmonotonous temperature dependence of the quantum-tunneling action in this model, where the most efficient transition rate corresponds to zero temperature. This model calculation is the first analytically tractable example where open-system quantum annealing algorithm outperforms simulated annealing, which can, in principle, be realized using an analog quantum computer.
Markov Chain-Like Quantum Biological Modeling of Mutations, Aging, and Evolution
Directory of Open Access Journals (Sweden)
Ivan B. Djordjevic
2015-08-01
Full Text Available Recent evidence suggests that quantum mechanics is relevant in photosynthesis, magnetoreception, enzymatic catalytic reactions, olfactory reception, photoreception, genetics, electron-transfer in proteins, and evolution; to mention few. In our recent paper published in Life, we have derived the operator-sum representation of a biological channel based on codon basekets, and determined the quantum channel model suitable for study of the quantum biological channel capacity. However, this model is essentially memoryless and it is not able to properly model the propagation of mutation errors in time, the process of aging, and evolution of genetic information through generations. To solve for these problems, we propose novel quantum mechanical models to accurately describe the process of creation spontaneous, induced, and adaptive mutations and their propagation in time. Different biological channel models with memory, proposed in this paper, include: (i Markovian classical model, (ii Markovian-like quantum model, and (iii hybrid quantum-classical model. We then apply these models in a study of aging and evolution of quantum biological channel capacity through generations. We also discuss key differences of these models with respect to a multilevel symmetric channel-based Markovian model and a Kimura model-based Markovian process. These models are quite general and applicable to many open problems in biology, not only biological channel capacity, which is the main focus of the paper. We will show that the famous quantum Master equation approach, commonly used to describe different biological processes, is just the first-order approximation of the proposed quantum Markov chain-like model, when the observation interval tends to zero. One of the important implications of this model is that the aging phenotype becomes determined by different underlying transition probabilities in both programmed and random (damage Markov chain-like models of aging, which
International Nuclear Information System (INIS)
Kogan, I.I.
1991-01-01
The quantum geometrodynamics of the open topological membrane is described in terms of 2+1 topologically massive gravity (TMG) where the inverse graviton mass is proportional to the 2D central charge and thus is the measure of the off-criticality. The hamiltonian quantization of TMG on Riemann surfaces is considered and the moduli space appears as the subspace of the quantum-mechanical configuration space containing, besides the moduli, the first-order time derivatives of half of the moduli. The appearance of the first-order time derivatives as coordinates, not momenta, is due to the third-order derivative in the TMG lagrangian. The hamiltonian for the latter leads us to the discrete levels picture which looks like the topologically massive gauge theory (TMGT) case, where we also get the Landau levels picture and the lowest Landau level corresponds to the Hilbert space of the Chern-Simons theory (CST). The connection between the positivity of the energy and the complex structure on the moduli space is discussed. (orig.)
Jaschke, Daniel; Wall, Michael L.; Carr, Lincoln D.
2018-04-01
Numerical simulations are a powerful tool to study quantum systems beyond exactly solvable systems lacking an analytic expression. For one-dimensional entangled quantum systems, tensor network methods, amongst them Matrix Product States (MPSs), have attracted interest from different fields of quantum physics ranging from solid state systems to quantum simulators and quantum computing. Our open source MPS code provides the community with a toolset to analyze the statics and dynamics of one-dimensional quantum systems. Here, we present our open source library, Open Source Matrix Product States (OSMPS), of MPS methods implemented in Python and Fortran2003. The library includes tools for ground state calculation and excited states via the variational ansatz. We also support ground states for infinite systems with translational invariance. Dynamics are simulated with different algorithms, including three algorithms with support for long-range interactions. Convenient features include built-in support for fermionic systems and number conservation with rotational U(1) and discrete Z2 symmetries for finite systems, as well as data parallelism with MPI. We explain the principles and techniques used in this library along with examples of how to efficiently use the general interfaces to analyze the Ising and Bose-Hubbard models. This description includes the preparation of simulations as well as dispatching and post-processing of them.
ProjectQ: An Open Source Software Framework for Quantum Computing
Steiger, Damian S.; Häner, Thomas; Troyer, Matthias
2016-01-01
We introduce ProjectQ, an open source software effort for quantum computing. The first release features a compiler framework capable of targeting various types of hardware, a high-performance simulator with emulation capabilities, and compiler plug-ins for circuit drawing and resource estimation. We introduce our Python-embedded domain-specific language, present the features, and provide example implementations for quantum algorithms. The framework allows testing of quantum algorithms through...
ProjectQ: an open source software framework for quantum computing
Directory of Open Access Journals (Sweden)
Damian S. Steiger
2018-01-01
Full Text Available We introduce ProjectQ, an open source software effort for quantum computing. The first release features a compiler framework capable of targeting various types of hardware, a high-performance simulator with emulation capabilities, and compiler plug-ins for circuit drawing and resource estimation. We introduce our Python-embedded domain-specific language, present the features, and provide example implementations for quantum algorithms. The framework allows testing of quantum algorithms through simulation and enables running them on actual quantum hardware using a back-end connecting to the IBM Quantum Experience cloud service. Through extension mechanisms, users can provide back-ends to further quantum hardware, and scientists working on quantum compilation can provide plug-ins for additional compilation, optimization, gate synthesis, and layout strategies.
Advances in quantum mechanics contemporary trends and open problems
Dell'Antonio, Gianfausto
2017-01-01
This volume collects recent contributions on the contemporary trends in the mathematics of quantum mechanics, and more specifically in mathematical problems arising in quantum many-body dynamics, quantum graph theory, cold atoms, unitary gases, with particular emphasis on the developments of the specific mathematical tools needed, including: linear and non-linear Schrödinger equations, topological invariants, non-commutative geometry, resonances and operator extension theory, among others. Most of contributors are international leading experts or respected young researchers in mathematical physics, PDE, and operator theory. All their material is the fruit of recent studies that have already become a reference in the community. Offering a unified perspective of the mathematics of quantum mechanics, it is a valuable resource for researchers in the field.
OpenFlow Extensions for Programmable Quantum Networks
2017-06-19
Introduction 1 2. Background 1 2.1 Quantum Networks 2 2.2 Software -Defined Networks 3 3. Approach 3 3.1 Metadata 4 3.2 Switch 4 3.3 Controller 5... software -defined networks . Stanford (CA): Stanford University HotNets; 2010. 9. Raychev N. Algorithm for switching 4-bit packages in full quantum...applications to communicate. Advances in network protocols and architectures have led to the development of software -defined programmable networks
Quantum trajectory approach to the geometric phase: open bipartite systems
International Nuclear Information System (INIS)
Yi, X X; Liu, D P; Wang, W
2005-01-01
Through the quantum trajectory approach, we calculate the geometric phase acquired by a bipartite system subjected to decoherence. The subsystems that compose the bipartite system interact with each other and then are entangled in the evolution. The geometric phase due to the quantum jump for both the bipartite system and its subsystems is calculated and analysed. As an example, we present two coupled spin-1/2 particles to detail the calculations
Quantum metrology in open systems: dissipative Cramér-Rao bound.
Alipour, S; Mehboudi, M; Rezakhani, A T
2014-03-28
Estimation of parameters is a pivotal task throughout science and technology. The quantum Cramér-Rao bound provides a fundamental limit of precision allowed to be achieved under quantum theory. For closed quantum systems, it has been shown how the estimation precision depends on the underlying dynamics. Here, we propose a general formulation for metrology scenarios in open quantum systems, aiming to relate the precision more directly to properties of the underlying dynamics. This feature may be employed to enhance an estimation precision, e.g., by quantum control techniques. Specifically, we derive a Cramér-Rao bound for a fairly large class of open system dynamics, which is governed by a (time-dependent) dynamical semigroup map. We illustrate the utility of this scenario through three examples.
Resonator reset in circuit QED by optimal control for large open quantum systems
Boutin, Samuel; Andersen, Christian Kraglund; Venkatraman, Jayameenakshi; Ferris, Andrew J.; Blais, Alexandre
2017-10-01
We study an implementation of the open GRAPE (gradient ascent pulse engineering) algorithm well suited for large open quantum systems. While typical implementations of optimal control algorithms for open quantum systems rely on explicit matrix exponential calculations, our implementation avoids these operations, leading to a polynomial speedup of the open GRAPE algorithm in cases of interest. This speedup, as well as the reduced memory requirements of our implementation, are illustrated by comparison to a standard implementation of open GRAPE. As a practical example, we apply this open-system optimization method to active reset of a readout resonator in circuit QED. In this problem, the shape of a microwave pulse is optimized such as to empty the cavity from measurement photons as fast as possible. Using our open GRAPE implementation, we obtain pulse shapes, leading to a reset time over 4 times faster than passive reset.
Inhomogeneous electrochemiluminescence. II Markovian encounter theory of the phenomenon
International Nuclear Information System (INIS)
Gladkikh, V.; Burshtein, A.I.
2005-01-01
The free energy dependence of the electro-chemiluminescence quantum yield is specified, with the Markovian encounter theory accounting for the reversibility of triplet production competing with the irreversible recombination to the ground state. It is shown that diffusional ion recombination is highly inhomogeneous in space. It proceeds at either large positive ionization free energy (mainly to the triplet product) or at large negative free energy when recombination to the ground state dominates. On the contrary at medium free energies, the quasi-resonant generation of triplets is under kinetic control and therefore much more homogeneous. In this case, both recombination products are generated in comparable amounts. The multiple reversible ionization is shown to act as an independent quenching mechanism previously unknown. The role of the triplet quenching at the electrode is also specified. These effects reduce noticeably the luminescence quantum yield but only at larger triplet life times and in different free energy regions
Researching on Hawking Effect in a Kerr Space Time via Open Quantum System Approach
International Nuclear Information System (INIS)
Liu, Wen-Biao; Liu, Xian-Ming
2014-01-01
It has been proposed that Hawking radiation from a Schwarzschild or a de Sitter spacetime can be understood as the manifestation of thermalization phenomena in the framework of an open quantum system. Through examining the time evolution of a detector interacting with vacuum massless scalar fields, it is found that the detector would spontaneously excite with a probability the same as the thermal radiation at Hawking temperature. Following the proposals, the Hawking effect in a Kerr space time is investigated in the framework of an open quantum systems. It is shown that Hawking effect of the Kerr space time can also be understood as the the manifestation of thermalization phenomena via open quantum system approach. Furthermore, it is found that near horizon local conformal symmetry plays the key role in the quantum effect of the Kerr space time
Dynamics and thermodynamics of linear quantum open systems.
Martinez, Esteban A; Paz, Juan Pablo
2013-03-29
We analyze the evolution of the quantum state of networks of quantum oscillators coupled with arbitrary external environments. We show that the reduced density matrix of the network always obeys a local master equation with a simple analytical solution. We use this to study the emergence of thermodynamical laws in the long time regime demonstrating two main results: First, we show that it is impossible to build a quantum absorption refrigerator using linear networks (thus, nonlinearity is an essential resource for such refrigerators recently studied by Levy and Kosloff [Phys. Rev. Lett. 108, 070604 (2012)] and Levy et al. [Phys. Rev. B 85, 061126 (2012)]). Then, we show that the third law imposes constraints on the low frequency behavior of the environmental spectral densities.
Sugisaki, Kenji; Yamamoto, Satoru; Nakazawa, Shigeaki; Toyota, Kazuo; Sato, Kazunobu; Shiomi, Daisuke; Takui, Takeji
2016-08-18
Quantum computers are capable to efficiently perform full configuration interaction (FCI) calculations of atoms and molecules by using the quantum phase estimation (QPE) algorithm. Because the success probability of the QPE depends on the overlap between approximate and exact wave functions, efficient methods to prepare accurate initial guess wave functions enough to have sufficiently large overlap with the exact ones are highly desired. Here, we propose a quantum algorithm to construct the wave function consisting of one configuration state function, which is suitable for the initial guess wave function in QPE-based FCI calculations of open-shell molecules, based on the addition theorem of angular momentum. The proposed quantum algorithm enables us to prepare the wave function consisting of an exponential number of Slater determinants only by a polynomial number of quantum operations.
Mean field dynamics of some open quantum systems.
Merkli, Marco; Rafiyi, Alireza
2018-04-01
We consider a large number N of quantum particles coupled via a mean field interaction to another quantum system (reservoir). Our main result is an expansion for the averages of observables, both of the particles and of the reservoir, in inverse powers of [Formula: see text]. The analysis is based directly on the Dyson series expansion of the propagator. We analyse the dynamics, in the limit [Formula: see text], of observables of a fixed number n of particles, of extensive particle observables and their fluctuations, as well as of reservoir observables. We illustrate our results on the infinite mode Dicke model and on various energy-conserving models.
Mean field dynamics of some open quantum systems
Merkli, Marco; Rafiyi, Alireza
2018-04-01
We consider a large number N of quantum particles coupled via a mean field interaction to another quantum system (reservoir). Our main result is an expansion for the averages of observables, both of the particles and of the reservoir, in inverse powers of √{N }. The analysis is based directly on the Dyson series expansion of the propagator. We analyse the dynamics, in the limit N →∞ , of observables of a fixed number n of particles, of extensive particle observables and their fluctuations, as well as of reservoir observables. We illustrate our results on the infinite mode Dicke model and on various energy-conserving models.
Entropy of open quantum systems and the Poisson distribution
International Nuclear Information System (INIS)
Bashkirov, A.G.; Sukhanov, A.D.
2000-01-01
The entropy of the harmonic oscillator and the Klein-Gordan-Fock quantum field with a static source, located in a coherent state, is considered. The expressions for the entropy in both cases coincide with the accuracy up to the numerical multiplier with the entropy for a black hole. Such a coincidence along with the known property of the gravitational field to provide for a decoherence of the quantum system, placed therein, makes it possible to suppose that the vacuum in the black hole vicinity is in a coherent state [ru
PsiQuaSP-A library for efficient computation of symmetric open quantum systems.
Gegg, Michael; Richter, Marten
2017-11-24
In a recent publication we showed that permutation symmetry reduces the numerical complexity of Lindblad quantum master equations for identical multi-level systems from exponential to polynomial scaling. This is important for open system dynamics including realistic system bath interactions and dephasing in, for instance, the Dicke model, multi-Λ system setups etc. Here we present an object-oriented C++ library that allows to setup and solve arbitrary quantum optical Lindblad master equations, especially those that are permutationally symmetric in the multi-level systems. PsiQuaSP (Permutation symmetry for identical Quantum Systems Package) uses the PETSc package for sparse linear algebra methods and differential equations as basis. The aim of PsiQuaSP is to provide flexible, storage efficient and scalable code while being as user friendly as possible. It is easily applied to many quantum optical or quantum information systems with more than one multi-level system. We first review the basics of the permutation symmetry for multi-level systems in quantum master equations. The application of PsiQuaSP to quantum dynamical problems is illustrated with several typical, simple examples of open quantum optical systems.
Open quantum system model of the one-dimensional Burgers equation with tunable shear viscosity
International Nuclear Information System (INIS)
Yepez, Jeffrey
2006-01-01
Presented is an analysis of an open quantum model of the time-dependent evolution of a flow field governed by the nonlinear Burgers equation in one spatial dimension. The quantum model is a system of qubits where there exists a minimum time interval in the time-dependent dynamics. Each temporally discrete unitary quantum-mechanical evolution is followed by state reduction of the quantum state. The mesoscopic behavior of this quantum model is described by a quantum Boltzmann equation with a naturally emergent entropy function and H theorem and the model obeys the detailed balance principle. The macroscopic-scale effective field theory for the quantum model is derived using a perturbative Chapman-Enskog expansion applied to the linearized quantum Boltzmann equation. The entropy function is consistent with the quantum-mechanical collision process and a Fermi-Dirac single-particle distribution function for the occupation probabilities of the qubit's energy eigenstates. Comparisons are presented between analytical predictions and numerical predictions and the agreement is excellent, indicating that the nonlinear Burgers equation with a tunable shear viscosity is the operative macroscopic scale effective field theory
Imaging electron wave functions inside open quantum rings.
Martins, F; Hackens, B; Pala, M G; Ouisse, T; Sellier, H; Wallart, X; Bollaert, S; Cappy, A; Chevrier, J; Bayot, V; Huant, S
2007-09-28
Combining scanning gate microscopy (SGM) experiments and simulations, we demonstrate low temperature imaging of the electron probability density |Psi|(2)(x,y) in embedded mesoscopic quantum rings. The tip-induced conductance modulations share the same temperature dependence as the Aharonov-Bohm effect, indicating that they originate from electron wave function interferences. Simulations of both |Psi|(2)(x,y) and SGM conductance maps reproduce the main experimental observations and link fringes in SGM images to |Psi|(2)(x,y).
Optimized auxiliary representation of non-Markovian impurity problems by a Lindblad equation
International Nuclear Information System (INIS)
Dorda, A; Sorantin, M; Linden, W von der; Arrigoni, E
2017-01-01
We present a general scheme to address correlated nonequilibrium quantum impurity problems based on a mapping onto an auxiliary open quantum system of small size. The infinite fermionic reservoirs of the original system are thereby replaced by a small number N B of noninteracting auxiliary bath sites whose dynamics are described by a Lindblad equation, which can then be exactly solved by numerical methods such as Lanczos or matrix-product states. The mapping becomes exponentially exact with increasing N B , and is already quite accurate for small N B . Due to the presence of the intermediate bath sites, the overall dynamics acting on the impurity site is non-Markovian. While in previous work we put the focus on the manybody solution of the associated Lindblad problem, here we discuss the mapping scheme itself, which is an essential part of the overall approach. On the one hand, we provide technical details together with an in-depth discussion of the employed algorithms, and on the other hand, we present a detailed convergence study. The latter clearly demonstrates the above-mentioned exponential convergence of the procedure with increasing N B . Furthermore, the influence of temperature and an external bias voltage on the reservoirs is investigated. The knowledge of the particular convergence behavior is of great value to assess the applicability of the scheme to certain physical situations. Moreover, we study different geometries for the auxiliary system. On the one hand, this is of importance for advanced manybody solution techniques such as matrix product states which work well for short-ranged couplings, and on the other hand, it allows us to gain more insights into the underlying mechanisms when mapping non-Markovian reservoirs onto Lindblad-type impurity problems. Finally, we present results for the spectral function of the Anderson impurity model in and out of equilibrium and discuss the accuracy obtained with the different geometries of the auxiliary system
Al-Khalili, Jim
2003-01-01
In this lively look at quantum science, a physicist takes you on an entertaining and enlightening journey through the basics of subatomic physics. Along the way, he examines the paradox of quantum mechanics--beautifully mathematical in theory but confoundingly unpredictable in the real world. Marvel at the Dual Slit experiment as a tiny atom passes through two separate openings at the same time. Ponder the peculiar communication of quantum particles, which can remain in touch no matter how far apart. Join the genius jewel thief as he carries out a quantum measurement on a diamond without ever touching the object in question. Baffle yourself with the bizzareness of quantum tunneling, the equivalent of traveling partway up a hill, only to disappear then reappear traveling down the opposite side. With its clean, colorful layout and conversational tone, this text will hook you into the conundrum that is quantum mechanics.
Effect of two-qutrit entanglement on quantum speed limit time of a bipartite V-type open system
Energy Technology Data Exchange (ETDEWEB)
Behzadi, N., E-mail: n.behzadi@tabrizu.ac.ir [Research Institute for Fundamental Sciences, University of Tabriz (Iran, Islamic Republic of); Ahansaz, B.; Ektesabi, A.; Faizi, E. [Physics Department, Azarbaijan Shahid Madani University, Tabriz (Iran, Islamic Republic of)
2017-03-15
In the present paper, quantum speed limit (QSL) time of a bipartite V-type three-level atomic system under the effect of two-qutrit entanglement is investigated. Each party interacts with own independent reservoir. By considering two local unitarily equivalent Werner states and the Horodecki PPT state, as initial states, the QSL time is evaluated for each of them in the respective entangled regions. It is counterintuitively observed that the effect of entanglement on the QSL time driven from each of the initial Werner states are completely different when the degree of non-Markovianity is considerable. In addition, it is interesting that the effect of entanglement of the non-equivalent Horodecki state on the calculated QSL time displays an intermediate behavior relative to the cases obtained for the Werner states.
Nonlocal non-Markovian effects in dephasing environments
International Nuclear Information System (INIS)
Xie Dong; Wang An-Min
2014-01-01
We study the nonlocal non-Markovian effects through local interactions between two subsystems and the corresponding two environments. It has been found that the initial correlations between two environments can turn a Markovian to a non-Markovian regime with extra control on the local interaction time. We further research the nonlocal non-Markovian effects from two situations: without extra control, the nonlocal non-Markovian effects only appear under the condition that two local dynamics are non-Markovian–non-Markovian (both of the two local dynamics are non-Markovian) or Markovian–non-Markovian, but not under the condition of Markovian–Markovian; with extra control, the nonlocal non-Markovian effects can occur under the condition of Markovian–Markovian. It shows that the function of correlations between two environments has an upper bound, which makes a flow of information from the environment back to the global system beginning finitely earlier than that back to one of the two local systems, not infinitely. Then, we proposed two special ways to distribute classical correlations between two environments without initial correlations. Finally, from numerical solutions in the spin star configuration, we found that the self-correlation (internal correlation) of each environment promotes the nonlocal non-Markovian effects. (general)
Tomograms for open quantum systems: In(finite) dimensional optical and spin systems
International Nuclear Information System (INIS)
Thapliyal, Kishore; Banerjee, Subhashish; Pathak, Anirban
2016-01-01
Tomograms are obtained as probability distributions and are used to reconstruct a quantum state from experimentally measured values. We study the evolution of tomograms for different quantum systems, both finite and infinite dimensional. In realistic experimental conditions, quantum states are exposed to the ambient environment and hence subject to effects like decoherence and dissipation, which are dealt with here, consistently, using the formalism of open quantum systems. This is extremely relevant from the perspective of experimental implementation and issues related to state reconstruction in quantum computation and communication. These considerations are also expected to affect the quasiprobability distribution obtained from experimentally generated tomograms and nonclassicality observed from them. -- Highlights: •Tomograms are constructed for open quantum systems. •Finite and infinite dimensional quantum systems are studied. •Finite dimensional systems (phase states, single & two qubit spin states) are studied. •A dissipative harmonic oscillator is considered as an infinite dimensional system. •Both pure dephasing as well as dissipation effects are studied.
Tomograms for open quantum systems: In(finite) dimensional optical and spin systems
Energy Technology Data Exchange (ETDEWEB)
Thapliyal, Kishore, E-mail: tkishore36@yahoo.com [Jaypee Institute of Information Technology, A-10, Sector-62, Noida, UP-201307 (India); Banerjee, Subhashish, E-mail: subhashish@iitj.ac.in [Indian Institute of Technology Jodhpur, Jodhpur 342011 (India); Pathak, Anirban, E-mail: anirban.pathak@gmail.com [Jaypee Institute of Information Technology, A-10, Sector-62, Noida, UP-201307 (India)
2016-03-15
Tomograms are obtained as probability distributions and are used to reconstruct a quantum state from experimentally measured values. We study the evolution of tomograms for different quantum systems, both finite and infinite dimensional. In realistic experimental conditions, quantum states are exposed to the ambient environment and hence subject to effects like decoherence and dissipation, which are dealt with here, consistently, using the formalism of open quantum systems. This is extremely relevant from the perspective of experimental implementation and issues related to state reconstruction in quantum computation and communication. These considerations are also expected to affect the quasiprobability distribution obtained from experimentally generated tomograms and nonclassicality observed from them. -- Highlights: •Tomograms are constructed for open quantum systems. •Finite and infinite dimensional quantum systems are studied. •Finite dimensional systems (phase states, single & two qubit spin states) are studied. •A dissipative harmonic oscillator is considered as an infinite dimensional system. •Both pure dephasing as well as dissipation effects are studied.
QuTiP: An open-source Python framework for the dynamics of open quantum systems
Johansson, J. R.; Nation, P. D.; Nori, Franco
2012-08-01
We present an object-oriented open-source framework for solving the dynamics of open quantum systems written in Python. Arbitrary Hamiltonians, including time-dependent systems, may be built up from operators and states defined by a quantum object class, and then passed on to a choice of master equation or Monte Carlo solvers. We give an overview of the basic structure for the framework before detailing the numerical simulation of open system dynamics. Several examples are given to illustrate the build up to a complete calculation. Finally, we measure the performance of our library against that of current implementations. The framework described here is particularly well suited to the fields of quantum optics, superconducting circuit devices, nanomechanics, and trapped ions, while also being ideal for use in classroom instruction. Catalogue identifier: AEMB_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEMB_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GNU General Public License, version 3 No. of lines in distributed program, including test data, etc.: 16 482 No. of bytes in distributed program, including test data, etc.: 213 438 Distribution format: tar.gz Programming language: Python Computer: i386, x86-64 Operating system: Linux, Mac OSX, Windows RAM: 2+ Gigabytes Classification: 7 External routines: NumPy (http://numpy.scipy.org/), SciPy (http://www.scipy.org/), Matplotlib (http://matplotlib.sourceforge.net/) Nature of problem: Dynamics of open quantum systems. Solution method: Numerical solutions to Lindblad master equation or Monte Carlo wave function method. Restrictions: Problems must meet the criteria for using the master equation in Lindblad form. Running time: A few seconds up to several tens of minutes, depending on size of underlying Hilbert space.
International Nuclear Information System (INIS)
Bhan, Jaemi; Kwon, Younghun
2007-01-01
Recently Yeo showed that thermal states in Heisenberg XX model with periodic boundary condition could be used for three-party quantum teleportation. However it is hard to implement the periodic boundary condition in spin chain. So instead of imposing the periodic boundary condition, we consider open boundary condition in Heisenberg XX model and investigate the possibility of using thermal states in Heisenberg XX model with open boundary condition. Using this way, we find the best fidelity conditions to three known protocols in three-party quantum teleportation. It turns out that the best fidelity in every protocol would be 23
Fused integrable lattice models with quantum impurities and open boundaries
International Nuclear Information System (INIS)
Doikou, Anastasia
2003-01-01
The alternating integrable spin chain and the RSOS(q 1 ,q 2 ;p) model in the presence of a quantum impurity are investigated. The boundary free energy due to the impurity is derived, the ratios of the corresponding g functions at low and high temperature are specified and their relevance to boundary flows in unitary minimal and generalized coset models is discussed. Finally, the alternating spin chain with diagonal and non-diagonal integrable boundaries is studied, and the corresponding boundary free energy and g functions are derived
Bulk-mediated surface diffusion: non-Markovian desorption dynamics
International Nuclear Information System (INIS)
Revelli, Jorge A; Budde, Carlos E; Prato, Domingo; Wio, Horacio S
2005-01-01
Here we analyse the dynamics of adsorbed molecules within the bulk-mediated surface diffusion framework, when the particle's desorption mechanism is characterized by a non-Markovian process, while the particle's adsorption as well as its motion in the bulk is governed by Markovian dynamics. We study the diffusion of particles in both semi-infinite and finite cubic lattices, analysing the conditional probability to find the system on the reference absorptive plane as well as the surface dispersion as functions of time. The results are compared with known Markovian cases showing the differences that can be exploited to distinguish between Markovian and non-Markovian desorption mechanisms in experimental situations
Hard decoding algorithm for optimizing thresholds under general Markovian noise
Chamberland, Christopher; Wallman, Joel; Beale, Stefanie; Laflamme, Raymond
2017-04-01
Quantum error correction is instrumental in protecting quantum systems from noise in quantum computing and communication settings. Pauli channels can be efficiently simulated and threshold values for Pauli error rates under a variety of error-correcting codes have been obtained. However, realistic quantum systems can undergo noise processes that differ significantly from Pauli noise. In this paper, we present an efficient hard decoding algorithm for optimizing thresholds and lowering failure rates of an error-correcting code under general completely positive and trace-preserving (i.e., Markovian) noise. We use our hard decoding algorithm to study the performance of several error-correcting codes under various non-Pauli noise models by computing threshold values and failure rates for these codes. We compare the performance of our hard decoding algorithm to decoders optimized for depolarizing noise and show improvements in thresholds and reductions in failure rates by several orders of magnitude. Our hard decoding algorithm can also be adapted to take advantage of a code's non-Pauli transversal gates to further suppress noise. For example, we show that using the transversal gates of the 5-qubit code allows arbitrary rotations around certain axes to be perfectly corrected. Furthermore, we show that Pauli twirling can increase or decrease the threshold depending upon the code properties. Lastly, we show that even if the physical noise model differs slightly from the hypothesized noise model used to determine an optimized decoder, failure rates can still be reduced by applying our hard decoding algorithm.
Role of short periodic orbits in quantum maps with continuous openings
Prado, Carlos A.; Carlo, Gabriel G.; Benito, R. M.; Borondo, F.
2018-04-01
We apply a recently developed semiclassical theory of short periodic orbits to the continuously open quantum tribaker map. In this paradigmatic system the trajectories are partially bounced back according to continuous reflectivity functions. This is relevant in many situations that include optical microresonators and more complicated boundary conditions. In a perturbative regime, the shortest periodic orbits belonging to the classical repeller of the open map—a cantor set given by a region of exactly zero reflectivity—prove to be extremely robust in supporting a set of long-lived resonances of the continuously open quantum maps. Moreover, for steplike functions a significant reduction in the number needed is obtained, similarly to the completely open situation. This happens despite a strong change in the spectral properties when compared to the discontinuous reflectivity case. In order to give a more realistic interpretation of these results we compare with a Fresnel-type reflectivity function.
Time-dependent generalized Gibbs ensembles in open quantum systems
Lange, Florian; Lenarčič, Zala; Rosch, Achim
2018-04-01
Generalized Gibbs ensembles have been used as powerful tools to describe the steady state of integrable many-particle quantum systems after a sudden change of the Hamiltonian. Here, we demonstrate numerically that they can be used for a much broader class of problems. We consider integrable systems in the presence of weak perturbations which break both integrability and drive the system to a state far from equilibrium. Under these conditions, we show that the steady state and the time evolution on long timescales can be accurately described by a (truncated) generalized Gibbs ensemble with time-dependent Lagrange parameters, determined from simple rate equations. We compare the numerically exact time evolutions of density matrices for small systems with a theory based on block-diagonal density matrices (diagonal ensemble) and a time-dependent generalized Gibbs ensemble containing only a small number of approximately conserved quantities, using the one-dimensional Heisenberg model with perturbations described by Lindblad operators as an example.
Slow Dynamics and Thermodynamics of Open Quantum Systems.
Cavina, Vasco; Mari, Andrea; Giovannetti, Vittorio
2017-08-04
We develop a perturbation theory of quantum (and classical) master equations with slowly varying parameters, applicable to systems which are externally controlled on a time scale much longer than their characteristic relaxation time. We apply this technique to the analysis of finite-time isothermal processes in which, differently from quasistatic transformations, the state of the system is not able to continuously relax to the equilibrium ensemble. Our approach allows one to formally evaluate perturbations up to arbitrary order to the work and heat exchange associated with an arbitrary process. Within first order in the perturbation expansion, we identify a general formula for the efficiency at maximum power of a finite-time Carnot engine. We also clarify under which assumptions and in which limit one can recover previous phenomenological results as, for example, the Curzon-Ahlborn efficiency.
Linked cluster expansions for open quantum systems on a lattice
Biella, Alberto; Jin, Jiasen; Viyuela, Oscar; Ciuti, Cristiano; Fazio, Rosario; Rossini, Davide
2018-01-01
We propose a generalization of the linked-cluster expansions to study driven-dissipative quantum lattice models, directly accessing the thermodynamic limit of the system. Our method leads to the evaluation of the desired extensive property onto small connected clusters of a given size and topology. We first test this approach on the isotropic spin-1/2 Hamiltonian in two dimensions, where each spin is coupled to an independent environment that induces incoherent spin flips. Then we apply it to the study of an anisotropic model displaying a dissipative phase transition from a magnetically ordered to a disordered phase. By means of a Padé analysis on the series expansions for the average magnetization, we provide a viable route to locate the phase transition and to extrapolate the critical exponent for the magnetic susceptibility.
Linear-algebraic bath transformation for simulating complex open quantum systems
International Nuclear Information System (INIS)
Huh, Joonsuk; Mostame, Sarah; Fujita, Takatoshi; Aspuru-Guzik, Alán; Yung, Man-Hong
2014-01-01
In studying open quantum systems, the environment is often approximated as a collection of non-interacting harmonic oscillators, a configuration also known as the star-bath model. It is also well known that the star-bath can be transformed into a nearest-neighbor interacting chain of oscillators. The chain-bath model has been widely used in renormalization group approaches. The transformation can be obtained by recursion relations or orthogonal polynomials. Based on a simple linear algebraic approach, we propose a bath partition strategy to reduce the system-bath coupling strength. As a result, the non-interacting star-bath is transformed into a set of weakly coupled multiple parallel chains. The transformed bath model allows complex problems to be practically implemented on quantum simulators, and it can also be employed in various numerical simulations of open quantum dynamics. (paper)
Dissipative tunneling through a potential barrier in the Lindblad theory of open quantum systems
International Nuclear Information System (INIS)
Isar, A.
2000-01-01
In the Lindblad theory for open quantum systems, and analytical expression of the tunneling probability through an inverted parabola is obtained. This probability depends on the environment coefficient and increase with the dissipation and the temperature of the thermal bath. (author)
Boundary conditions for open quantum systems driven far from equilibrium
Frensley, William R.
1990-07-01
This is a study of simple kinetic models of open systems, in the sense of systems that can exchange conserved particles with their environment. The system is assumed to be one dimensional and situated between two particle reservoirs. Such a system is readily driven far from equilibrium if the chemical potentials of the reservoirs differ appreciably. The openness of the system modifies the spatial boundary conditions on the single-particle Liouville-von Neumann equation, leading to a non-Hermitian Liouville operator. If the open-system boundary conditions are time reversible, exponentially growing (unphysical) solutions are introduced into the time dependence of the density matrix. This problem is avoided by applying time-irreversible boundary conditions to the Wigner distribution function. These boundary conditions model the external environment as ideal particle reservoirs with properties analogous to those of a blackbody. This time-irreversible model may be numerically evaluated in a discrete approximation and has been applied to the study of a resonant-tunneling semiconductor diode. The physical and mathematical properties of the irreversible kinetic model, in both its discrete and its continuum formulations, are examined in detail. The model demonstrates the distinction in kinetic theory between commutator superoperators, which may become non-Hermitian to describe irreversible behavior, and anticommutator superoperators, which remain Hermitian and are used to evaluate physical observables.
Transport efficiency in open quantum systems with static and dynamical disorder
Zhang, Yang; Celardo, G. Luca; Borgonovi, Fausto; Kaplan, Lev
2017-12-01
We study, under very general conditions and in a variety of geometries, quantum enhancement of transport in open systems. Both static disorder and dephasing associated with dynamical disorder (or finite temperature) are fully included in the analysis. We show that quantum coherence effects may significantly enhance transport in open quantum systems even in the semiclassical regime (where the decoherence rate is greater than the inter-site hopping amplitude), as long as the static disorder is sufficiently strong. When the strengths of static and dynamical disorder are fixed, there is an optimal opening strength at which the coherent transport enhancement is optimized. Analytic results are obtained in two simple paradigmatic tight-binding models of large systems: the linear chain and the fully connected network. The physical behavior is also reflected, for example, in the FMO photosynthetic complex, which may be viewed as being intermediate between these paradigmatic models. We furthermore show that a nonzero dephasing rate assists transport in an open linear chain when the disorder strength exceeds a critical value, and obtain this critical disorder strength as a function of the degree of opening.
General response formula and application to topological insulator in quantum open system.
Shen, H Z; Qin, M; Shao, X Q; Yi, X X
2015-11-01
It is well-known that the quantum linear response theory is based on the first-order perturbation theory for a system in thermal equilibrium. Hence, this theory breaks down when the system is in a steady state far from thermal equilibrium and the response up to higher order in perturbation is not negligible. In this paper, we develop a nonlinear response theory for such quantum open system. We first formulate this theory in terms of general susceptibility, after which we apply it to the derivation of Hall conductance for open system at finite temperature. As an example, the Hall conductance of the two-band model is derived. Then we calculate the Hall conductance for a two-dimensional ferromagnetic electron gas and a two-dimensional lattice model. The calculations show that the transition points of topological phase are robust against the environment. Our results provide a promising platform for the coherent manipulation of the nonlinear response in quantum open system, which has potential applications for quantum information processing and statistical physics.
Open-Source Development Experiences in Scientific Software: The HANDE Quantum Monte Carlo Project
Directory of Open Access Journals (Sweden)
J. S. Spencer
2015-11-01
Full Text Available The HANDE quantum Monte Carlo project offers accessible stochastic algorithms for general use for scientists in the field of quantum chemistry. HANDE is an ambitious and general high-performance code developed by a geographically-dispersed team with a variety of backgrounds in computational science. In the course of preparing a public, open-source release, we have taken this opportunity to step back and look at what we have done and what we hope to do in the future. We pay particular attention to development processes, the approach taken to train students joining the project, and how a flat hierarchical structure aids communication.
2016-02-15
series of sunny days interrupted only rarely by rain–a pattern now all too familiar to residents. Analogously, a one- dimensional spin system in a...computation of Cq(L) that is independent of the diverging embedding dimension . Another source of difficulty is the exponentially increasing number of words...alternatives. For example, more general quantum hidden Markov models (QHMMs) may yield a greater advantage3. Proving minimality among QHMMs is of great
Hsiang, J-T; Chou, C H; Subaşı, Y; Hu, B L
2018-01-01
In a series of papers, we intend to take the perspective of open quantum systems and examine from their nonequilibrium dynamics the conditions when the physical quantities, their relations, and the laws of thermodynamics become well defined and viable for quantum many-body systems. We first describe how an open-system nonequilibrium dynamics (ONEq) approach is different from the closed combined system + environment in a global thermal state (CGTs) setup. Only after the open system equilibrates will it be amenable to conventional thermodynamics descriptions, thus quantum thermodynamics (QTD) comes at the end rather than assumed in the beginning. The linkage between the two comes from the reduced density matrix of ONEq in that stage having the same form as that of the system in the CGTs. We see the open-system approach having the advantage of dealing with nonequilibrium processes as many experiments in the near future will call for. Because it spells out the conditions of QTD's existence, it can also aid us in addressing the basic issues in quantum thermodynamics from first principles in a systematic way. We then study one broad class of open quantum systems where the full nonequilibrium dynamics can be solved exactly, that of the quantum Brownian motion of N strongly coupled harmonic oscillators, interacting strongly with a scalar-field environment. In this paper, we focus on the internal energy, heat capacity, and the third law. We show for this class of physical models, amongst other findings, the extensive property of the internal energy, the positivity of the heat capacity, and the validity of the third law from the perspective of the behavior of the heat capacity toward zero temperature. These conclusions obtained from exact solutions and quantitative analysis clearly disprove claims of negative specific heat in such systems and dispel allegations that in such systems the validity of the third law of thermodynamics relies on quantum entanglement. They are
Non-Markovian effect on the geometric phase of a dissipative qubit
International Nuclear Information System (INIS)
Chen Juanjuan; Tong Qingjun; An Junhong; Luo Honggang; Oh, C. H.
2010-01-01
We studied the geometric phase of a two-level atom coupled to an environment with Lorentzian spectral density. The non-Markovian effect on the geometric phase is explored analytically and numerically. In the weak coupling limit, the lowest order correction to the geometric phase is derived analytically and the general case is calculated numerically. It was found that the correction to the geometric phase is significantly large if the spectral width is small, and in this case the non-Markovian dynamics has a significant impact on the geometric phase. When the spectral width increases, the correction to the geometric phase becomes negligible, which shows the robustness of the geometric phase to the environmental white noises. The result is significant to the quantum information processing based on the geometric phase.
Fully Quantum Fluctuation Theorems
Åberg, Johan
2018-02-01
Systems that are driven out of thermal equilibrium typically dissipate random quantities of energy on microscopic scales. Crooks fluctuation theorem relates the distribution of these random work costs to the corresponding distribution for the reverse process. By an analysis that explicitly incorporates the energy reservoir that donates the energy and the control system that implements the dynamic, we obtain a quantum generalization of Crooks theorem that not only includes the energy changes in the reservoir but also the full description of its evolution, including coherences. Moreover, this approach opens up the possibility for generalizations of the concept of fluctuation relations. Here, we introduce "conditional" fluctuation relations that are applicable to nonequilibrium systems, as well as approximate fluctuation relations that allow for the analysis of autonomous evolution generated by global time-independent Hamiltonians. We furthermore extend these notions to Markovian master equations, implicitly modeling the influence of the heat bath.
Characterization of Unruh channel in the context of open quantum systems
International Nuclear Information System (INIS)
Banerjee, Subhashish; Alok, Ashutosh Kumar; Omkar, S.; Srikanth, R.
2017-01-01
In this work, we study an important facet of field theories in curved spacetime, viz. the Unruh effect, by making use of ideas of statistical mechanics and quantum foundations. Aspects of decoherence and dissipation, natural artifacts of open quantum systems, along with foundational issues such as the trade-off between coherence and mixing as well as various aspects of quantum correlations are investigated in detail for the Unruh effect. We show how the Unruh effect can be quantified mathematically by the Choi matrix approach. We study how environmentally induced decoherence modifies the effect of the Unruh channel. The differing effects of a dissipative or non-dissipative environment are noted. Further, useful parameters characterizing channel performance such as gate and channel fidelity are applied here to the Unruh channel, both with and without external influences. Squeezing, which is known to play an important role in the context of particle creation, is shown to be a useful resource in a number of scenarios.
Ujevic, Sebastian; Mendoza, Michel
2010-07-01
We propose numerical simulations of longitudinal magnetoconductance through a finite antidot lattice located inside an open quantum dot with a magnetic field applied perpendicular to the plane. The system is connected to reservoirs using quantum point contacts. We discuss the relationship between the longitudinal magnetoconductance and the generation of transversal couplings between the induced open quantum dots in the system. The system presents longitudinal magnetoconductance maps with crossovers (between transversal bands) and closings (longitudinal decoupling) of fundamental quantum states related to the open quantum dots induced by the antidot lattice. A relationship is observed between the distribution of antidots and the formed conductance bands, allowing a systematic follow up of the bands as a function of the applied magnetic field and quantum point-contact width. We observed a high conductance intensity [between n and (n+1) quantum of conductance, n=1,2,… ] in the regions of crossover and closing of states. This suggests transversal couplings between the induced open quantum dots of the system that can be modulated by varying both the antidots potential and the quantum point-contact width. A new continuous channel (not expected) is induced by the variation in the contact width and generate Fano resonances in the conductance. These resonances can be manipulated by the applied magnetic field.
Open quantum system and the damping of collective modes in deep inelastic collisions
International Nuclear Information System (INIS)
Sandulescu, A.
1985-01-01
In the framework of the Lindblad theory for open quantum systems the following results are obtained: a generalization of the fundamental constraints on quantum mechanical diffusion coefficients which appear in the corresponding master equations, a generalization of pure state condition and generalized Schrodinger type nonlinear equation for an open system. Also, the Schroedinger, Heisenberfg and Weyl-Wigner-Moyal representations of the Lindblad equation are given explicitly. On the basis of these representations, it is shown that various master equations for the damped quantum oscillator used in the literature for the description of the damped collective modes are particular cases of the Lindblad equation and that the majority of these equations are not satisfying the constraints on quantum mechanical diffusion coefficients. The solutions of the differential equations for the variances are put in a new synthetic for, suggested by a direct computation of the variances from the time dependent Weyl operators. The solution of the Lindblad equation in the Weyl-Wigner-Moyal representation is of Gaussian type if the initial form of the Wigner function is taken to be a Gaussian corresponding to a coherent wave furction
Quantum continual measurements and a posteriori collapse on CCR
International Nuclear Information System (INIS)
Belavkin, V.P.
1992-01-01
A quantum stochastic model for the Markovian dynamics of an open system under the nondemolition unsharp observation which is continuous in time, is given. A stochastic equation for the posterior evolution of a quantum continuously observed system is derived and the spontaneous collapse (stochastically continuous reduction of the wave packet) is described. The quantum Langevin evolution equation is solved for the case of a quasi-free Hamiltonian in the initial CCR algebra with a linear output channel, and the posterior dynamics corresponding to an initial Gaussian state is found. It is shown for an example of the posterior dynamics of a quantum oscillator that any mixed state under a complete nondemolition measurement collapses exponentially to a pure Gaussian one. (orig.)
Non-markovian boltzmann equation
International Nuclear Information System (INIS)
Kremp, D.; Bonitz, M.; Kraeft, W.D.; Schlanges, M.
1997-01-01
A quantum kinetic equation for strongly interacting particles (generalized binary collision approximation, ladder or T-matrix approximation) is derived in the framework of the density operator technique. In contrast to conventional kinetic theory, which is valid on large time scales as compared to the collision (correlation) time only, our approach retains the full time dependencies, especially also on short time scales. This means retardation and memory effects resulting from the dynamics of binary correlations and initial correlations are included. Furthermore, the resulting kinetic equation conserves total energy (the sum of kinetic and potential energy). The second aspect of generalization is the inclusion of many-body effects, such as self-energy, i.e., renormalization of single-particle energies and damping. To this end we introduce an improved closure relation to the Bogolyubov endash Born endash Green endash Kirkwood endash Yvon hierarchy. Furthermore, in order to express the collision integrals in terms of familiar scattering quantities (Mo/ller operator, T-matrix), we generalize the methods of quantum scattering theory by the inclusion of medium effects. To illustrate the effects of memory and damping, the results of numerical simulations are presented. copyright 1997 Academic Press, Inc
Superradiance, disorder, and the non-Hermitian Hamiltonian in open quantum systems
Energy Technology Data Exchange (ETDEWEB)
Celardo, G. L.; Biella, A.; Giusteri, G. G.; Mattiotti, F. [Dipartimento di Matematica e Fisica and Interdisciplinary Laboratories for Advanced Materials Physics, Università Cattolica, via Musei 41, 25121 Brescia (Italy); Zhang, Y.; Kaplan, L. [Department of Physics and Engineering Physics, Tulane University, New Orleans, Louisiana 70118 (United States)
2014-10-15
We first briefly review the non-Hermitian effective Hamiltonian approach to open quantum systems and the associated phenomenon of superradiance. We next discuss the superradiance crossover in the presence of disorder and the relationship between superradiance and the localization transition. Finally, we investigate the regime of validity of the energy-independent effective Hamiltonian approximation and show that the results obtained by these methods are applicable to realistic physical systems.
Markovian dynamics on complex reaction networks
Energy Technology Data Exchange (ETDEWEB)
Goutsias, J., E-mail: goutsias@jhu.edu; Jenkinson, G., E-mail: jenkinson@jhu.edu
2013-08-10
Complex networks, comprised of individual elements that interact with each other through reaction channels, are ubiquitous across many scientific and engineering disciplines. Examples include biochemical, pharmacokinetic, epidemiological, ecological, social, neural, and multi-agent networks. A common approach to modeling such networks is by a master equation that governs the dynamic evolution of the joint probability mass function of the underlying population process and naturally leads to Markovian dynamics for such process. Due however to the nonlinear nature of most reactions and the large size of the underlying state-spaces, computation and analysis of the resulting stochastic population dynamics is a difficult task. This review article provides a coherent and comprehensive coverage of recently developed approaches and methods to tackle this problem. After reviewing a general framework for modeling Markovian reaction networks and giving specific examples, the authors present numerical and computational techniques capable of evaluating or approximating the solution of the master equation, discuss a recently developed approach for studying the stationary behavior of Markovian reaction networks using a potential energy landscape perspective, and provide an introduction to the emerging theory of thermodynamic analysis of such networks. Three representative problems of opinion formation, transcription regulation, and neural network dynamics are used as illustrative examples.
Markovian dynamics on complex reaction networks
International Nuclear Information System (INIS)
Goutsias, J.; Jenkinson, G.
2013-01-01
Complex networks, comprised of individual elements that interact with each other through reaction channels, are ubiquitous across many scientific and engineering disciplines. Examples include biochemical, pharmacokinetic, epidemiological, ecological, social, neural, and multi-agent networks. A common approach to modeling such networks is by a master equation that governs the dynamic evolution of the joint probability mass function of the underlying population process and naturally leads to Markovian dynamics for such process. Due however to the nonlinear nature of most reactions and the large size of the underlying state-spaces, computation and analysis of the resulting stochastic population dynamics is a difficult task. This review article provides a coherent and comprehensive coverage of recently developed approaches and methods to tackle this problem. After reviewing a general framework for modeling Markovian reaction networks and giving specific examples, the authors present numerical and computational techniques capable of evaluating or approximating the solution of the master equation, discuss a recently developed approach for studying the stationary behavior of Markovian reaction networks using a potential energy landscape perspective, and provide an introduction to the emerging theory of thermodynamic analysis of such networks. Three representative problems of opinion formation, transcription regulation, and neural network dynamics are used as illustrative examples
Quantum dynamics of quantum bits
International Nuclear Information System (INIS)
Nguyen, Bich Ha
2011-01-01
The theory of coherent oscillations of the matrix elements of the density matrix of the two-state system as a quantum bit is presented. Different calculation methods are elaborated in the case of a free quantum bit. Then the most appropriate methods are applied to the study of the density matrices of the quantum bits interacting with a classical pumping radiation field as well as with the quantum electromagnetic field in a single-mode microcavity. The theory of decoherence of a quantum bit in Markovian approximation is presented. The decoherence of a quantum bit interacting with monoenergetic photons in a microcavity is also discussed. The content of the present work can be considered as an introduction to the study of the quantum dynamics of quantum bits. (review)
Accuracy of the adiabatic-impulse approximation for closed and open quantum systems
Tomka, Michael; Campos Venuti, Lorenzo; Zanardi, Paolo
2018-03-01
We study the adiabatic-impulse approximation (AIA) as a tool to approximate the time evolution of quantum states when driven through a region of small gap. Such small-gap regions are a common situation in adiabatic quantum computing and having reliable approximations is important in this context. The AIA originates from the Kibble-Zurek theory applied to continuous quantum phase transitions. The Kibble-Zurek mechanism was developed to predict the power-law scaling of the defect density across a continuous quantum phase transition. Instead, here we quantify the accuracy of the AIA via the trace norm distance with respect to the exact evolved state. As expected, we find that for short times or fast protocols, the AIA outperforms the simple adiabatic approximation. However, for large times or slow protocols, the situation is actually reversed and the AIA provides a worse approximation. Nevertheless, we found a variation of the AIA that can perform better than the adiabatic one. This counterintuitive modification consists in crossing the region of small gap twice. Our findings are illustrated by several examples of driven closed and open quantum systems.
Time-dependent density functional theory of open quantum systems in the linear-response regime.
Tempel, David G; Watson, Mark A; Olivares-Amaya, Roberto; Aspuru-Guzik, Alán
2011-02-21
Time-dependent density functional theory (TDDFT) has recently been extended to describe many-body open quantum systems evolving under nonunitary dynamics according to a quantum master equation. In the master equation approach, electronic excitation spectra are broadened and shifted due to relaxation and dephasing of the electronic degrees of freedom by the surrounding environment. In this paper, we develop a formulation of TDDFT linear-response theory (LR-TDDFT) for many-body electronic systems evolving under a master equation, yielding broadened excitation spectra. This is done by mapping an interacting open quantum system onto a noninteracting open Kohn-Sham system yielding the correct nonequilibrium density evolution. A pseudoeigenvalue equation analogous to the Casida equations of the usual LR-TDDFT is derived for the Redfield master equation, yielding complex energies and Lamb shifts. As a simple demonstration, we calculate the spectrum of a C(2 +) atom including natural linewidths, by treating the electromagnetic field vacuum as a photon bath. The performance of an adiabatic exchange-correlation kernel is analyzed and a first-order frequency-dependent correction to the bare Kohn-Sham linewidth based on the Görling-Levy perturbation theory is calculated.
Mean first-passage times in confined media: from Markovian to non-Markovian processes
International Nuclear Information System (INIS)
Bénichou, O; Voituriez, R; Guérin, T
2015-01-01
We review recent theoretical works that enable the accurate evaluation of the mean first passage time (MFPT) of a random walker to a target in confinement for Markovian (memory-less) and non-Markovian walkers. For the Markovian problem, we present a general theory which allows one to accurately evaluate the MFPT and its extensions to related first-passage observables such as splitting probabilities and occupation times. We show that this analytical approach provides a universal scaling dependence of the MFPT on both the volume of the confining domain and the source–target distance in the case of general scale-invariant processes. This analysis is applicable to a broad range of stochastic processes characterized by length scale-invariant properties, and reveals the key role that can be played by the starting position of the random walker. We then present an extension to non-Markovian walks by taking the specific example of a tagged monomer of a polymer chain looking for a target in confinement. We show that the MFPT can be calculated accurately by computing the distribution of the positions of all the monomers in the chain at the instant of reaction. Such a theory can be used to derive asymptotic relations that generalize the scaling dependence with the volume and the initial distance to the target derived for Markovian walks. Finally, we present an application of this theory to the problem of the first contact time between the two ends of a polymer chain, and review the various theoretical approaches of this non- Markovian problem. (topical review)
Gessner, Manuel; Breuer, Heinz-Peter
2013-04-01
We obtain exact analytic expressions for a class of functions expressed as integrals over the Haar measure of the unitary group in d dimensions. Based on these general mathematical results, we investigate generic dynamical properties of complex open quantum systems, employing arguments from ensemble theory. We further generalize these results to arbitrary eigenvalue distributions, allowing a detailed comparison of typical regular and chaotic systems with the help of concepts from random matrix theory. To illustrate the physical relevance and the general applicability of our results we present a series of examples related to the fields of open quantum systems and nonequilibrium quantum thermodynamics. These include the effect of initial correlations, the average quantum dynamical maps, the generic dynamics of system-environment pure state entanglement and, finally, the equilibration of generic open and closed quantum systems.
Finite-difference time-domain simulation of thermal noise in open cavities
International Nuclear Information System (INIS)
Andreasen, Jonathan; Cao Hui; Taflove, Allen; Kumar, Prem; Cao Changqi
2008-01-01
A numerical model based on the finite-difference time-domain (FDTD) method is developed to simulate thermal noise in open cavities owing to output coupling. The absorbing boundary of the FDTD grid is treated as a blackbody, whose thermal radiation penetrates the cavity in the grid. The calculated amount of thermal noise in a one-dimensional dielectric cavity recovers the standard result of the quantum Langevin equation in the Markovian regime. Our FDTD simulation also demonstrates that in the non-Markovian regime the buildup of the intracavity noise field depends on the ratio of the cavity photon lifetime to the coherence time of thermal radiation. The advantage of our numerical method is that the thermal noise is introduced in the time domain without prior knowledge of cavity modes
International Nuclear Information System (INIS)
Hsiang, J.-T.; Hu, B.L.
2015-01-01
The existence and uniqueness of a steady state for nonequilibrium systems (NESS) is a fundamental subject and a main theme of research in statistical mechanics for decades. For Gaussian systems, such as a chain of classical harmonic oscillators connected at each end to a heat bath, and for classical anharmonic oscillators under specified conditions, definitive answers exist in the form of proven theorems. Answering this question for quantum many-body systems poses a challenge for the present. In this work we address this issue by deriving the stochastic equations for the reduced system with self-consistent backaction from the two baths, calculating the energy flow from one bath to the chain to the other bath, and exhibiting a power balance relation in the total (chain + baths) system which testifies to the existence of a NESS in this system at late times. Its insensitivity to the initial conditions of the chain corroborates to its uniqueness. The functional method we adopt here entails the use of the influence functional, the coarse-grained and stochastic effective actions, from which one can derive the stochastic equations and calculate the average values of physical variables in open quantum systems. This involves both taking the expectation values of quantum operators of the system and the distributional averages of stochastic variables stemming from the coarse-grained environment. This method though formal in appearance is compact and complete. It can also easily accommodate perturbative techniques and diagrammatic methods from field theory. Taken all together it provides a solid platform for carrying out systematic investigations into the nonequilibrium dynamics of open quantum systems and quantum thermodynamics. -- Highlights: •Nonequilibrium steady state (NESS) for interacting quantum many-body systems. •Derivation of stochastic equations for quantum oscillator chain with two heat baths. •Explicit calculation of the energy flow from one bath to the
International Nuclear Information System (INIS)
Brune, M.; Hagley, E.; Dreyer, J.; Maitre, X.; Maali, A.; Wunderlich, C.; Raimond, J.M.; Haroche, S.
1996-01-01
A mesoscopic superposition of quantum states involving radiation fields with classically distinct phases was created and its progressive decoherence observed. The experiment involved Rydberg atoms interacting one at a time with a few photon coherent fields trapped in a high Q microwave cavity. The mesoscopic superposition was the equivalent of an open-quote open-quote atom+measuringapparatus close-quote close-quote system in which the open-quote open-quote meter close-quote close-quote was pointing simultaneously towards two different directions emdash a open-quote open-quote Schroedinger cat.close-quote close-quote The decoherence phenomenon transforming this superposition into a statistical mixture was observed while it unfolded, providing a direct insight into a process at the heart of quantum measurement. copyright 1996 The American Physical Society
International Nuclear Information System (INIS)
Berman, G.P.; Borgonovi, F.; Dalvit, D.A.R.
2009-01-01
We review our results on a mathematical dynamical theory for observables for open many-body quantum nonlinear bosonic systems for a very general class of Hamiltonians. We show that non-quadratic (nonlinear) terms in a Hamiltonian provide a singular 'quantum' perturbation for observables in some 'mesoscopic' region of parameters. In particular, quantum effects result in secular terms in the dynamical evolution, that grow in time. We argue that even for open quantum nonlinear systems in the deep quasi-classical region, these quantum effects can survive after decoherence and relaxation processes take place. We demonstrate that these quantum effects in open quantum systems can be observed, for example, in the frequency Fourier spectrum of the dynamical observables, or in the corresponding spectral density of noise. Estimates are presented for Bose-Einstein condensates, low temperature mechanical resonators, and nonlinear optical systems prepared in large amplitude coherent states. In particular, we show that for Bose-Einstein condensate systems the characteristic time of deviation of quantum dynamics for observables from the corresponding classical dynamics coincides with the characteristic time-scale of the well-known quantum nonlinear effect of phase diffusion.
Efficient steady-state solver for hierarchical quantum master equations
Zhang, Hou-Dao; Qiao, Qin; Xu, Rui-Xue; Zheng, Xiao; Yan, YiJing
2017-07-01
Steady states play pivotal roles in many equilibrium and non-equilibrium open system studies. Their accurate evaluations call for exact theories with rigorous treatment of system-bath interactions. Therein, the hierarchical equations-of-motion (HEOM) formalism is a nonperturbative and non-Markovian quantum dissipation theory, which can faithfully describe the dissipative dynamics and nonlinear response of open systems. Nevertheless, solving the steady states of open quantum systems via HEOM is often a challenging task, due to the vast number of dynamical quantities involved. In this work, we propose a self-consistent iteration approach that quickly solves the HEOM steady states. We demonstrate its high efficiency with accurate and fast evaluations of low-temperature thermal equilibrium of a model Fenna-Matthews-Olson pigment-protein complex. Numerically exact evaluation of thermal equilibrium Rényi entropies and stationary emission line shapes is presented with detailed discussion.
Entanglement transfer from electrons to photons in quantum dots: an open quantum system approach
International Nuclear Information System (INIS)
Budich, Jan C; Trauzettel, Bjoern
2010-01-01
We investigate entanglement transfer from a system of two spin-entangled electron-hole pairs, each placed in a separate single mode cavity, to the photons emitted due to cavity leakage. Dipole selection rules and a splitting between the light hole and the heavy hole subbands are the crucial ingredients establishing a one-to-one correspondence between electron spins and circular photon polarizations. To account for the measurement of the photons as well as dephasing effects, we choose a stochastic Schroedinger equation and a conditional master equation approach, respectively. The influence of interactions with the environment as well as asymmetries in the coherent couplings on the photon entanglement is analysed for two concrete measurement schemes. The first one is designed to violate the Clauser-Horne-Shimony-Holt (CHSH) inequality, while the second one employs the visibility of interference fringes to prove the entanglement of the photons. Because of the spatial separation of the entangled electronic system over two quantum dots, a successful verification of entangled photons emitted by this system would imply the detection of nonlocal spin entanglement of massive particles in a solid state structure.
Chen, Peng-Fei; Sun, Wen-Yang; Ming, Fei; Huang, Ai-Jun; Wang, Dong; Ye, Liu
2018-01-01
Quantum objects are susceptible to noise from their surrounding environments, interaction with which inevitably gives rise to quantum decoherence or dissipation effects. In this work, we examine how different types of local noise under an open system affect entropic uncertainty relations for two incompatible measurements. Explicitly, we observe the dynamics of the entropic uncertainty in the presence of quantum memory under two canonical categories of noisy environments: unital (phase flip) and nonunital (amplitude damping). Our study shows that the measurement uncertainty exhibits a non-monotonic dynamical behavior—that is, the amount of the uncertainty will first inflate, and subsequently decrease, with the growth of decoherence strengths in the two channels. In contrast, the uncertainty decreases monotonically with the growth of the purity of the initial state shared in prior. In order to reduce the measurement uncertainty in noisy environments, we put forward a remarkably effective strategy to steer the magnitude of uncertainty by means of a local non-unitary operation (i.e. weak measurement) on the qubit of interest. It turns out that this non-unitary operation can greatly reduce the entropic uncertainty, upon tuning the operation strength. Our investigations might thereby offer an insight into the dynamics and steering of entropic uncertainty in open systems.
The quantum open system theory for quarkonium during finite temperature medium
International Nuclear Information System (INIS)
Akamatsu, Yukinao
2015-01-01
This paper explains theoretical studies on the dynamics of heavy quarkonium in a finite temperature medium. As a first step of understanding the dynamics of heavy quarkonium in a medium, it explains firstly the definition of potential acting between heavy quarks in a finite temperature medium, and next the stochastic potential and decoherence. While the conventional definition based on thermodynamics lacks theoretical validity, theoretically reasonable definition can be obtained by the spectral decomposition of Wilson loop in the medium. When calculating the potential with this definition, the imaginary part appears, leading to the lacking of theoretical integrity when used in the potential terms of Schroedinger equation, but it is eliminated by the concept of stochastic potential. Decoherence given by thermal fluctuation to wave function is an important physical process of the dynamics of heavy quarkonium in a finite temperature medium. There is a limit of stochastic potential that cannot describe the irreversible process, and this limitation can be overcome by a more comprehensive system based on the theory of quantum open system. By dealing with the heavy quarkonium as quantum open system, phenomena such as color shielding, thermal fluctuation, and dissipation in the quark-gluon plasma, become describable in the way of quantum theory. (A.O.)
Directory of Open Access Journals (Sweden)
C. A. Chatzidimitriou-Dreismann
2011-06-01
Full Text Available Decoherence of quantum entangled particles is observed in most systems, and is usually caused by system-environment interactions. Disentangling two subsystems A and B of a quantum system AB is tantamount to erasure of quantum phase relations between A and B. It is widely believed that this erasure is an innocuous process, which e.g. does not affect the energies of A and B. Surprisingly, recent theoretical investigations by different groups showed that disentangling two systems, i.e. their decoherence, can cause an increase of their energies. Applying this result to the context of neutron Compton scattering from H2 molecules, we provide for the first time experimental evidence which supports this prediction. The results reveal that the neutron-proton collision leading to the cleavage of the H-H bond in the sub-femtosecond timescale is accompanied by larger energy transfer (by about 3% than conventional theory predicts. It is proposed to interpreted the results by considering the neutron-proton collisional system as an entangled open quantum system being subject to decoherence owing to the interactions with the “environment” (i.e., two electrons plus second proton of H2.
Application of quantum Darwinism to a structured environment
Pleasance, Graeme; Garraway, Barry M.
2017-12-01
Quantum Darwinism extends the traditional formalism of decoherence to explain the emergence of classicality in a quantum universe. A classical description emerges when the environment tends to redundantly acquire information about the pointer states of an open system. In light of recent interest, we apply the theoretical tools of the framework to a qubit coupled with many bosonic subenvironments. We examine the degree to which the same classical information is encoded across collections of (i) complete subenvironments and (ii) residual "pseudomode" components of each subenvironment, the conception of which provides a dynamic representation of the reservoir memory. Overall, significant redundancy of information is found as a typical result of the decoherence process. However, by examining its decomposition in terms of classical and quantum correlations, we discover classical information to be nonredundant in both cases i and ii. Moreover, with the full collection of pseudomodes, certain dynamical regimes realize opposite effects, where either the total classical or quantum correlations predominantly decay over time. Finally, when the dynamics are non-Markovian, we find that redundant information is suppressed in line with information backflow to the qubit. By quantifying redundancy, we concretely show it to act as a witness to non-Markovianity in the same way as the trace distance does for nondivisible dynamical maps.
Dynamics of density fluctuations in a non-Markovian Boltzmann- Langevin model
International Nuclear Information System (INIS)
Ayik, S.
1996-01-01
In the course of the past few years, the nuclear Boltzmann-Langevin (BL)model has emerged as a promising microscopic model for nuclear dynamics at intermediate energies. The BL model goes beyond the much employed Boltzmann-Uehling-Uhlenbeck (BUU) model, and hence it provides a basis for describing dynamics of density fluctuations and addressing processes exhibiting spontaneous symmetry breaking and catastrophic transformations in nuclear collisions, such as induced fission and multifragmentation. In these standard models, the collision term is treated in a Markovian approximation by assuming that two-body collisions are local in both space and time, in accordance with Boltzmann's original treatment. This simplification is usually justified by the fact that the duration of a two-body collision is short on the time scale characteristic of the macroscopic evolution of the system. As a result, transport properties of the collective motion has then a classical character. However, when the system possesses fast collective modes with characteristic energies that are not small in comparision with the temperature, then the quantum-statistical effects are important and the standard Markovian treatment is inadequate. In this case, it is necessary to improve the one-body transport model by including the memory effect due to the finite duration of two-body collisions. First we briefly describe the non-Markovian extension of the BL model by including the finite memory time associated with two-body collisions. Then, using this non-Markovian model in a linear response framework, we investigate the effect of the memory time on the agitation of unstable modes in nuclear matter in the spinodal zone, and calculate the collisional relaxation rates of nuclear collective vibrations
Multi-valley effective mass theory for device-level modeling of open quantum dynamics
Jacobson, N. Tobias; Baczewski, Andrew D.; Frees, Adam; Gamble, John King; Montano, Ines; Moussa, Jonathan E.; Muller, Richard P.; Nielsen, Erik
2015-03-01
Simple models for semiconductor-based quantum information processors can provide useful qualitative descriptions of device behavior. However, as experimental implementations have matured, more specific guidance from theory has become necessary, particularly in the form of quantitatively reliable yet computationally efficient modeling. Besides modeling static device properties, improved characterization of noisy gate operations requires a more sophisticated description of device dynamics. Making use of recent developments in multi-valley effective mass theory, we discuss device-level simulations of the open system quantum dynamics of a qubit interacting with phonons and other noise sources. Sandia is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the US Department of Energy National Nuclear Security Administration under Contract No. DE-AC04-94AL85000.
Creation of Two-Particle Entanglement in Open Macroscopic Quantum Systems
Directory of Open Access Journals (Sweden)
M. Merkli
2012-01-01
Full Text Available We consider an open quantum system of N not directly interacting spins (qubits in contact with both local and collective thermal environments. The qubit-environment interactions are energy conserving. We trace out the variables of the thermal environments and N−2 qubits to obtain the time-dependent reduced density matrix for two arbitrary qubits. We numerically simulate the reduced dynamics and the creation of entanglement (concurrence as a function of the parameters of the thermal environments and the number of qubits, N. Our results demonstrate that the two-qubit entanglement generally decreases as N increases. We show analytically that, in the limit N→∞, no entanglement can be created. This indicates that collective thermal environments cannot create two-qubit entanglement when many qubits are located within a region of the size of the environment coherence length. We discuss possible relevance of our consideration to recent quantum information devices and biosystems.
Intermittency and dynamical Lee-Yang zeros of open quantum systems.
Hickey, James M; Flindt, Christian; Garrahan, Juan P
2014-12-01
We use high-order cumulants to investigate the Lee-Yang zeros of generating functions of dynamical observables in open quantum systems. At long times the generating functions take on a large-deviation form with singularities of the associated cumulant generating functions-or dynamical free energies-signifying phase transitions in the ensemble of dynamical trajectories. We consider a driven three-level system as well as the dissipative Ising model. Both systems exhibit dynamical intermittency in the statistics of quantum jumps. From the short-time behavior of the dynamical Lee-Yang zeros, we identify critical values of the counting field which we attribute to the observed intermittency and dynamical phase coexistence. Furthermore, for the dissipative Ising model we construct a trajectory phase diagram and estimate the value of the transverse field where the stationary state changes from being ferromagnetic (inactive) to paramagnetic (active).
Non-additive dissipation in open quantum networks out of equilibrium
Mitchison, Mark T.; Plenio, Martin B.
2018-03-01
We theoretically study a simple non-equilibrium quantum network whose dynamics can be expressed and exactly solved in terms of a time-local master equation. Specifically, we consider a pair of coupled fermionic modes, each one locally exchanging energy and particles with an independent, macroscopic thermal reservoir. We show that the generator of the asymptotic master equation is not additive, i.e. it cannot be expressed as a sum of contributions describing the action of each reservoir alone. Instead, we identify an additional interference term that generates coherences in the energy eigenbasis, associated with the current of conserved particles flowing in the steady state. Notably, non-additivity arises even for wide-band reservoirs coupled arbitrarily weakly to the system. Our results shed light on the non-trivial interplay between multiple thermal noise sources in modular open quantum systems.
Holographic control of information and dynamical topology change for composite open quantum systems
Aref'eva, I. Ya.; Volovich, I. V.; Inozemcev, O. V.
2017-12-01
We analyze how the compositeness of a system affects the characteristic time of equilibration. We study the dynamics of open composite quantum systems strongly coupled to the environment after a quantum perturbation accompanied by nonequilibrium heating. We use a holographic description of the evolution of entanglement entropy. The nonsmooth character of the evolution with holographic entanglement is a general feature of composite systems, which demonstrate a dynamical change of topology in the bulk space and a jumplike velocity change of entanglement entropy propagation. Moreover, the number of jumps depends on the system configuration and especially on the number of composite parts. The evolution of the mutual information of two composite systems inherits these jumps. We present a detailed study of the mutual information for two subsystems with one of them being bipartite. We find five qualitatively different types of behavior of the mutual information dynamics and indicate the corresponding regions of the system parameters.
Opening the Pandora's box of quantum spinor fields
Energy Technology Data Exchange (ETDEWEB)
Bonora, L. [International School for Advanced Studies-SISSA, Trieste (Italy); Silva, J.M.H. da [Universidade Estadual Paulista-UNESP, Departamento de Fisica e Quimica, Guaratingueta, SP (Brazil); Rocha, R. da [Universidade Federal do ABC-UFABC, Centro de Matematica, Computacao e Cognicao, Santo Andre (Brazil)
2018-02-15
Lounesto's classification of spinors is a comprehensive and exhaustive algorithm that, based on the bilinears covariants, discloses the possibility of a large variety of spinors, comprising regular and singular spinors and their unexpected applications in physics and including the cases of Dirac, Weyl, and Majorana as very particular spinor fields. In this paper we pose the problem of an analogous classification in the framework of second quantization. We first discuss in general the nature of the problem. Then we start the analysis of two basic bilinear covariants, the scalar and pseudoscalar, in the second quantized setup, with expressions applicable to the quantum field theory extended to all types of spinors. One can see that an ampler set of possibilities opens up with respect to the classical case. A quantum reconstruction algorithm is also proposed. The Feynman propagator is extended for spinors in all classes. (orig.)
Microwave Imaging Using a Tunable Reflectarray Antenna and Superradiance in Open Quantum Systems
Tayebi, Amin
two different nanostructures, a solid state device suitable for quantum computing and spherical plasmonic nanoantennas and waveguides. These three physically different systems are all investigated within a single quantum theory; the effective non-Hermitian Hamiltonian framework. The non-Hermitian Hamiltonian approach is a convenient mathematical formalism for the description of open quantum systems. This method based on the Feshbach projection formalism provides an alternative to popular methods such as the Feynman diagrammatic techniques and the master equation approach that are commonly used for studying open quantum systems. It is formally exact but very flexible and can be adjusted to many specific situations. One bright phenomenon emerging in the situation with a sufficiently strong continuum coupling in the case when the number of open channels is relatively small compared to the number of involved intrinsic states is the so-called superradiance. Being an analog of superradiance in quantum optics, this term stands for the formation in the system of a collective superposition of the intrinsic states coherently coupled to the same decay channel. The footprint of superradiance in each system is investigated in detail. In the quantum transport problem, signal transmission is greatly enhanced at the transition to superradiance. In the proposed solid state based charge qubit, the superradiant states effectively protect the remaining internal states from decaying into the continuum and hence increase the lifetime of the device. Finally, the superradiance phenomenon provides us a tool to manipulate light at the nanoscale. It is responsible for the existence of modes with distinct radiation properties in a system of coupled plasmonic nanoantennas: superradiant states with enhanced and dark modes with extremely damped radiation. Furthermore, similar to the quantum case, energy transport through a plasmonic waveguide is greatly enhanced.
Quantum trajectories: Memory and continuous observation
Barchielli, Alberto; Pellegrini, Clément; Petruccione, Francesco
2012-12-01
Starting from a generalization of the quantum trajectory theory [based on the stochastic Schrödinger equation (SSE)], non-Markovian models of quantum dynamics are derived. In order to describe non-Markovian effects, the approach used in this article is based on the introduction of random coefficients in the usual linear SSE. A major interest is that this allows a consistent theory of quantum measurement in continuous time to be developed for these non-Markovian quantum trajectory models. In this context, the notions of “instrument,” “a priori,” and “a posteriori” states can be introduced. The key point is that by starting from a stochastic equation on the Hilbert space of the system, we are able to respect the complete positivity of the mean dynamics for the statistical operator and the requirements of the axioms of quantum measurement theory. The flexibility of the theory is next illustrated by a concrete physical model of a noisy oscillator where non-Markovian effects come from the random environment, colored noises, randomness in the stimulating light, and delay effects. The statistics of the emitted photons and the heterodyne and homodyne spectra are studied, and we show how these quantities are sensitive to the non-Markovian features of the system dynamics, so that, in principle, the observation and analysis of the fluorescent light could reveal the presence of non-Markovian effects and allow for a measure of the spectra of the noises affecting the system dynamics.
Energy Technology Data Exchange (ETDEWEB)
Ding, Zhi-yong [School of Physics & Material Science, Anhui University, Hefei 230039 (China); School of Physics & Electronic Engineering, Fuyang Normal University, Fuyang 236037 (China); He, Juan, E-mail: juanhe78@163.com [School of Physics & Electronic Engineering, Fuyang Normal University, Fuyang 236037 (China); Ye, Liu, E-mail: yeliu@ahu.edu.cn [School of Physics & Material Science, Anhui University, Hefei 230039 (China)
2017-02-15
A feasible scheme for protecting the Greenberger–Horne–Zeilinger (GHZ) entanglement state in non-Markovian environments is proposed. It consists of prior weak measurement on each qubit before the interaction with decoherence environments followed by post quantum measurement reversals. It is shown that both the fidelity and concurrence of the GHZ state can be effectively improved. Meanwhile, we also verified that our scenario can enhance tripartite nonlocality remarkably. In addition, the result indicates that the larger the weak measurement strength, the better the effectiveness of the scheme with the lower success probability.
A simple solvable model of quantum field theory of open strings
International Nuclear Information System (INIS)
Kazakov, V.A.; AN SSSR, Moscow
1990-01-01
A model of quantum field theory of open strings without any embedding (D=0) is solved. The world sheets of interacting strings are represented by dynamical planar graphs with dynamical holes of arbitrary sizes. The phenomenon of spontaneous tearing of the world sheet is noticed, which gives a singularity at zero coupling constant of string interaction. This phenomenon can be considered as a nonperturbative effect, similar to renormalons in planar field theories and is closely related to the α' → 0 limit of string field theories. (orig.)
Non-Markovian modification of the golden rule rate expression
International Nuclear Information System (INIS)
Basilevsky, M. V.; Davidovich, G. V.; Titov, S. V.; Voronin, A. I.
2006-01-01
The reformulation of the standard golden rule approach considered in this paper for treating reactive tunneling reduces the computation of the reaction rate to a derivation of band shapes for energy levels of reactant and product states. This treatment is based on the assumption that the medium environment is actively involved as a partner in the energy exchange with the reactive subsystem but its reorganization effect is negligible. Starting from the quantum relaxation equation for the density matrix, the required band shapes are represented in terms of the spectral density function, exhibiting the continuum spectrum inherent to the interaction between the reactants and the medium in the total reactive system. The simplest Lorentzian spectral bands, obtained under Redfield approximation, proved to be unsatisfactory because they produced a divergent rate expression at low temperature. The problem is resolved by invoking a refined spectral band shape, which behaves as Lorentzian one at the band center but decays exponentially at its tails. The corresponding closed non-Markovian rate expression is derived and investigated taking as an example the photochemical H-transfer reaction between fluorene and acridine proceeding in the fluorene molecular crystal. The kinetics in this reactive system was thoroughly studied experimentally in a wide temperature range [B. Prass et al., Ber. Bunsenges. Phys. Chem. 102, 498 (1998)
International Nuclear Information System (INIS)
Chen, Xin
2014-01-01
Understanding the roles of the temporary and spatial structures of quantum functional noise in open multilevel quantum molecular systems attracts a lot of theoretical interests. I want to establish a rigorous and general framework for functional quantum noises from the constructive and computational perspectives, i.e., how to generate the random trajectories to reproduce the kernel and path ordering of the influence functional with effective Monte Carlo methods for arbitrary spectral densities. This construction approach aims to unify the existing stochastic models to rigorously describe the temporary and spatial structure of Gaussian quantum noises. In this paper, I review the Euclidean imaginary time influence functional and propose the stochastic matrix multiplication scheme to calculate reduced equilibrium density matrices (REDM). In addition, I review and discuss the Feynman-Vernon influence functional according to the Gaussian quadratic integral, particularly its imaginary part which is critical to the rigorous description of the quantum detailed balance. As a result, I establish the conditions under which the influence functional can be interpreted as the average of exponential functional operator over real-valued Gaussian processes for open multilevel quantum systems. I also show the difference between the local and nonlocal phonons within this framework. With the stochastic matrix multiplication scheme, I compare the normalized REDM with the Boltzmann equilibrium distribution for open multilevel quantum systems
Cascade of Quantum Transitions and Magnetocaloric Anomalies in an Open Nanowire
Val'kov, V. V.; Mitskan, V. A.; Shustin, M. S.
2017-12-01
A sequence of magnetocaloric anomalies occurring with the change in a magnetic field H is predicted for an open nanowire with the Rashba spin-orbit coupling and the induced superconducting pairing potential. The nature of such anomalies is due to the cascade of quantum transitions related to the successive changes in the fermion parity of the nanowire ground state with the growth of the magnetic field. It is shown that the critical H c values fall within the parameter range corresponding to the nontrivial values of the Z 2 topological invariant of the corresponding 1D band Hamiltonian characteristic of the D symmetry class. It is demonstrated that such features in the behavior of the open nanowire are retained even in the presence of Coulomb interactions.
Quantumness-generating capability of quantum dynamics
Li, Nan; Luo, Shunlong; Mao, Yuanyuan
2018-04-01
We study quantumness-generating capability of quantum dynamics, where quantumness refers to the noncommutativity between the initial state and the evolving state. In terms of the commutator of the square roots of the initial state and the evolving state, we define a measure to quantify the quantumness-generating capability of quantum dynamics with respect to initial states. Quantumness-generating capability is absent in classical dynamics and hence is a fundamental characteristic of quantum dynamics. For qubit systems, we present an analytical form for this measure, by virtue of which we analyze several prototypical dynamics such as unitary dynamics, phase damping dynamics, amplitude damping dynamics, and random unitary dynamics (Pauli channels). Necessary and sufficient conditions for the monotonicity of quantumness-generating capability are also identified. Finally, we compare these conditions for the monotonicity of quantumness-generating capability with those for various Markovianities and illustrate that quantumness-generating capability and quantum Markovianity are closely related, although they capture different aspects of quantum dynamics.
Carollo, Federico; Garrahan, Juan P; Lesanovsky, Igor; Pérez-Espigares, Carlos
2017-11-01
We consider a class of either fermionic or bosonic noninteracting open quantum chains driven by dissipative interactions at the boundaries and study the interplay of coherent transport and dissipative processes, such as bulk dephasing and diffusion. Starting from the microscopic formulation, we show that the dynamics on large scales can be described in terms of fluctuating hydrodynamics. This is an important simplification as it allows us to apply the methods of macroscopic fluctuation theory to compute the large deviation (LD) statistics of time-integrated currents. In particular, this permits us to show that fermionic open chains display a third-order dynamical phase transition in LD functions. We show that this transition is manifested in a singular change in the structure of trajectories: while typical trajectories are diffusive, rare trajectories associated with atypical currents are ballistic and hyperuniform in their spatial structure. We confirm these results by numerically simulating ensembles of rare trajectories via the cloning method, and by exact numerical diagonalization of the microscopic quantum generator.
Optimal management of non-Markovian biological populations
Williams, B.K.
2007-01-01
Wildlife populations typically are described by Markovian models, with population dynamics influenced at each point in time by current but not previous population levels. Considerable work has been done on identifying optimal management strategies under the Markovian assumption. In this paper we generalize this work to non-Markovian systems, for which population responses to management are influenced by lagged as well as current status and/or controls. We use the maximum principle of optimal control theory to derive conditions for the optimal management such a system, and illustrate the effects of lags on the structure of optimal habitat strategies for a predator-prey system.
A review of progress in the physics of open quantum systems: theory and experiment.
Rotter, I; Bird, J P
2015-11-01
This report on progress explores recent advances in our theoretical and experimental understanding of the physics of open quantum systems (OQSs). The study of such systems represents a core problem in modern physics that has evolved to assume an unprecedented interdisciplinary character. OQSs consist of some localized, microscopic, region that is coupled to an external environment by means of an appropriate interaction. Examples of such systems may be found in numerous areas of physics, including atomic and nuclear physics, photonics, biophysics, and mesoscopic physics. It is the latter area that provides the main focus of this review, an emphasis that is driven by the capacity that exists to subject mesoscopic devices to unprecedented control. We thus provide a detailed discussion of the behavior of mesoscopic devices (and other OQSs) in terms of the projection-operator formalism, according to which the system under study is considered to be comprised of a localized region (Q), embedded into a well-defined environment (P) of scattering wavefunctions (with Q + P = 1). The Q subspace must be treated using the concepts of non-Hermitian physics, and of particular interest here is: the capacity of the environment to mediate a coupling between the different states of Q; the role played by the presence of exceptional points (EPs) in the spectra of OQSs; the influence of EPs on the rigidity of the wavefunction phases, and; the ability of EPs to initiate a dynamical phase transition (DPT). EPs are singular points in the continuum, at which two resonance states coalesce, that is where they exhibit a non-avoided crossing. DPTs occur when the quantum dynamics of the open system causes transitions between non-analytically connected states, as a function of some external control parameter. Much like conventional phase transitions, the behavior of the system on one side of the DPT does not serve as a reliable indicator of that on the other. In
Markovian description of unbiased polymer translocation
International Nuclear Information System (INIS)
Mondaini, Felipe; Moriconi, L.
2012-01-01
We perform, with the help of cloud computing resources, extensive Langevin simulations which provide compelling evidence in favor of a general Markovian framework for unbiased three-dimensional polymer translocation. Our statistical analysis consists of careful evaluations of (i) two-point correlation functions of the translocation coordinate and (ii) the empirical probabilities of complete polymer translocation (taken as a function of the initial number of monomers on a given side of the membrane). We find good agreement with predictions derived from the Markov chain approach recently addressed in the literature by the present authors. -- Highlights: ► We investigate unbiased polymer translocation through membrane pores. ► Large statistical ensembles have been produced with the help of cloud computing resources. ► We evaluate the two-point correlation function of the translocation coordinate. ► We evaluate empirical probabilities for complete polymer translocation. ► Unbiased polymer translocation is described as a Markov stochastic process.
Markovian description of unbiased polymer translocation
Energy Technology Data Exchange (ETDEWEB)
Mondaini, Felipe [Instituto de Física, Universidade Federal do Rio de Janeiro, C.P. 68528, 21945-970 Rio de Janeiro, RJ (Brazil); Centro Federal de Educação Tecnológica Celso Suckow da Fonseca, UnED Angra dos Reis, Angra dos Reis, 23953-030, RJ (Brazil); Moriconi, L., E-mail: moriconi@if.ufrj.br [Instituto de Física, Universidade Federal do Rio de Janeiro, C.P. 68528, 21945-970 Rio de Janeiro, RJ (Brazil)
2012-10-01
We perform, with the help of cloud computing resources, extensive Langevin simulations which provide compelling evidence in favor of a general Markovian framework for unbiased three-dimensional polymer translocation. Our statistical analysis consists of careful evaluations of (i) two-point correlation functions of the translocation coordinate and (ii) the empirical probabilities of complete polymer translocation (taken as a function of the initial number of monomers on a given side of the membrane). We find good agreement with predictions derived from the Markov chain approach recently addressed in the literature by the present authors. -- Highlights: ► We investigate unbiased polymer translocation through membrane pores. ► Large statistical ensembles have been produced with the help of cloud computing resources. ► We evaluate the two-point correlation function of the translocation coordinate. ► We evaluate empirical probabilities for complete polymer translocation. ► Unbiased polymer translocation is described as a Markov stochastic process.
Markovian Processes for Quantitative Information Leakage
DEFF Research Database (Denmark)
Biondi, Fabrizio
Quantification of information leakage is a successful approach for evaluating the security of a system. It models the system to be analyzed as a channel with the secret as the input and an output as observable by the attacker as the output, and applies information theory to quantify the amount...... and randomized processes with Markovian models and to compute their information leakage for a very general model of attacker. We present the QUAIL tool that automates such analysis and is able to compute the information leakage of an imperative WHILE language. Finally, we show how to use QUAIL to analyze some...... of information transmitted through such channel, thus effectively quantifying how many bits of the secret can be inferred by the attacker by analyzing the system’s output. Channels are usually encoded as matrices of conditional probabilities, known as channel matrices. Such matrices grow exponentially...
International Nuclear Information System (INIS)
Asplund, Erik; Kluener, Thorsten
2012-01-01
In this paper, control of open quantum systems with emphasis on the control of surface photochemical reactions is presented. A quantum system in a condensed phase undergoes strong dissipative processes. From a theoretical viewpoint, it is important to model such processes in a rigorous way. In this work, the description of open quantum systems is realized within the surrogate Hamiltonian approach [R. Baer and R. Kosloff, J. Chem. Phys. 106, 8862 (1997)]. An efficient and accurate method to find control fields is optimal control theory (OCT) [W. Zhu, J. Botina, and H. Rabitz, J. Chem. Phys. 108, 1953 (1998); Y. Ohtsuki, G. Turinici, and H. Rabitz, J. Chem. Phys. 120, 5509 (2004)]. To gain control of open quantum systems, the surrogate Hamiltonian approach and OCT, with time-dependent targets, are combined. Three open quantum systems are investigated by the combined method, a harmonic oscillator immersed in an ohmic bath, CO adsorbed on a platinum surface, and NO adsorbed on a nickel oxide surface. Throughout this paper, atomic units, i.e., (ℎ/2π)=m e =e=a 0 = 1, have been used unless otherwise stated.
Asplund, Erik; Klüner, Thorsten
2012-03-28
In this paper, control of open quantum systems with emphasis on the control of surface photochemical reactions is presented. A quantum system in a condensed phase undergoes strong dissipative processes. From a theoretical viewpoint, it is important to model such processes in a rigorous way. In this work, the description of open quantum systems is realized within the surrogate hamiltonian approach [R. Baer and R. Kosloff, J. Chem. Phys. 106, 8862 (1997)]. An efficient and accurate method to find control fields is optimal control theory (OCT) [W. Zhu, J. Botina, and H. Rabitz, J. Chem. Phys. 108, 1953 (1998); Y. Ohtsuki, G. Turinici, and H. Rabitz, J. Chem. Phys. 120, 5509 (2004)]. To gain control of open quantum systems, the surrogate hamiltonian approach and OCT, with time-dependent targets, are combined. Three open quantum systems are investigated by the combined method, a harmonic oscillator immersed in an ohmic bath, CO adsorbed on a platinum surface, and NO adsorbed on a nickel oxide surface. Throughout this paper, atomic units, i.e., ℏ = m(e) = e = a(0) = 1, have been used unless otherwise stated.
TIPPtool: Compositional Specification and Analysis of Markovian Performance Models
Hermanns, H.; Halbwachs, N.; Peled, D.; Mertsiotakis, V.; Siegle, M.
1999-01-01
In this short paper we briefly describe a tool which is based on a Markovian stochastic process algebra. The tool offers both model specification and quantitative model analysis in a compositional fashion, wrapped in a userfriendly graphical front-end.
a markovian study of manpow an study of manpower planning
African Journals Online (AJOL)
eobe
The Markovian method of manpower planning foretell the future. ... ive years from a soft drink manufacturing company based in Lagos, Nigeria company based ... ces management approach. ... handbook have also used Markov processes for.
Markovian approach: From Ising model to stochastic radiative transfer
International Nuclear Information System (INIS)
Kassianov, E.; Veron, D.
2009-01-01
The origin of the Markovian approach can be traced back to 1906; however, it gained explicit recognition in the last few decades. This overview outlines some important applications of the Markovian approach, which illustrate its immense prestige, respect, and success. These applications include examples in the statistical physics, astronomy, mathematics, computational science and the stochastic transport problem. In particular, the overview highlights important contributions made by Pomraning and Titov to the neutron and radiation transport theory in a stochastic medium with homogeneous statistics. Using simple probabilistic assumptions (Markovian approximation), they have introduced a simplified, but quite realistic, representation of the neutron/radiation transfer through a two-component discrete stochastic mixture. New concepts and methodologies introduced by these two distinguished scientists allow us to generalize the Markovian treatment to the stochastic medium with inhomogeneous statistics and demonstrate its improved predictive performance for the down-welling shortwave fluxes. (authors)
Non-Markovian features of deeply inelastic collisions
International Nuclear Information System (INIS)
Pal, D.; Chattopadhyay, S.; Kar, K.
1988-01-01
To study the effect of memory in the diffusion processes (of charge, mass etc) observed in deeply inelastic heavy-ion reactions, we derive non-Markovian transport equations for the exponential and Gaussian memory kernels. The centroid and the variance of the distribution are expressed in terms of the memory time, drift and diffusion coefficients. The predictions based on this theory show better agreement with the experimental data than the Markovian results. (author)
Sensitivity Analysis Based on Markovian Integration by Parts Formula
Directory of Open Access Journals (Sweden)
Yongsheng Hang
2017-10-01
Full Text Available Sensitivity analysis is widely applied in financial risk management and engineering; it describes the variations brought by the changes of parameters. Since the integration by parts technique for Markov chains is well developed in recent years, in this paper we apply it for computation of sensitivity and show the closed-form expressions for two commonly-used time-continuous Markovian models. By comparison, we conclude that our approach outperforms the existing technique of computing sensitivity on Markovian models.
Fitting Markovian binary trees using global and individual demographic data
Hautphenne, Sophie; Massaro, Melanie; Turner, Katharine
2017-01-01
We consider a class of branching processes called Markovian binary trees, in which the individuals lifetime and reproduction epochs are modeled using a transient Markovian arrival process (TMAP). We estimate the parameters of the TMAP based on population data containing information on age-specific fertility and mortality rates. Depending on the degree of detail of the available data, a weighted non-linear regression method or a maximum likelihood method is applied. We discuss the optimal choi...
A quantum dynamics study of the benzopyran ring opening guided by laser pulses
Saab, Mohamad; Doriol, Loïc Joubert; Lasorne, Benjamin; Guérin, Stéphane; Gatti, Fabien
2014-10-01
The ring-opening photoisomerization of benzopyran, which occurs via a photochemical route involving a conical intersection, has been studied with quantum dynamics calculations using the multi-configuration time-dependent Hartree method (MCTDH). We introduce a mechanistic strategy to control the conversion of benzopyran to merocyanine with laser pulses. We use a six-dimensional model developed in a previous work for the potential energy surfaces (PES) based on an extension of the vibronic-coupling Hamiltonian model (diabatization method by ansatz), which depends on the most active degrees of freedom. The main objective of these quantum dynamics simulations is to provide a set of strategies that could help experimentalists to control the photoreactivity vs. photostability ratio (selectivity). In this work we present: (i) a pump-dump technique used to control the photostability, (ii) a two-step strategy to enhance the reactivity of the system: first, a pure vibrational excitation in the electronic ground state that prepares the system and, second, an ultraviolet excitation that brings the system to the first adiabatic electronic state; (iii) finally the effect of a non-resonant pulse (Stark effect) on the dynamics.
Exponential complexity and ontological theories of quantum mechanics
International Nuclear Information System (INIS)
Montina, A.
2008-01-01
Ontological theories of quantum mechanics describe a single system by means of well-defined classical variables and attribute the quantum uncertainties to our ignorance about the underlying reality represented by these variables. We consider the general class of ontological theories describing a quantum system by a set of variables with Markovian (either deterministic or stochastic) evolution. We provide proof that the number of continuous variables cannot be smaller than 2N-2, N being the Hilbert-space dimension. Thus, any ontological Markovian theory of quantum mechanics requires a number of variables which grows exponentially with the physical size. This result is relevant also in the framework of quantum Monte Carlo methods
Dynamics of Quantum Entanglement in Reservoir with Memory Effects
International Nuclear Information System (INIS)
Hao Xiang; Sha Jinqiao; Sun Jian; Zhu Shiqun
2012-01-01
The non-Markovian dynamics of quantum entanglement is studied by the Shabani-Lidar master equation when one of entangled quantum systems is coupled to a local reservoir with memory effects. The completely positive reduced dynamical map can be constructed in the Kraus representation. Quantum entanglement decays more slowly in the non-Markovian environment. The decoherence time for quantum entanglement can be markedly increased with the change of the memory kernel. It is found out that the entanglement sudden death between quantum systems and entanglement sudden birth between the system and reservoir occur at different instants. (general)
Jitonnom, Jitrayut; Mujika, Jon I; van der Kamp, Marc W; Mulholland, Adrian J
2017-12-05
Creatininase catalyzes the conversion of creatinine (a biosensor for kidney function) to creatine via a two-step mechanism: water addition followed by ring opening. Water addition is common to other known cyclic amidohydrolases, but the precise mechanism for ring opening is still under debate. The proton donor in this step is either His178 or a water molecule bound to one of the metal ions, and the roles of His178 and Glu122 are unclear. Here, the two possible reaction pathways have been fully examined by means of combined quantum mechanics/molecular mechanics simulations at the SCC-DFTB/CHARMM22 level of theory. The results indicate that His178 is the main catalytic residue for the whole reaction and explain its role as proton shuttle during the ring-opening step. In the first step, His178 provides electrostatic stabilization to the gem-diolate tetrahedral intermediate. In the second step, His178 abstracts the hydroxyl proton of the intermediate and delivers it to the cyclic amide nitrogen, leading to ring opening. The latter is the rate-limiting step with a free energy barrier of 18.5 kcal/mol, in agreement with the experiment. We find that Glu122 must be protonated during the enzyme reaction, so that it can form a stable hydrogen bond with its neighboring water molecule. Simulations of the E122Q mutant showed that this replacement disrupts the H-bond network formed by three conserved residues (Glu34, Ser78, and Glu122) and water, increasing the energy barrier. Our computational studies provide a comprehensive explanation for previous structural and kinetic observations, including why the H178A mutation causes a complete loss of activity but the E122Q mutation does not.
Energy Technology Data Exchange (ETDEWEB)
Basharov, A. M., E-mail: basharov@gmail.com [National Research Centre ' Kurchatov Institute,' (Russian Federation)
2012-09-15
It is shown that the effective Hamiltonian representation, as it is formulated in author's papers, serves as a basis for distinguishing, in a broadband environment of an open quantum system, independent noise sources that determine, in terms of the stationary quantum Wiener and Poisson processes in the Markov approximation, the effective Hamiltonian and the equation for the evolution operator of the open system and its environment. General stochastic differential equations of generalized Langevin (non-Wiener) type for the evolution operator and the kinetic equation for the density matrix of an open system are obtained, which allow one to analyze the dynamics of a wide class of localized open systems in the Markov approximation. The main distinctive features of the dynamics of open quantum systems described in this way are the stabilization of excited states with respect to collective processes and an additional frequency shift of the spectrum of the open system. As an illustration of the general approach developed, the photon dynamics in a single-mode cavity without losses on the mirrors is considered, which contains identical intracavity atoms coupled to the external vacuum electromagnetic field. For some atomic densities, the photons of the cavity mode are 'locked' inside the cavity, thus exhibiting a new phenomenon of radiation trapping and non-Wiener dynamics.
International Nuclear Information System (INIS)
Basharov, A. M.
2012-01-01
It is shown that the effective Hamiltonian representation, as it is formulated in author’s papers, serves as a basis for distinguishing, in a broadband environment of an open quantum system, independent noise sources that determine, in terms of the stationary quantum Wiener and Poisson processes in the Markov approximation, the effective Hamiltonian and the equation for the evolution operator of the open system and its environment. General stochastic differential equations of generalized Langevin (non-Wiener) type for the evolution operator and the kinetic equation for the density matrix of an open system are obtained, which allow one to analyze the dynamics of a wide class of localized open systems in the Markov approximation. The main distinctive features of the dynamics of open quantum systems described in this way are the stabilization of excited states with respect to collective processes and an additional frequency shift of the spectrum of the open system. As an illustration of the general approach developed, the photon dynamics in a single-mode cavity without losses on the mirrors is considered, which contains identical intracavity atoms coupled to the external vacuum electromagnetic field. For some atomic densities, the photons of the cavity mode are “locked” inside the cavity, thus exhibiting a new phenomenon of radiation trapping and non-Wiener dynamics.
Symplectic evolution of Wigner functions in Markovian open systems.
Brodier, O; Almeida, A M Ozorio de
2004-01-01
The Wigner function is known to evolve classically under the exclusive action of a quadratic Hamiltonian. If the system also interacts with the environment through Lindblad operators that are complex linear functions of position and momentum, then the general evolution is the convolution of a non-Hamiltonian classical propagation of the Wigner function with a phase space Gaussian that broadens in time. We analyze the consequences of this in the three generic cases of elliptic, hyperbolic, and parabolic Hamiltonians. The Wigner function always becomes positive in a definite time, which does not depend on the initial pure state. We observe the influence of classical dynamics and dissipation upon this threshold. We also derive an exact formula for the evolving linear entropy as the average of a narrowing Gaussian taken over a probability distribution that depends only on the initial state. This leads to a long time asymptotic formula for the growth of linear entropy. We finally discuss the possibility of recovering the initial state.
International Nuclear Information System (INIS)
Berggren, Karl-Fredrik; Yakimenko, Irina I; Hakanen, Jani
2010-01-01
A heuristic model for particle states and current flow in open ballistic two-dimensional (2D) quantum dots/wave billiards is proposed. The model makes use of complex potentials first introduced in phenomenological nuclear inelastic scattering theory (the optical model). Here we assume that external input and output leads connecting the system to the source and the drain regions may be represented by complex potentials. In this way, a current may be set up between the two 'pseudo-leads'. Probability densities and current flows for an open quantum dot are analyzed here numerically and the results are compared with the microwave measurements used to emulate the system. The model is of conceptual as well as practical interest. In addition to quantum billiards, it may be used as a tool per se to analyze transport in classical wave analogues, such as microwave resonators, acoustic resonators, effects of leakage on such systems, etc.
International Nuclear Information System (INIS)
Sandulescu, A.; Stefanescu, E.
1987-07-01
On the basis of Lindblad theory of open quantum systems we obtain new optical equations for the system of two-level atom interacting with a single mode of the electromagnetic field. The conventional Block equations in a generalized form with field phases are obtained in the hypothesis that all the terms are slowly varying in the rotating frame.(authors)
QmeQ 1.0: An open-source Python package for calculations of transport through quantum dot devices
DEFF Research Database (Denmark)
Kiršanskas, Gediminas; Pedersen, Jonas Nyvold; Karlström, Olov
2017-01-01
QmeQ is an open-source Python package for numerical modeling of transport through quantum dot devices with strong electron–electron interactions using various approximate master equation approaches. The package provides a framework for calculating stationary particle or energy currents driven...
Lozada Aguilar, Miguel Ángel; Khrennikov, Andrei; Oleschko, Klaudia
2018-04-01
As was recently shown by the authors, quantum probability theory can be used for the modelling of the process of decision-making (e.g. probabilistic risk analysis) for macroscopic geophysical structures such as hydrocarbon reservoirs. This approach can be considered as a geophysical realization of Hilbert's programme on axiomatization of statistical models in physics (the famous sixth Hilbert problem). In this conceptual paper, we continue development of this approach to decision-making under uncertainty which is generated by complexity, variability, heterogeneity, anisotropy, as well as the restrictions to accessibility of subsurface structures. The belief state of a geological expert about the potential of exploring a hydrocarbon reservoir is continuously updated by outputs of measurements, and selection of mathematical models and scales of numerical simulation. These outputs can be treated as signals from the information environment E. The dynamics of the belief state can be modelled with the aid of the theory of open quantum systems: a quantum state (representing uncertainty in beliefs) is dynamically modified through coupling with E; stabilization to a steady state determines a decision strategy. In this paper, the process of decision-making about hydrocarbon reservoirs (e.g. `explore or not?'; `open new well or not?'; `contaminated by water or not?'; `double or triple porosity medium?') is modelled by using the Gorini-Kossakowski-Sudarshan-Lindblad equation. In our model, this equation describes the evolution of experts' predictions about a geophysical structure. We proceed with the information approach to quantum theory and the subjective interpretation of quantum probabilities (due to quantum Bayesianism). This article is part of the theme issue `Hilbert's sixth problem'.
Lozada Aguilar, Miguel Ángel; Khrennikov, Andrei; Oleschko, Klaudia
2018-04-28
As was recently shown by the authors, quantum probability theory can be used for the modelling of the process of decision-making (e.g. probabilistic risk analysis) for macroscopic geophysical structures such as hydrocarbon reservoirs. This approach can be considered as a geophysical realization of Hilbert's programme on axiomatization of statistical models in physics (the famous sixth Hilbert problem). In this conceptual paper , we continue development of this approach to decision-making under uncertainty which is generated by complexity, variability, heterogeneity, anisotropy, as well as the restrictions to accessibility of subsurface structures. The belief state of a geological expert about the potential of exploring a hydrocarbon reservoir is continuously updated by outputs of measurements, and selection of mathematical models and scales of numerical simulation. These outputs can be treated as signals from the information environment E The dynamics of the belief state can be modelled with the aid of the theory of open quantum systems: a quantum state (representing uncertainty in beliefs) is dynamically modified through coupling with E ; stabilization to a steady state determines a decision strategy. In this paper, the process of decision-making about hydrocarbon reservoirs (e.g. 'explore or not?'; 'open new well or not?'; 'contaminated by water or not?'; 'double or triple porosity medium?') is modelled by using the Gorini-Kossakowski-Sudarshan-Lindblad equation. In our model, this equation describes the evolution of experts' predictions about a geophysical structure. We proceed with the information approach to quantum theory and the subjective interpretation of quantum probabilities (due to quantum Bayesianism).This article is part of the theme issue 'Hilbert's sixth problem'. © 2018 The Author(s).
Larsen, Ask Hjorth; De Giovannini, Umberto; Rubio, Angel
2016-01-01
We present a review of different computational methods to describe time-dependent phenomena in open quantum systems and their extension to a density-functional framework. We focus the discussion on electron emission processes in atoms and molecules addressing excited-state lifetimes and dissipative processes. Initially we analyze the concept of an electronic resonance, a central concept in spectroscopy associated with a metastable state from which an electron eventually escapes (electronic lifetime). Resonances play a fundamental role in many time-dependent molecular phenomena but can be rationalized from a time-independent context in terms of scattering states. We introduce the method of complex scaling, which is used to capture resonant states as localized states in the spirit of usual bound-state methods, and work on its extension to static and time-dependent density-functional theory. In a time-dependent setting, complex scaling can be used to describe excitations in the continuum as well as wave packet dynamics leading to electron emission. This process can also be treated by using open boundary conditions which allow time-dependent simulations of emission processes without artificial reflections at the boundaries (i.e., borders of the simulation box). We compare in detail different schemes to implement open boundaries, namely transparent boundaries using Green functions, and absorbing boundaries in the form of complex absorbing potentials and mask functions. The last two are regularly used together with time-dependent density-functional theory to describe the electron emission dynamics of atoms and molecules. Finally, we discuss approaches to the calculation of energy and angle-resolved time-dependent pump-probe photoelectron spectroscopy of molecular systems.
A Perron-Frobenius Type of Theorem for Quantum Operations
Lagro, Matthew; Yang, Wei-Shih; Xiong, Sheng
2017-10-01
We define a special class of quantum operations we call Markovian and show that it has the same spectral properties as a corresponding Markov chain. We then consider a convex combination of a quantum operation and a Markovian quantum operation and show that under a norm condition its spectrum has the same properties as in the conclusion of the Perron-Frobenius theorem if its Markovian part does. Moreover, under a compatibility condition of the two operations, we show that its limiting distribution is the same as the corresponding Markov chain. We apply our general results to partially decoherent quantum random walks with decoherence strength 0 ≤ p ≤ 1. We obtain a quantum ergodic theorem for partially decoherent processes. We show that for 0 < p ≤ 1, the limiting distribution of a partially decoherent quantum random walk is the same as the limiting distribution for the classical random walk.
Remarks on time-dependent [current]-density functional theory for open quantum systems.
Yuen-Zhou, Joel; Aspuru-Guzik, Alán
2013-08-14
Time-dependent [current]-density functional theory for open quantum systems (OQS) has emerged as a formalism that can incorporate dissipative effects in the dynamics of many-body quantum systems. Here, we review and clarify some formal aspects of these theories that have been recently questioned in the literature. In particular, we provide theoretical support for the following conclusions: (1) contrary to what we and others had stated before, within the master equation framework, there is in fact a one-to-one mapping between vector potentials and current densities for fixed initial state, particle-particle interaction, and memory kernel; (2) regardless of the first conclusion, all of our recently suggested Kohn-Sham (KS) schemes to reproduce the current and particle densities of the original OQS, and in particular, the use of a KS closed driven system, remains formally valid; (3) the Lindblad master equation maintains the positivity of the density matrix regardless of the time-dependence of the Hamiltonian or the dissipation operators; (4) within the stochastic Schrödinger equation picture, a one-to-one mapping from stochastic vector potential to stochastic current density for individual trajectories has not been proven so far, except in the case where the vector potential is the same for every member of the ensemble, in which case, it reduces to the Lindblad master equation picture; (5) master equations may violate certain desired properties of the density matrix, such as positivity, but they remain as one of the most useful constructs to study OQS when the environment is not easily incorporated explicitly in the calculation. The conclusions support our previous work as formally rigorous, offer new insights into it, and provide a common ground to discuss related theories.
Markovian Interpretations of Dual Retrieval Processes
Gomes, C. F. A.; Nakamura, K.; Reyna, V. F.
2013-01-01
A half-century ago, at the dawn of the all-or-none learning era, Estes showed that finite Markov chains supply a tractable, comprehensive framework for discrete-change data of the sort that he envisioned for shifts in conditioning states in stimulus sampling theory. Shortly thereafter, such data rapidly accumulated in many spheres of human learning and animal conditioning, and Estes’ work stimulated vigorous development of Markov models to handle them. A key outcome was that the data of the workhorse paradigms of episodic memory, recognition and recall, proved to be one- and two-stage Markovian, respectively, to close approximations. Subsequently, Markov modeling of recognition and recall all but disappeared from the literature, but it is now reemerging in the wake of dual-process conceptions of episodic memory. In recall, in particular, Markov models are being used to measure two retrieval operations (direct access and reconstruction) and a slave familiarity operation. In the present paper, we develop this family of models and present the requisite machinery for fit evaluation and significance testing. Results are reviewed from selected experiments in which the recall models were used to understand dual memory processes. PMID:24948840
Markovian Interpretations of Dual Retrieval Processes.
Gomes, C F A; Brainerd, C J; Nakamura, K; Reyna, V F
2014-04-01
A half-century ago, at the dawn of the all-or-none learning era, Estes showed that finite Markov chains supply a tractable, comprehensive framework for discrete-change data of the sort that he envisioned for shifts in conditioning states in stimulus sampling theory. Shortly thereafter, such data rapidly accumulated in many spheres of human learning and animal conditioning, and Estes' work stimulated vigorous development of Markov models to handle them. A key outcome was that the data of the workhorse paradigms of episodic memory, recognition and recall, proved to be one- and two-stage Markovian, respectively, to close approximations. Subsequently, Markov modeling of recognition and recall all but disappeared from the literature, but it is now reemerging in the wake of dual-process conceptions of episodic memory. In recall, in particular, Markov models are being used to measure two retrieval operations (direct access and reconstruction) and a slave familiarity operation. In the present paper, we develop this family of models and present the requisite machinery for fit evaluation and significance testing. Results are reviewed from selected experiments in which the recall models were used to understand dual memory processes.
Dynamics of non-Markovian exclusion processes
International Nuclear Information System (INIS)
Khoromskaia, Diana; Grosskinsky, Stefan; Harris, Rosemary J
2014-01-01
Driven diffusive systems are often used as simple discrete models of collective transport phenomena in physics, biology or social sciences. Restricting attention to one-dimensional geometries, the asymmetric simple exclusion process (ASEP) plays a paradigmatic role to describe noise-activated driven motion of entities subject to an excluded volume interaction and many variants have been studied in recent years. While in the standard ASEP the noise is Poissonian and the process is therefore Markovian, in many applications the statistics of the activating noise has a non-standard distribution with possible memory effects resulting from internal degrees of freedom or external sources. This leads to temporal correlations and can significantly affect the shape of the current-density relation as has been studied recently for a number of scenarios. In this paper we report a general framework to derive the fundamental diagram of ASEPs driven by non-Poissonian noise by using effectively only two simple quantities, viz., the mean residual lifetime of the jump distribution and a suitably defined temporal correlation length. We corroborate our results by detailed numerical studies for various noise statistics under periodic boundary conditions and discuss how our approach can be applied to more general driven diffusive systems. (paper)
Dynamics of non-Markovian exclusion processes
Khoromskaia, Diana; Harris, Rosemary J.; Grosskinsky, Stefan
2014-12-01
Driven diffusive systems are often used as simple discrete models of collective transport phenomena in physics, biology or social sciences. Restricting attention to one-dimensional geometries, the asymmetric simple exclusion process (ASEP) plays a paradigmatic role to describe noise-activated driven motion of entities subject to an excluded volume interaction and many variants have been studied in recent years. While in the standard ASEP the noise is Poissonian and the process is therefore Markovian, in many applications the statistics of the activating noise has a non-standard distribution with possible memory effects resulting from internal degrees of freedom or external sources. This leads to temporal correlations and can significantly affect the shape of the current-density relation as has been studied recently for a number of scenarios. In this paper we report a general framework to derive the fundamental diagram of ASEPs driven by non-Poissonian noise by using effectively only two simple quantities, viz., the mean residual lifetime of the jump distribution and a suitably defined temporal correlation length. We corroborate our results by detailed numerical studies for various noise statistics under periodic boundary conditions and discuss how our approach can be applied to more general driven diffusive systems.
The Quixote project: Collaborative and Open Quantum Chemistry data management in the Internet age.
Adams, Sam; de Castro, Pablo; Echenique, Pablo; Estrada, Jorge; Hanwell, Marcus D; Murray-Rust, Peter; Sherwood, Paul; Thomas, Jens; Townsend, Joe
2011-10-14
Computational Quantum Chemistry has developed into a powerful, efficient, reliable and increasingly routine tool for exploring the structure and properties of small to medium sized molecules. Many thousands of calculations are performed every day, some offering results which approach experimental accuracy. However, in contrast to other disciplines, such as crystallography, or bioinformatics, where standard formats and well-known, unified databases exist, this QC data is generally destined to remain locally held in files which are not designed to be machine-readable. Only a very small subset of these results will become accessible to the wider community through publication.In this paper we describe how the Quixote Project is developing the infrastructure required to convert output from a number of different molecular quantum chemistry packages to a common semantically rich, machine-readable format and to build respositories of QC results. Such an infrastructure offers benefits at many levels. The standardised representation of the results will facilitate software interoperability, for example making it easier for analysis tools to take data from different QC packages, and will also help with archival and deposition of results. The repository infrastructure, which is lightweight and built using Open software components, can be implemented at individual researcher, project, organisation or community level, offering the exciting possibility that in future many of these QC results can be made publically available, to be searched and interpreted just as crystallography and bioinformatics results are today.Although we believe that quantum chemists will appreciate the contribution the Quixote infrastructure can make to the organisation and and exchange of their results, we anticipate that greater rewards will come from enabling their results to be consumed by a wider community. As the respositories grow they will become a valuable source of chemical data for use by other
The Quixote project: Collaborative and Open Quantum Chemistry data management in the Internet age
Directory of Open Access Journals (Sweden)
Adams Sam
2011-10-01
Full Text Available Abstract Computational Quantum Chemistry has developed into a powerful, efficient, reliable and increasingly routine tool for exploring the structure and properties of small to medium sized molecules. Many thousands of calculations are performed every day, some offering results which approach experimental accuracy. However, in contrast to other disciplines, such as crystallography, or bioinformatics, where standard formats and well-known, unified databases exist, this QC data is generally destined to remain locally held in files which are not designed to be machine-readable. Only a very small subset of these results will become accessible to the wider community through publication. In this paper we describe how the Quixote Project is developing the infrastructure required to convert output from a number of different molecular quantum chemistry packages to a common semantically rich, machine-readable format and to build respositories of QC results. Such an infrastructure offers benefits at many levels. The standardised representation of the results will facilitate software interoperability, for example making it easier for analysis tools to take data from different QC packages, and will also help with archival and deposition of results. The repository infrastructure, which is lightweight and built using Open software components, can be implemented at individual researcher, project, organisation or community level, offering the exciting possibility that in future many of these QC results can be made publically available, to be searched and interpreted just as crystallography and bioinformatics results are today. Although we believe that quantum chemists will appreciate the contribution the Quixote infrastructure can make to the organisation and and exchange of their results, we anticipate that greater rewards will come from enabling their results to be consumed by a wider community. As the respositories grow they will become a valuable source of
'quantumness' measures in the decohering harmonic oscillator
Indian Academy of Sciences (India)
We studied the behaviour under decoherence of four different measures of the distance between quantum states and classical states for the harmonic oscillator coupled to a linear Markovian bath. Three of these are relative measures, using different definitions of the distance between the given quantum states and the set of ...
Non-Markovian near-infrared Q branch of HCl diluted in liquid Ar.
Padilla, Antonio; Pérez, Justo
2013-08-28
By using a non-Markovian spectral theory based in the Kubo cumulant expansion technique, we have qualitatively studied the infrared Q branch observed in the fundamental absorption band of HCl diluted in liquid Ar. The statistical parameters of the anisotropic interaction present in this spectral theory were calculated by means of molecular dynamics techniques, and found that the values of the anisotropic correlation times are significantly greater (by a factor of two) than those previously obtained by fitting procedures or microscopic cell models. This fact is decisive for the observation in the theoretical spectral band of a central Q resonance which is absent in the abundant previous researches carried out with the usual theories based in Kubo cumulant expansion techniques. Although the theory used in this work only allows a qualitative study of the Q branch, we can employ it to study the unknown characteristics of the Q resonance which are difficult to obtain with the quantum simulation techniques recently developed. For example, in this study we have found that the Q branch is basically a non-Markovian (or memory) effect produced by the spectral line interferences, where the PR interferential profile basically determines the Q branch spectral shape. Furthermore, we have found that the Q resonance is principally generated by the first rotational states of the first two vibrational levels, those more affected by the action of the dissolvent.
2016-08-24
to the seven-qubit Steane code [29] and also represents the smallest instance of a 2D topological color code [30]. Since the realized quantum error...Quantum Computations on a Topologically Encoded Qubit, Science 345, 302 (2014). [17] M. Cramer, M. B. Plenio, S. T. Flammia, R. Somma, D. Gross, S. D...Memory, J. Math . Phys. (N.Y.) 43, 4452 (2002). [20] B. M. Terhal, Quantum Error Correction for Quantum Memories, Rev. Mod. Phys. 87, 307 (2015). [21] D
Ahmed, Ibrahim; Nepomechie, Rafael I.; Wang, Chunguang
2017-07-01
We argue that the Hamiltonians for A(2)2n open quantum spin chains corresponding to two choices of integrable boundary conditions have the symmetries Uq(Bn) and Uq(Cn) , respectively. We find a formula for the Dynkin labels of the Bethe states (which determine the degeneracies of the corresponding eigenvalues) in terms of the numbers of Bethe roots of each type. With the help of this formula, we verify numerically (for a generic value of the anisotropy parameter) that the degeneracies and multiplicities of the spectra implied by the quantum group symmetries are completely described by the Bethe ansatz.
Markovian agents models for wireless sensor networks deployed in environmental protection
International Nuclear Information System (INIS)
Cerotti, Davide; Gribaudo, Marco; Bobbio, Andrea
2014-01-01
Wireless sensor networks (WSNs) are gaining popularity as distributed monitoring systems in safety critical applications, when the location to be controlled may be dangerous for a human operator or difficult to access. Fire is one of the major thread in urban as well as in open environments, and WSNs are receiving increasing attention as a mean to build effective and timely fire protection systems. The present paper presents a novel analytical technique for the study of the propagation of a fire in a wide open area and the interaction with a WSN deployed to monitor the outbreak of the fire and to send a warning signal to a base station. For the complex scenario under study, an analytical modeling and analysis technique based on Markovian agents (MAs) is discussed. It is shown that, even if the overall state space of the models is huge, nevertheless an analytical solution is feasible, by exploiting the locality of the interactions among MAs, based on a message passing mechanism combined with a perception function. - Highlights: • We present a revised theory of Markovian agent models, detailing the analysis techniques and its complexity • We a target a complex application of a wireless sensor network (WSN) that monitors forest fire. • The model captures the propagation of fire, heat, and the detection by the WSN. • We compute key performance indices such us the fire propagation front, and message travel time. • We perform an extensive set of experiments to study the effectiveness of the WSN in detecting forest fire
Segnorile, H H; Zamar, R C
2013-10-21
An experimental study of NMR spin decoherence in nematic liquid crystals is presented. Decoherence dynamics can be put in evidence by means of refocusing experiments of the dipolar interactions. The experimental technique used in this work is based on the MREV8 pulse sequence. The aim of the work is to detect the main features of the irreversible quantum decoherence in liquid crystals, on the basis of the theory presented by the authors recently. The focus is laid on experimentally probing the eigen-selection process in the intermediate time scale, between quantum interference of a closed system and thermalization, as a signature of the quantum spin decoherence of the open quantum system, as well as on quantifying the effects of non-idealities as possible sources of signal decays which could mask the intrinsic decoherence. In order to contrast experiment and theory, the theory was adapted to obtain the decoherence function corresponding to the MREV8 reversion experiments. Non-idealities of the experimental setting, like external field inhomogeneity, pulse misadjustments, and the presence of non-reverted spin interaction terms are analysed in detail within this framework, and their effects on the observed signal decay are numerically estimated. It is found that though all these non-idealities could in principle affect the evolution of the spin dynamics, their influence can be mitigated and they do not present the characteristic behaviour of the irreversible spin decoherence. As unique characteristic of decoherence, the experimental results clearly show the occurrence of eigen-selectivity in the intermediate timescale, in complete agreement with the theoretical predictions. We conclude that the eigen-selection effect is the fingerprint of decoherence associated with a quantum open spin system in liquid crystals. Besides, these features of the results account for the quasi-equilibrium states of the spin system, which were observed previously in these mesophases, and
Single trapped cold ions: a testing ground for quantum mechanics
International Nuclear Information System (INIS)
Maniscalco, S
2005-01-01
In this article I review some results obtained during my PhD work in the group of Professor Messina, at the University of Palermo. I discuss some proposals aimed at exploring fundamental issues of quantum theory, e.g. entanglement and quantum superpositions, in the context of single trapped ions. This physical context turns out to be extremely well suited both for studying fundamental features of quantum mechanics, such as the quantum-classical border, and for technological applications such as quantum logic gates and quantum registers. I focus on some procedures for engineering nonclassical states of the vibrational motion of the centre of mass of the ion. I consider both the case in which the ion interacts with classical laser beams and the case of interaction with a quantized mode of light. In particular, I discuss the generation of Schroedinger cat-like states, Bell states and Greenberger-Horn-Zeilinger states. The schemes for generating nonclassical states stem from two different quantum processes: the parity effect and the quantum state manipulation via quantum non-demolition measurement. Finally, I consider a microscopic theory of the interaction of a quantum harmonic oscillator (the centre of mass of the ion in the trapped ion context) with a bosonic thermal environment. Using an exact approach to the dynamics, I discuss a quantum theory of heating of trapped ions able to describe both the short time non-Markovian regime and the thermalization process. I conclude showing briefly how the trapped ion systems can be used as simulators of key models of open quantum systems such as the Caldeira-Leggett model. (phd tutorial)
Effective description of the short-time dynamics in open quantum systems
Rossi, Matteo A. C.; Foti, Caterina; Cuccoli, Alessandro; Trapani, Jacopo; Verrucchi, Paola; Paris, Matteo G. A.
2017-09-01
We address the dynamics of a bosonic system coupled to either a bosonic or a magnetic environment and derive a set of sufficient conditions that allow one to describe the dynamics in terms of the effective interaction with a classical fluctuating field. We find that for short interaction times the dynamics of the open system is described by a Gaussian noise map for several different interaction models and independently on the temperature of the environment. In order to go beyond a qualitative understanding of the origin and physical meaning of the above short-time constraint, we take a general viewpoint and, based on an algebraic approach, suggest that any quantum environment can be described by classical fields whenever global symmetries lead to the definition of environmental operators that remain well defined when increasing the size, i.e., the number of dynamical variables, of the environment. In the case of the bosonic environment this statement is exactly demonstrated via a constructive procedure that explicitly shows why a large number of environmental dynamical variables and, necessarily, global symmetries, entail the set of conditions derived in the first part of the work.
Exact Open Quantum System Dynamics Using the Hierarchy of Pure States (HOPS).
Hartmann, Richard; Strunz, Walter T
2017-12-12
We show that the general and numerically exact Hierarchy of Pure States method (HOPS) is very well applicable to calculate the reduced dynamics of an open quantum system. In particular, we focus on environments with a sub-Ohmic spectral density (SD) resulting in an algebraic decay of the bath correlation function (BCF). The universal applicability of HOPS, reaching from weak to strong coupling for zero and nonzero temperature, is demonstrated by solving the spin-boson model for which we find perfect agreement with other methods, each one suitable for a special regime of parameters. The challenges arising in the strong coupling regime are not only reflected in the computational effort needed for the HOPS method to converge but also in the necessity for an importance sampling mechanism, accounted for by the nonlinear variant of HOPS. In order to include nonzero-temperature effects in the strong coupling regime we found that it is highly favorable for the HOPS method to use the zero-temperature BCF and include temperature via a stochastic Hermitian contribution to the system Hamiltonian.
Kim, Jeongnim; Baczewski, Andrew D.; Beaudet, Todd D.; Benali, Anouar; Chandler Bennett, M.; Berrill, Mark A.; Blunt, Nick S.; Josué Landinez Borda, Edgar; Casula, Michele; Ceperley, David M.; Chiesa, Simone; Clark, Bryan K.; Clay, Raymond C., III; Delaney, Kris T.; Dewing, Mark; Esler, Kenneth P.; Hao, Hongxia; Heinonen, Olle; Kent, Paul R. C.; Krogel, Jaron T.; Kylänpää, Ilkka; Li, Ying Wai; Lopez, M. Graham; Luo, Ye; Malone, Fionn D.; Martin, Richard M.; Mathuriya, Amrita; McMinis, Jeremy; Melton, Cody A.; Mitas, Lubos; Morales, Miguel A.; Neuscamman, Eric; Parker, William D.; Pineda Flores, Sergio D.; Romero, Nichols A.; Rubenstein, Brenda M.; Shea, Jacqueline A. R.; Shin, Hyeondeok; Shulenburger, Luke; Tillack, Andreas F.; Townsend, Joshua P.; Tubman, Norm M.; Van Der Goetz, Brett; Vincent, Jordan E.; ChangMo Yang, D.; Yang, Yubo; Zhang, Shuai; Zhao, Luning
2018-05-01
QMCPACK is an open source quantum Monte Carlo package for ab initio electronic structure calculations. It supports calculations of metallic and insulating solids, molecules, atoms, and some model Hamiltonians. Implemented real space quantum Monte Carlo algorithms include variational, diffusion, and reptation Monte Carlo. QMCPACK uses Slater–Jastrow type trial wavefunctions in conjunction with a sophisticated optimizer capable of optimizing tens of thousands of parameters. The orbital space auxiliary-field quantum Monte Carlo method is also implemented, enabling cross validation between different highly accurate methods. The code is specifically optimized for calculations with large numbers of electrons on the latest high performance computing architectures, including multicore central processing unit and graphical processing unit systems. We detail the program’s capabilities, outline its structure, and give examples of its use in current research calculations. The package is available at http://qmcpack.org.
Wang, Xihua
2011-10-26
Colloidal quantum dots (CQDs) enable multijunction solar cells using a single material programmed using the quantum size effect. Here we report the systematic engineering of 1.6 eV PbS CQD solar cells, optimal as the front cell responsible for visible-wavelength harvesting in tandem photovoltaics. We rationally optimize each of the device\\'s collecting electrodes-the heterointerface with electron-accepting TiO2 and the deep-work-function hole-collecting MoO3 for ohmic contact-for maximum efficiency. We report an open-circuit voltage of 0.70 V, the highest observed in a colloidal quantum dot solar cell operating at room temperature. We report an AM1.5 solar power conversion efficiency of 3.5%, the highest observed in >1.5 eV bandgap CQD PV device. © 2011 American Chemical Society.
Study of open systems with molecules in isotropic liquids
Kondo, Yasushi; Matsuzaki, Masayuki
2018-05-01
We are interested in dynamics of a system in an environment, or an open system. Such phenomena as crossover from Markovian to non-Markovian relaxation and thermal equilibration are of our interest. Open systems have experimentally been studied with ultra cold atoms, ions in traps, optics, and cold electric circuits because well-isolated systems can be prepared here and thus the effects of environments can be controlled. We point out that some molecules solved in isotropic liquid are well isolated and thus they can also be employed for studying open systems in Nuclear Magnetic Resonance (NMR) experiments. First, we provide a short review on related phenomena of open systems that helps readers to understand our motivation. We, then, present two experiments as examples of our approach with molecules in isotropic liquids. Crossover from Markovian to non-Markovian relaxation was realized in one NMR experiment, while relaxation-like phenomena were observed in approximately isolated systems in the other.
Monte Carlo simulation of fully Markovian stochastic geometries
International Nuclear Information System (INIS)
Lepage, Thibaut; Delaby, Lucie; Malvagi, Fausto; Mazzolo, Alain
2010-01-01
The interest in resolving the equation of transport in stochastic media has continued to increase these last years. For binary stochastic media it is often assumed that the geometry is Markovian, which is never the case in usual environments. In the present paper, based on rigorous mathematical theorems, we construct fully two-dimensional Markovian stochastic geometries and we study their main properties. In particular, we determine a percolation threshold p c , equal to 0.586 ± 0.0015 for such geometries. Finally, Monte Carlo simulations are performed through these geometries and the results compared to homogeneous geometries. (author)
Continuous-variable quantum teleportation in bosonic structured environments
Energy Technology Data Exchange (ETDEWEB)
He Guangqiang; Zhang Jingtao; Zhu Jun; Zeng Guihua [State Key Laboratory of Advanced Optical Communication Systems and Networks, Department of Electronic Engineering, Shanghai Jiaotong University, Shanghai 200240 (China)
2011-09-15
The effects of dynamics of continuous-variable entanglement under the various kinds of environments on quantum teleportation are quantitatively investigated. Only under assumption of the weak system-reservoir interaction, the evolution of teleportation fidelity is analytically derived and is numerically plotted in terms of environment parameters including reservoir temperature and its spectral density, without Markovian and rotating wave approximations. We find that the fidelity of teleportation is a monotonically decreasing function for Markovian interaction in Ohmic-like environments, while it oscillates for non-Markovian ones. According to the dynamical laws of teleportation, teleportation with better performances can be implemented by selecting the appropriate time.
DEFF Research Database (Denmark)
Flindt, Christian; Novotny, Tomás; Braggio, Alessandro
2010-01-01
Recent experimental progress has made it possible to detect in real-time single electrons tunneling through Coulomb blockade nanostructures, thereby allowing for precise measurements of the statistical distribution of the number of transferred charges, the so-called full counting statistics...... interactions. Our recursive method can treat systems with many states as well as non-Markovian dynamics. We illustrate our approach with three examples of current experimental relevance: bunching transport through a two-level quantum dot, transport through a nanoelectromechanical system with dynamical Franck...
International Nuclear Information System (INIS)
Ujevic, Sebastian; Mendoza, Michel
2011-01-01
Full text. We propose numerical simulations of longitudinal magneto conductance through a finite anti dot lattice located inside an open quantum dot with a magnetic field applied perpendicular to the plane. The system is connected to reservoirs using quantum point contacts. We discuss the relationship between the longitudinal magneto conductance and the generation of transversal couplings between the induced open quantum dots in the system. The system presents longitudinal magneto conductance maps with crossovers (between transversal bands) and closings (longitudinal decoupling) of fundamental quantum states related to the open quantum dots induced by the anti dot lattice. A relationship is observed between the distribution of anti dots and the formed conductance bands, allowing a systematic follow-up of the bands as a function of the applied magnetic field and quantum point contact width. We observed a high conductance intensity (between n- and (n + 1)-quantum of conductance, n = 1; 2...) in the regions of crossover and closing of states. This suggests transversal couplings between the induced open quantum dots of the system that can be modulated by varying both the anti dots potential and the quantum point contact width. A new continuous channel (not expected) is induced by the variation of the contact width and generate Fano resonances in the conductance. These resonances can be manipulated by the applied magnetic field
QuTiP 2: A Python framework for the dynamics of open quantum systems
Johansson, J. R.; Nation, P. D.; Nori, Franco
2013-04-01
We present version 2 of QuTiP, the Quantum Toolbox in Python. Compared to the preceding version [J.R. Johansson, P.D. Nation, F. Nori, Comput. Phys. Commun. 183 (2012) 1760.], we have introduced numerous new features, enhanced performance, and made changes in the Application Programming Interface (API) for improved functionality and consistency within the package, as well as increased compatibility with existing conventions used in other scientific software packages for Python. The most significant new features include efficient solvers for arbitrary time-dependent Hamiltonians and collapse operators, support for the Floquet formalism, and new solvers for Bloch-Redfield and Floquet-Markov master equations. Here we introduce these new features, demonstrate their use, and give a summary of the important backward-incompatible API changes introduced in this version. Catalog identifier: AEMB_v2_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEMB_v2_0.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland Licensing provisions: GNU General Public License, version 3 No. of lines in distributed program, including test data, etc.: 33625 No. of bytes in distributed program, including test data, etc.: 410064 Distribution format: tar.gz Programming language: Python. Computer: i386, x86-64. Operating system: Linux, Mac OSX. RAM: 2+ Gigabytes Classification: 7. External routines: NumPy, SciPy, Matplotlib, Cython Catalog identifier of previous version: AEMB_v1_0 Journal reference of previous version: Comput. Phys. Comm. 183 (2012) 1760 Does the new version supercede the previous version?: Yes Nature of problem: Dynamics of open quantum systems Solution method: Numerical solutions to Lindblad, Floquet-Markov, and Bloch-Redfield master equations, as well as the Monte Carlo wave function method. Reasons for new version: Compared to the preceding version we have introduced numerous new features, enhanced performance, and made changes in
The Foundations of Quantum Mechanics: Historical Analysis and Open Questions -- Cesena, 2004
Garola, Claudio; Rossi, Arcangelo; Sozzo, Sandro
Introduction / C. Garola, A. Rossi and S. Sozzo -- If Bertlmann had three feet / A. Afriat -- Macroscopic interpretability of quantum component systems / R. Ascoli -- Premeasurement versus measurement: a basic form of complementarity / G. Auletta and G. Tarozzi -- Remarks on conditioning / E. G. Beltrametti -- Entangled state preparation in experiments on quantum non-locality / V. Berardi and A. Garuccio -- The first steps of quantum electrodynamics: what is it that's being quantized? / S. Bergia -- On the meaning of element in the science of italic tradition, the question of physical objectivity (and/or physical meaning) and quantum mechanics / G. Boscarino -- Mathematics and epistemology in Planck's theoretical work (1898-1915) / P. Campogalliani -- On the free motion with noise / B. Carazza and R. Tedeschi -- Field quantization and wave/particle duality / M. Cini -- Parastatistics in econophysics? / D. Costantini and U. Garibaldi -- Theory-laden instruments and quantum mechanics / S. D'Agostino -- Quantum non-locality and the mathematical representation of experience / V. Fano -- On the notion of proposition in classical and quantum mechanics / C. Garola and S. Sozzo -- The electromagnetic conception of nature and the origins of quantum physics / E. A. Giannetto -- What we talk about when we talk about universe computability / S. Guccione -- Bohm and Bohmian mechanics / G. Introzzi and M. Rossetti -- An objective background for quantum theory relying on thermodynamic concepts / L. Lanz and B. Vacchini -- The entrance of quantum mechanics in Italy: from Garbasso to Fermi / M. Leone and N. Robotti -- The measure of momentum in quantum mechanics / F. Logiurato and C. Tarsitani -- On the two-slit interference experiment: a statistical discussion / M. Minozzo -- Why the reactivity of the elements is a relational property, and why it matters / V. Mosini -- Detecting non compatible properties in double-slit experiment without erasure / G. Nisticò -- If you can
Recursive approach for non-Markovian time-convolutionless master equations
Gasbarri, G.; Ferialdi, L.
2018-02-01
We consider a general open system dynamics and we provide a recursive method to derive the associated non-Markovian master equation in a perturbative series. The approach relies on a momenta expansion of the open system evolution. Unlike previous perturbative approaches of this kind, the method presented in this paper provides a recursive definition of each perturbative term. Furthermore, we give an intuitive diagrammatic description of each term of the series, which provides a useful analytical tool to build them and to derive their structure in terms of commutators and anticommutators. We eventually apply our formalism to the evolution of the observables of the reduced system, by showing how the method can be applied to the adjoint master equation, and by developing a diagrammatic description of the associated series.
Bonitz, Michael
2016-01-01
This book presents quantum kinetic theory in a comprehensive way. The focus is on density operator methods and on non-equilibrium Green functions. The theory allows to rigorously treat nonequilibrium dynamics in quantum many-body systems. Of particular interest are ultrafast processes in plasmas, condensed matter and trapped atoms that are stimulated by rapidly developing experiments with short pulse lasers and free electron lasers. To describe these experiments theoretically, the most powerful approach is given by non-Markovian quantum kinetic equations that are discussed in detail, including computational aspects.
Markovian Building Blocks for Individual-Based Modelling
DEFF Research Database (Denmark)
Nilsson, Lars Anders Fredrik
2007-01-01
previous exposure to Markov chains in continuous time (see e.g. Grimmett and Stirzaker, 2001)). Markovian arrival processes are very general point processes that are relatively easy to analyse. They have, so far, been largely unknown to the ecological modelling community. The article C deals...
Femtosecond Non-Markovian Optical Dynamics in Solution
Nibbering, Erik T.J.; Wiersma, Douwe A.; Duppen, Koos
1991-01-01
Femtosecond photon-echo experiments on sodium resorufin in dimethylsulfoxide at room temperature show that optical dephasing in solution is of non-Markovian character. A single Gauss-Markov stochastic modulation process is used to interpret both the femtosecond light-scattering results and the
Solutions for a non-Markovian diffusion equation
International Nuclear Information System (INIS)
Lenzi, E.K.; Evangelista, L.R.; Lenzi, M.K.; Ribeiro, H.V.; Oliveira, E.C. de
2010-01-01
Solutions for a non-Markovian diffusion equation are investigated. For this equation, we consider a spatial and time dependent diffusion coefficient and the presence of an absorbent term. The solutions exhibit an anomalous behavior which may be related to the solutions of fractional diffusion equations and anomalous diffusion.
Application of Markovian model to school enrolment projection ...
African Journals Online (AJOL)
Application of Markovian model to school enrolment projection process. VU Ekhosuehi, AA Osagiede. Abstract. No Abstract. Global Journal of Mathematical Sciences Vol. 5(1) 2006: 9-16. Full Text: EMAIL FREE FULL TEXT EMAIL FREE FULL TEXT · DOWNLOAD FULL TEXT DOWNLOAD FULL TEXT.
A note on Markovian manpower models | Osagiede | Journal of the ...
African Journals Online (AJOL)
In modelling manpower systems, most authors rely on Markov-based theoretic methodology as an analytic tool to unify the states of the system with the axiomatic foundation that there is a one-stage dependence of events. In this study, Markovian manpower models are surveyed. Specific areas are highlighted as future ...
Transport benchmarks for one-dimensional binary Markovian mixtures revisited
International Nuclear Information System (INIS)
Malvagi, F.
2013-01-01
The classic benchmarks for transport through a binary Markovian mixture are revisited to look at the probability distribution function of the chosen 'results': reflection, transmission and scalar flux. We argue that the knowledge of the ensemble averaged results is not sufficient for reliable predictions: a measure of the dispersion must also be obtained. An algorithm to estimate this dispersion is tested. (author)
The integrable quantum group invariant A2n-1(2) and Dn+1(2) open spin chains
Nepomechie, Rafael I.; Pimenta, Rodrigo A.; Retore, Ana L.
2017-11-01
A family of A2n(2) integrable open spin chains with Uq (Cn) symmetry was recently identified in arxiv:arXiv:1702.01482. We identify here in a similar way a family of A2n-1(2) integrable open spin chains with Uq (Dn) symmetry, and two families of Dn+1(2) integrable open spin chains with Uq (Bn) symmetry. We discuss the consequences of these symmetries for the degeneracies and multiplicities of the spectrum. We propose Bethe ansatz solutions for two of these models, whose completeness we check numerically for small values of n and chain length N. We find formulas for the Dynkin labels in terms of the numbers of Bethe roots of each type, which are useful for determining the corresponding degeneracies. In an appendix, we briefly consider Dn+1(2) chains with other integrable boundary conditions, which do not have quantum group symmetry.
The integrable quantum group invariant A2n−1(2 and Dn+1(2 open spin chains
Directory of Open Access Journals (Sweden)
Rafael I. Nepomechie
2017-11-01
Full Text Available A family of A2n(2 integrable open spin chains with Uq(Cn symmetry was recently identified in arXiv:1702.01482. We identify here in a similar way a family of A2n−1(2 integrable open spin chains with Uq(Dn symmetry, and two families of Dn+1(2 integrable open spin chains with Uq(Bn symmetry. We discuss the consequences of these symmetries for the degeneracies and multiplicities of the spectrum. We propose Bethe ansatz solutions for two of these models, whose completeness we check numerically for small values of n and chain length N. We find formulas for the Dynkin labels in terms of the numbers of Bethe roots of each type, which are useful for determining the corresponding degeneracies. In an appendix, we briefly consider Dn+1(2 chains with other integrable boundary conditions, which do not have quantum group symmetry.
Energy Technology Data Exchange (ETDEWEB)
Hughes, Keith H., E-mail: keith.hughes@bangor.ac.uk [School of Chemistry, Bangor University, Bangor, Gwynedd LL57 2UW (United Kingdom); Cahier, Benjamin [School of Chemistry, Bangor University, Bangor, Gwynedd LL57 2UW (United Kingdom); Martinazzo, Rocco [Dipartimento di Chimica Università degli Studi di Milano, v. Golgi 19, 20133 Milano (Italy); Tamura, Hiroyuki [WPI-Advanced Institute for Material Research, Tohoku University, 2-1-1 Katahira, Aoba-ku, Sendai 980-8577 (Japan); Burghardt, Irene [Institute of Physical and Theoretical Chemistry, Goethe University Frankfurt, Max-von-Laue-Str. 7, 60438 Frankfurt/Main (Germany)
2014-10-17
Highlights: • Quantum dynamical study of exciton dissociation at a heterojunction interface. • The non-Markovian quantum dynamics involves a highly structured spectral density. • Spectral density is reconstructed from an effective mode transformation of the Hamiltonian. • The dynamics is studied using the hierarchical equations of motion approach. • It was found that the temperature has little effect on the charge transfer. - Abstract: We extend our recent quantum dynamical study of the exciton dissociation and charge transfer at an oligothiophene–fullerene heterojunction interface (Tamura et al., 2012) [6] by investigating the process using the non-perturbative hierarchical equations of motion (HEOM) approach. Based upon an effective mode reconstruction of the spectral density the effect of temperature on the charge transfer is studied using reduced density matrices. It was found that the temperature had little effect on the charge transfer and a coherent dynamics persists over the first few tens of femtoseconds, indicating that the primary charge transfer step proceeds by an activationless pathway.
International Nuclear Information System (INIS)
Kuznetsova, E. I.; Fel'dman, E. B.
2006-01-01
A method for exactly diagonalizing the XY Hamiltonian of an alternating open chain of spins s = 1/2 has been proposed on the basis of the Jordan-Wigner transformation and analysis of the dynamics of spinless fermions. The multiple-quantum spin dynamics of alternating open chains at high temperatures has been analyzed and the intensities of multiple-quantum coherences have been calculated. The problem of the transfer of a quantum state from one end of the alternating chain to the other is studied. It has been shown that the ideal transfer of qubits is possible in alternating chains with a larger number of spins than that in homogeneous chains
Synthesis of strongly fluorescent graphene quantum dots by cage-opening buckminsterfullerene
Czech Academy of Sciences Publication Activity Database
Chua, C. K.; Sofer, Z.; Šimek, P.; Jankovský, O.; Klímová, K.; Bakardjieva, Snejana; Hrdličková-Kučková, Š.; Pumera, M.
2015-01-01
Roč. 9, č. 3 (2015), s. 2548-2555 ISSN 1936-0851 Institutional support: RVO:61388980 Keywords : fullerenes * graphene * luminescence * oxidation * quantum dots Subject RIV: CA - Inorganic Chemistry Impact factor: 13.334, year: 2015
International Nuclear Information System (INIS)
Melas, Evangelos
2011-01-01
The Bondi-Metzner-Sachs group B is the common asymptotic group of all asymptotically flat (lorentzian) space-times, and is the best candidate for the universal symmetry group of General Relativity. However, in quantum gravity, complexified or euclidean versions of General Relativity are frequently considered. McCarthy has shown that there are forty-two generalizations of B for these versions of the theory and a variety of further ones, either real in any signature, or complex. A firm foundation for quantum gravity can be laid by following through the analogue of Wigner's programme for special relativity with B replacing the Poincare group P. Here the main results which have been obtained so far in this research programme are reported and the more important open problems are stated.
Cui, Ping
celebrated Marcus' inversion and Kramers' turnover behaviors, the new theory also shows some distinct quantum solvation effects that can alter the ET mechanism. Moreover, the present theory predicts further for the ET reaction thermodynamics, such as equilibrium Gibbs free-energy and entropy, some interesting solvent-dependent features that are calling for experimental verification. In Chapter 6, we discuss the constructed QDTs, in terms of their unified mathematical structure that supports a linear dynamics space, and thus facilitates their applications to various physical problems. The involving details are exemplified with the CODDE form of QDT. As the linear space is concerned, we identify the Schrodinger versus Heisenberg picture and the forward versus backward propagation of the reduced, dissipative Liouville dynamics. For applications we discuss the reduced linear response theory and the optimal control problems, in which the correlated effects of non-Markovian dissipation and field driving are shown to be important. In Chapter 7, we turn to quantum transport, i.e., electric current through molecular or mesoscopic systems under finite applied voltage. By viewing the nonequilibrium transport setup as a quantum open system, we develop a reduced-density-matrix approach to quantum transport. The resulting current is explicitly expressed in terms of the molecular reduced density matrix by tracing out the degrees of freedom of the electrodes at finite bias and temperature. We propose a conditional quantum master equation theory, which is an extension of the conventional (or unconditional) QDT by tracing out the well-defined bath subsets individually, instead of the entire bath degrees of freedom. Both the current and the noise spectrum can be conveniently analyzed in terms of the conditional reduced density matrix dynamics. By far, the QDT (including the conditional one) has only been exploited in second-order form. A self-consistent Born approximation for the system
Isar, Aurelian
1995-01-01
The harmonic oscillator with dissipation is studied within the framework of the Lindblad theory for open quantum systems. By using the Wang-Uhlenbeck method, the Fokker-Planck equation, obtained from the master equation for the density operator, is solved for the Wigner distribution function, subject to either the Gaussian type or the delta-function type of initial conditions. The obtained Wigner functions are two-dimensional Gaussians with different widths. Then a closed expression for the density operator is extracted. The entropy of the system is subsequently calculated and its temporal behavior shows that this quantity relaxes to its equilibrium value.
Chakraborty, Sagnik
2018-03-01
We present a general framework for the information backflow (IB) approach of Markovianity that not only includes a large number, if not all, of IB prescriptions proposed so far but also is equivalent to completely positive divisibility for invertible evolutions. Following the common approach of IB, where monotonic decay of some physical property or some information quantifier is seen as the definition of Markovianity, we propose in our framework a general description of what should be called a proper "physicality quantifier" to define Markovianity. We elucidate different properties of our framework and use them to argue that an infinite family of non-Markovianity measures can be constructed, which would capture varied strengths of non-Markovianity in the dynamics. Moreover, we show that generalized trace-distance measure in two dimensions serve as a sufficient criteria for IB Markovianity for a number of prescriptions suggested earlier in the literature.
Reliability importance analysis of Markovian systems at steady state using perturbation analysis
Energy Technology Data Exchange (ETDEWEB)
Phuc Do Van [Institut Charles Delaunay - FRE CNRS 2848, Systems Modeling and Dependability Group, Universite de technologie de Troyes, 12, rue Marie Curie, BP 2060-10010 Troyes cedex (France); Barros, Anne [Institut Charles Delaunay - FRE CNRS 2848, Systems Modeling and Dependability Group, Universite de technologie de Troyes, 12, rue Marie Curie, BP 2060-10010 Troyes cedex (France)], E-mail: anne.barros@utt.fr; Berenguer, Christophe [Institut Charles Delaunay - FRE CNRS 2848, Systems Modeling and Dependability Group, Universite de technologie de Troyes, 12, rue Marie Curie, BP 2060-10010 Troyes cedex (France)
2008-11-15
Sensitivity analysis has been primarily defined for static systems, i.e. systems described by combinatorial reliability models (fault or event trees). Several structural and probabilistic measures have been proposed to assess the components importance. For dynamic systems including inter-component and functional dependencies (cold spare, shared load, shared resources, etc.), and described by Markov models or, more generally, by discrete events dynamic systems models, the problem of sensitivity analysis remains widely open. In this paper, the perturbation method is used to estimate an importance factor, called multi-directional sensitivity measure, in the framework of Markovian systems. Some numerical examples are introduced to show why this method offers a promising tool for steady-state sensitivity analysis of Markov processes in reliability studies.
Reliability importance analysis of Markovian systems at steady state using perturbation analysis
International Nuclear Information System (INIS)
Phuc Do Van; Barros, Anne; Berenguer, Christophe
2008-01-01
Sensitivity analysis has been primarily defined for static systems, i.e. systems described by combinatorial reliability models (fault or event trees). Several structural and probabilistic measures have been proposed to assess the components importance. For dynamic systems including inter-component and functional dependencies (cold spare, shared load, shared resources, etc.), and described by Markov models or, more generally, by discrete events dynamic systems models, the problem of sensitivity analysis remains widely open. In this paper, the perturbation method is used to estimate an importance factor, called multi-directional sensitivity measure, in the framework of Markovian systems. Some numerical examples are introduced to show why this method offers a promising tool for steady-state sensitivity analysis of Markov processes in reliability studies
A model of epigenetic evolution based on theory of open quantum systems.
Asano, Masanari; Basieva, Irina; Khrennikov, Andrei; Ohya, Masanori; Tanaka, Yoshiharu; Yamato, Ichiro
2013-12-01
We present a very general model of epigenetic evolution unifying (neo-)Darwinian and (neo-)Lamarckian viewpoints. The evolution is represented in the form of adaptive dynamics given by the quantum(-like) master equation. This equation describes development of the information state of epigenome under the pressure of an environment. We use the formalism of quantum mechanics in the purely operational framework. (Hence, our model has no direct relation to quantum physical processes inside a cell.) Thus our model is about probabilities for observations which can be done on epigenomes and it does not provide a detailed description of cellular processes. Usage of the operational approach provides a possibility to describe by one model all known types of cellular epigenetic inheritance.
A relativistic theory for continuous measurement of quantum fields
International Nuclear Information System (INIS)
Diosi, L.
1990-04-01
A formal theory for the continuous measurement of relativistic quantum fields is proposed. The corresponding scattering equations were derived. The proposed formalism reduces to known equations in the Markovian case. Two recent models for spontaneous quantum state reduction have been recovered in the framework of this theory. A possible example of the relativistic continuous measurement has been outlined in standard Quantum Electrodynamics. The continuous measurement theory possesses an alternative formulation in terms of interacting quantum and stochastic fields. (author) 23 refs
Control and filtering for semi-Markovian jump systems
Li, Fanbiao; Wu, Ligang
2017-01-01
This book presents up-to-date research developments and novel methodologies on semi-Markovian jump systems (S-MJS). It presents solutions to a series of problems with new approaches for the control and filtering of S-MJS, including stability analysis, sliding mode control, dynamic output feedback control, robust filter design, and fault detection. A set of newly developed techniques such as piecewise analysis method, positively invariant set approach, event-triggered method, and cone complementary linearization approaches are presented. Control and Filtering for Semi-Markovian Jump Systems is a comprehensive reference for researcher and practitioners working in control engineering, system sciences and applied mathematics, and is also a useful source of information for senior undergraduates and graduates in these areas. The readers will benefit from some new concepts, new models and new methodologies with practical significance in control engineering and signal processing.
From BBGKY hierarchy to non-Markovian evolution equations
International Nuclear Information System (INIS)
Gerasimenko, V.I.; Shtyk, V.O.; Zagorodny, A.G.
2009-01-01
The problem of description of the evolution of the microscopic phase density and its generalizations is discussed. With this purpose, the sequence of marginal microscopic phase densities is introduced, and the appropriate BBGKY hierarchy for these microscopic distributions and their average values is formulated. The microscopic derivation of the generalized evolution equation for the average value of the microscopic phase density is given, and the non-Markovian generalization of the Fokker-Planck collision integral is proposed
International Nuclear Information System (INIS)
Nikitin, N. V.; Sotnikov, V.P.; Toms, K. S.
2015-01-01
A radically new class of Bell inequalities in Wigner’s form was obtained on the basis of Kolmorov’s axiomatization of probability theory and the hypothesis of locality. These inequalities take explicitly into account the dependence on time (time-dependent Bell inequalities in Wigner’s form). By using these inequalities, one can propose a means for experimentally testing Bohr’ complementarity principle in the relativistic region. The inequalities in question open broad possibilities for studying correlations of nonrelativistic and relativistic quantum systems in external fields. The violation of the time-dependent inequalities in quantum mechanics was studied by considering the behavior of a pair of anticorrelated spins in a constant external magnetic field and oscillations of neutral pseudoscalar mesons. The decay of a pseudoscalar particle to a fermion–antifermion pair is considered within quantum field theory. In order to test experimentally the inequalities proposed in the present study, it is not necessary to perform dedicated noninvasive measurements required in the Leggett–Garg approach, for example
QmeQ 1.0: An open-source Python package for calculations of transport through quantum dot devices
Kiršanskas, Gediminas; Pedersen, Jonas Nyvold; Karlström, Olov; Leijnse, Martin; Wacker, Andreas
2017-12-01
QmeQ is an open-source Python package for numerical modeling of transport through quantum dot devices with strong electron-electron interactions using various approximate master equation approaches. The package provides a framework for calculating stationary particle or energy currents driven by differences in chemical potentials or temperatures between the leads which are tunnel coupled to the quantum dots. The electronic structures of the quantum dots are described by their single-particle states and the Coulomb matrix elements between the states. When transport is treated perturbatively to lowest order in the tunneling couplings, the possible approaches are Pauli (classical), first-order Redfield, and first-order von Neumann master equations, and a particular form of the Lindblad equation. When all processes involving two-particle excitations in the leads are of interest, the second-order von Neumann approach can be applied. All these approaches are implemented in QmeQ. We here give an overview of the basic structure of the package, give examples of transport calculations, and outline the range of applicability of the different approximate approaches.
Energy Technology Data Exchange (ETDEWEB)
Nikitin, N. V., E-mail: nnikit@mail.cern.ch; Sotnikov, V.P., E-mail: sotnikov@physics.msu.ru [Moscow State University, Faculty of Physics (Russian Federation); Toms, K. S., E-mail: ktoms@mail.cern.ch [The University of New Mexico, Department of Physics and Astronomy (United States)
2015-10-15
A radically new class of Bell inequalities in Wigner’s form was obtained on the basis of Kolmorov’s axiomatization of probability theory and the hypothesis of locality. These inequalities take explicitly into account the dependence on time (time-dependent Bell inequalities in Wigner’s form). By using these inequalities, one can propose a means for experimentally testing Bohr’ complementarity principle in the relativistic region. The inequalities in question open broad possibilities for studying correlations of nonrelativistic and relativistic quantum systems in external fields. The violation of the time-dependent inequalities in quantum mechanics was studied by considering the behavior of a pair of anticorrelated spins in a constant external magnetic field and oscillations of neutral pseudoscalar mesons. The decay of a pseudoscalar particle to a fermion–antifermion pair is considered within quantum field theory. In order to test experimentally the inequalities proposed in the present study, it is not necessary to perform dedicated noninvasive measurements required in the Leggett–Garg approach, for example.
Error Distributions on Large Entangled States with Non-Markovian Dynamics
DEFF Research Database (Denmark)
McCutcheon, Dara; Lindner, Netanel H.; Rudolph, Terry
2014-01-01
We investigate the distribution of errors on a computationally useful entangled state generated via the repeated emission from an emitter undergoing strongly non-Markovian evolution. For emitter-environment coupling of pure-dephasing form, we show that the probability that a particular patten...... of errors occurs has a bound of Markovian form, and thus, accuracy threshold theorems based on Markovian models should be just as effective. Beyond the pure-dephasing assumption, though complicated error structures can arise, they can still be qualitatively bounded by a Markovian error model....
Improving the security of quantum protocols via commit-and-open
I.B. Damgård (Ivan); S. Fehr (Serge); C. Luneman; L. Salvail (Louis); C. Schaffner (Christian)
2009-01-01
htmlabstractWe consider two-party quantum protocols starting with a transmission of some random BB84 qubits followed by classical messages. We show a general compiler improving the security of such protocols: if the original protocol is secure against an almost honest adversary, then the
Czech Academy of Sciences Publication Activity Database
Méndez-Bermúdez, J. A.; Luna-Acosta, G. A.; Šeba, Petr; Pichugin, K. N.
2002-01-01
Roč. 66, č. 4 (2002), 046207/1-046207/7 ISSN 1063-651X Grant - others:CONACyT(MX) 26163-E Institutional research plan: CEZ:AV0Z1010914 Keywords : quantum transport * resonance Subject RIV: BE - Theoretical Physics Impact factor: 2.397, year: 2002
Stochastic quantization of a topological quantum mechanical model
International Nuclear Information System (INIS)
Antunes, Sergio; Krein, Gastao; Menezes, Gabriel; Svaiter, Nami Fux
2011-01-01
Full text: Stochastic quantization of complex actions has been extensively studied in the literature. In these models, a Markovian Langevin equation is used in order to study the quantization of such systems. In such papers, the advantages of the Markovian stochastic quantization method were explored and exposed. However, many drawbacks of the method were also pointed out, such as instability of the simulations with absence of convergence and sometimes convergence to the wrong limit. Indeed, although several alternative methods have been proposed to deal with interesting physical systems where the action is complex, these approaches do not suggest any general way of solving the particular difficulties that arise in each situation. Here, we wish to make contributions to the program of stochastic quantization of theories with imaginary action by investigating the consequences of a non-Markovian stochastic quantization in a particular situation, namely a quantum mechanical topological action. We analyze the Markovian stochastic quantization for a topological quantum mechanical action which is analog to a Maxwell-Chern-Simons action in the Weyl gauge. Afterwards we consider a Langevin equation with memory kernel and Einstein's relations with colored noise. We show that convergence towards equilibrium is achieved in both regimes. We also sketch a simple numerical analysis to investigate the possible advantages of non-Markovian procedure over the usual Markovian quantization. Both retarded Green's function for the diffusion problem are considered in such analysis. We show that, although the results indicated that the effect of memory kernel, as usually expected, is to delay the convergence to equilibrium, non-Markovian systems imply a faster decay compared to Markovian ones as well as smoother convergence to equilibrium. (author)
Quantum behaviour of open pumped and damped Bose-Hubbard trimers
Chianca, C. V.; Olsen, M. K.
2018-01-01
We propose and analyse analogs of optical cavities for atoms using three-well inline Bose-Hubbard models with pumping and losses. With one well pumped and one damped, we find that both the mean-field dynamics and the quantum statistics show a qualitative dependence on the choice of damped well. The systems we analyse remain far from equilibrium, although most do enter a steady-state regime. We find quadrature squeezing, bipartite and tripartite inseparability and entanglement, and states exhibiting the EPR paradox, depending on the parameter regimes. We also discover situations where the mean-field solutions of our models are noticeably different from the quantum solutions for the mean fields. Due to recent experimental advances, it should be possible to demonstrate the effects we predict and investigate in this article.
The thermodynamic meaning of local temperature of nonequilibrium open quantum systems
Ye, LvZhou; Zheng, Xiao; Yan, YiJing; Di Ventra, Massimiliano
2016-01-01
Measuring the local temperature of nanoscale systems out of equilibrium has emerged as a new tool to study local heating effects and other local thermal properties of systems driven by external fields. Although various experimental protocols and theoretical definitions have been proposed to determine the local temperature, the thermodynamic meaning of the measured or defined quantities remains unclear. By performing analytical and numerical analysis of bias-driven quantum dot systems both in ...
International Nuclear Information System (INIS)
Kuznetsova, E.I.; Fel'dman, Eh.B.
2006-01-01
Paper deals with a method of exact diagonalization of XY-Hamiltonian of s=1/2 alternated open chain of spins based on the Jordan-Wigner transform and analysis of dynamics of spinless fermions. One studied the many-quantum spin dynamics of alternated chains under high temperatures and calculated the intensities of many-quantum coherencies. One attacked the problem dealing with transfer of a quantum state from one end of the alternated chain to the opposite end. It is shown that perfect transfer of cubits may take place in alternated chains with larger number of spins in contrast to homogeneous chains [ru
Non-Markovian dynamics in the theory of full counting statistics
DEFF Research Database (Denmark)
Flindt, Christian; Braggio, A.; Novotny, Tomas
2007-01-01
generating function corresponding to the resulting non-Markovian rate equation and find that the measured current cumulants behave significantly differently compared to those of a Markovian transport process. Our findings provide a novel interpretation of noise suppression found in a number of systems....
Jo, Jea Woong; Kim, Younghoon; Choi, Jongmin; de Arquer, F. Pelayo Garcí a; Walters, Grant; Sun, Bin; Ouellette, Olivier; Kim, Junghwan; Proppe, Andrew H.; Quintero-Bermudez, Rafael; Fan, James; Xu, Jixian; Tan, Chih Shan; Voznyy, Oleksandr; Sargent, Edward H.
2017-01-01
The energy disorder that arises from colloidal quantum dot (CQD) polydispersity limits the open-circuit voltage (VOC) and efficiency of CQD photovoltaics. This energy broadening is significantly deteriorated today during CQD ligand exchange and film assembly. Here, a new solution-phase ligand exchange that, via judicious incorporation of reactivity-engineered additives, provides improved monodispersity in final CQD films is reported. It has been found that increasing the concentration of the less reactive species prevents CQD fusion and etching. As a result, CQD solar cells with a VOC of 0.7 V (vs 0.61 V for the control) for CQD films with exciton peak at 1.28 eV and a power conversion efficiency of 10.9% (vs 10.1% for the control) is achieved.
Jo, Jea Woong
2017-10-09
The energy disorder that arises from colloidal quantum dot (CQD) polydispersity limits the open-circuit voltage (VOC) and efficiency of CQD photovoltaics. This energy broadening is significantly deteriorated today during CQD ligand exchange and film assembly. Here, a new solution-phase ligand exchange that, via judicious incorporation of reactivity-engineered additives, provides improved monodispersity in final CQD films is reported. It has been found that increasing the concentration of the less reactive species prevents CQD fusion and etching. As a result, CQD solar cells with a VOC of 0.7 V (vs 0.61 V for the control) for CQD films with exciton peak at 1.28 eV and a power conversion efficiency of 10.9% (vs 10.1% for the control) is achieved.
Analysis and design of singular Markovian jump systems
Wang, Guoliang; Yan, Xinggang
2014-01-01
This monograph is an up-to-date presentation of the analysis and design of singular Markovian jump systems (SMJSs) in which the transition rate matrix of the underlying systems is generally uncertain, partially unknown and designed. The problems addressed include stability, stabilization, H∞ control and filtering, observer design, and adaptive control. applications of Markov process are investigated by using Lyapunov theory, linear matrix inequalities (LMIs), S-procedure and the stochastic Barbalat's Lemma, among other techniques.Features of the book include:·???????? study of the stability pr
Perturbative approach to non-Markovian stochastic Schroedinger equations
International Nuclear Information System (INIS)
Gambetta, Jay; Wiseman, H.M.
2002-01-01
In this paper we present a perturbative procedure that allows one to numerically solve diffusive non-Markovian stochastic Schroedinger equations, for a wide range of memory functions. To illustrate this procedure numerical results are presented for a classically driven two-level atom immersed in an environment with a simple memory function. It is observed that as the order of the perturbation is increased the numerical results for the ensemble average state ρ red (t) approach the exact reduced state found via Imamog-barlu ' s enlarged system method [Phys. Rev. A 50, 3650 (1994)
Thermalization and out-of-equilibrium dynamics in open quantum many-body systems
Energy Technology Data Exchange (ETDEWEB)
Buchhold, Michael
2015-06-30
In this thesis, we address both the question whether or not a quantum system driven away from equilibrium is able to relax to a thermal state, which fulfills detailed balance, and if one can identify universal behavior in the non-equilibrium relaxation dynamics. As a first realization of driven quantum systems out of equilibrium, we investigate a system of Ising spins, interacting with the quantized radiation field in an optical cavity. For multiple cavity modes, this system forms a highly entangled and frustrated state with infinite correlation times, known as a quantum spin glass. In the thermalized system, the features of the spin glass are mirrored onto the photon degrees of freedom, leading to an emergent photon glass phase. Exploiting the inherent photon loss of the cavity, we make predictions of possible measurements on the escaping photons, which contain detailed information of the state inside the cavity and allow for a precise, non-destructive measurement of the glass state. As a further set of non-equilibrium systems, we consider one-dimensional quantum fluids driven out of equilibrium, whose universal low energy theory is formed by the so-called Luttinger Liquid description. In this thesis, we derive for the first time a kinetic equation for interacting Luttinger Liquids, which describes the time evolution of the excitation densities for arbitrary initial states. The resonant character of the interaction makes a straightforward derivation of the kinetic equation, using Fermis golden rule, impossible and we have to develop non-perturbative techniques in the Keldysh framework. We derive a closed expression for the time evolution of the excitation densities in terms of self-energies and vertex corrections. Close to equilibrium, the kinetic equation describes the exponential decay of excitations, with a decay rate σ{sup R}=ImΣ{sup R}, determined by the self-energy at equilibrium. However, for long times τ, it also reveals the presence of dynamical slow
Quantum Coherent Dynamics Enhanced by Synchronization with Nonequilibrium Environments
Ishikawa, Akira; Okada, Ryo; Uchiyama, Kazuharu; Hori, Hirokazu; Kobayashi, Kiyoshi
2018-05-01
We report the discovery of the anomalous enhancement of quantum coherent dynamics (CD) due to a non-Markovian mechanism originating from not thermal-equilibrium phonon baths but nonequilibrium coherent phonons. CD is an elementary process for quantum phenomena in nanosystems, such as excitation transfer (ET) in semiconductor nanostructures and light-harvesting systems. CD occurs in homogeneous nanosystems because system inhomogeneity typically destroys coherence. In real systems, however, nanosystems behave as open systems surrounded by environments such as phonon systems. Typically, CD in inhomogeneous nanosystems is enhanced by the absorption and emission of thermal-equilibrium phonons, and the enhancement is described by the conventional master equation. On the other hand, CD is also enhanced by synchronization between population dynamics in nanosystems and coherent phonons; namely, coherent phonons, which are self-consistently induced by phase matching with Rabi oscillation, are fed back to enhance CD. This anomalous enhancement of CD essentially originates from the nonequilibrium and dynamical non-Markovian nature of coherent phonon environments, and the enhancement is firstly predicted by applying time-dependent projection operators to nonequilibrium and dynamical environments. Moreover, CD is discussed by considering ET from a donor to an acceptor. It is found that the enhancement of ET by synchronization with coherent phonons depends on the competition between the output time from a system to an acceptor and the formation time of coherent phonons. These findings in this study will stimulate the design and manipulation of CD via structured environments from the viewpoint of application to nano-photoelectronic devices.
Gaussian Error Correction of Quantum States in a Correlated Noisy Channel
DEFF Research Database (Denmark)
Lassen, Mikael Østergaard; Berni, Adriano; Madsen, Lars Skovgaard
2013-01-01
Noise is the main obstacle for the realization of fault-tolerant quantum information processing and secure communication over long distances. In this work, we propose a communication protocol relying on simple linear optics that optimally protects quantum states from non-Markovian or correlated...... noise. We implement the protocol experimentally and demonstrate the near-ideal protection of coherent and entangled states in an extremely noisy channel. Since all real-life channels are exhibiting pronounced non-Markovian behavior, the proposed protocol will have immediate implications in improving...... the performance of various quantum information protocols....
International Nuclear Information System (INIS)
Casati, G.; Chirikov, B.V.
1996-01-01
Various fluctuations in quantum systems with discrete spectrum are discussed, including recent unpublished results. Open questions and unexplained peculiarities of quantum fluctuations are formulated [ru
International Nuclear Information System (INIS)
Rufeil-Fiori, E.; Pastawski, H.M.
2009-01-01
The decay dynamics of a local excitation interacting with a non-Markovian environment, modeled by a semi-infinite tight-binding chain, is exactly evaluated. We identify distinctive regimes for the dynamics. Sequentially: (i) early quadratic decay of the initial-state survival probability, up to a spreading time t S , (ii) exponential decay described by a self-consistent Fermi Golden Rule, and (iii) asymptotic behavior governed by quantum diffusion through the return processes, leading to an inverse power law decay. At this last cross-over time t R a survival collapse becomes possible. This could reduce the survival probability by several orders of magnitude. The cross-over times t S and t R allow to assess the range of applicability of the Fermi Golden Rule and give the conditions for the observation of the Zeno and anti-Zeno effect.
Quantum coherence and entanglement control for atom-cavity systems
Shu, Wenchong
Coherence and entanglement play a significant role in the quantum theory. Ideal quantum systems, "closed" to the outside world, remain quantum forever and thus manage to retain coherence and entanglement. Real quantum systems, however, are open to the environment and are therefore susceptible to the phenomenon of decoherence and disentanglement which are major hindrances to the effectiveness of quantum information processing tasks. In this thesis we have theoretically studied the evolution of coherence and entanglement in quantum systems coupled to various environments. We have also studied ways and means of controlling the decay of coherence and entanglement. We have studied the exact qubit entanglement dynamics of some interesting initial states coupled to a high-Q cavity containing zero photon, one photon, two photons and many photons respectively. We have found that an initially correlated environmental state can serve as an enhancer for entanglement decay or generation processes. More precisely, we have demonstrated that the degree of entanglement, including its collapse as well as its revival times, can be significantly modified by the correlated structure of the environmental modes. We have also studied dynamical decoupling (DD) technique --- a prominent strategy of controlling decoherence and preserving entanglement in open quantum systems. We have analyzed several DD control methods applied to qubit systems that can eliminate the system-environment coupling and prolong the quantum coherence time. Particularly, we have proposed a new DD sequence consisting a set of designed control operators that can universally protected an unknown qutrit state against colored phase and amplitude environment noises. In addition, in a non-Markovian regime, we have reformulated the quantum state diffusion (QSD) equation to incorporate the effect of the external control fields. Without any assumptions on the system-environment coupling and the size of environment, we have
Rate processes with non-Markovian dynamical disorder
International Nuclear Information System (INIS)
Goychuk, Igor
2005-01-01
Rate processes with dynamical disorder are investigated within a simple framework provided by unidirectional electron transfer (ET) with fluctuating transfer rate. The rate fluctuations are assumed to be described by a non-Markovian stochastic jump process which reflects conformational dynamics of an electron transferring donor-acceptor molecular complex. A tractable analytical expression is obtained for the relaxation of the donor population (in the Laplace-transformed time domain) averaged over the stationary conformational fluctuations. The corresponding mean transfer time is also obtained in an analytical form. The case of two-state fluctuations is studied in detail for a model incorporating substate diffusion within one of the conformations. It is shown that an increase of the conformational diffusion time results in a gradual transition from the regime of fast modulation characterized by the averaged ET rate to the regime of quasistatic disorder. This transition occurs at the conformational mean residence time intervals fixed much less than the inverse of the corresponding ET rates. An explanation of this paradoxical effect is provided. Moreover, its presence is also manifested for the simplest, exactly solvable non-Markovian model with a biexponential distribution of the residence times in one of the conformations. The nontrivial conditions for this phenomenon to occur are found
Continued-fraction representation of the Kraus map for non-Markovian reservoir damping
van Wonderen, A. J.; Suttorp, L. G.
2018-04-01
Quantum dissipation is studied for a discrete system that linearly interacts with a reservoir of harmonic oscillators at thermal equilibrium. Initial correlations between system and reservoir are assumed to be absent. The dissipative dynamics as determined by the unitary evolution of system and reservoir is described by a Kraus map consisting of an infinite number of matrices. For all Laplace-transformed Kraus matrices exact solutions are constructed in terms of continued fractions that depend on the pair correlation functions of the reservoir. By performing factorizations in the Kraus map a perturbation theory is set up that conserves in arbitrary perturbative order both positivity and probability of the density matrix. The latter is determined by an integral equation for a bitemporal matrix and a finite hierarchy for Kraus matrices. In the lowest perturbative order this hierarchy reduces to one equation for one Kraus matrix. Its solution is given by a continued fraction of a much simpler structure as compared to the non-perturbative case. In the lowest perturbative order our non-Markovian evolution equations are applied to the damped Jaynes–Cummings model. From the solution for the atomic density matrix it is found that the atom may remain in the state of maximum entropy for a significant time span that depends on the initial energy of the radiation field.
Quantum optimal control theory and dynamic coupling in the spin-boson model
International Nuclear Information System (INIS)
Jirari, H.; Poetz, W.
2006-01-01
A Markovian master equation describing the evolution of open quantum systems in the presence of a time-dependent external field is derived within the Bloch-Redfield formalism. It leads to a system-bath interaction which depends on the control field. Optimal control theory is used to select control fields which allow accelerated or decelerated system relaxation, or suppression of relaxation (dissipation) altogether, depending on the dynamics we impose on the quantum system. The control-dissipation correlation and the nonperturbative treatment of the control field are essential for reaching this goal. The optimal control problem is formulated within Pontryagin's minimum principle and the resulting optimal differential system is solved numerically. As an application, we study the dynamics of a spin-boson model in the strong coupling regime under the influence of an external control field. We show how trapping the system in unstable quantum states and transfer of population can be achieved by optimized control of the dissipative quantum system. We also used optimal control theory to find the driving field that generates the quantum Z gate. In several cases studied, we find that the selected optimal field which reduces the purity loss significantly is a multicomponent low-frequency field including higher harmonics, all of which lie below the phonon cutoff frequency. Finally, in the undriven case we present an analytic result for the Lamb shift at zero temperature
Kelly, Aaron; Brackbill, Nora; Markland, Thomas E
2015-03-07
In this article, we show how Ehrenfest mean field theory can be made both a more accurate and efficient method to treat nonadiabatic quantum dynamics by combining it with the generalized quantum master equation framework. The resulting mean field generalized quantum master equation (MF-GQME) approach is a non-perturbative and non-Markovian theory to treat open quantum systems without any restrictions on the form of the Hamiltonian that it can be applied to. By studying relaxation dynamics in a wide range of dynamical regimes, typical of charge and energy transfer, we show that MF-GQME provides a much higher accuracy than a direct application of mean field theory. In addition, these increases in accuracy are accompanied by computational speed-ups of between one and two orders of magnitude that become larger as the system becomes more nonadiabatic. This combination of quantum-classical theory and master equation techniques thus makes it possible to obtain the accuracy of much more computationally expensive approaches at a cost lower than even mean field dynamics, providing the ability to treat the quantum dynamics of atomistic condensed phase systems for long times.
Energy Technology Data Exchange (ETDEWEB)
Kelly, Aaron; Markland, Thomas E., E-mail: tmarkland@stanford.edu [Department of Chemistry, Stanford University, Stanford, California 94305 (United States); Brackbill, Nora [Department of Physics, Stanford University, Stanford, California 94305 (United States)
2015-03-07
In this article, we show how Ehrenfest mean field theory can be made both a more accurate and efficient method to treat nonadiabatic quantum dynamics by combining it with the generalized quantum master equation framework. The resulting mean field generalized quantum master equation (MF-GQME) approach is a non-perturbative and non-Markovian theory to treat open quantum systems without any restrictions on the form of the Hamiltonian that it can be applied to. By studying relaxation dynamics in a wide range of dynamical regimes, typical of charge and energy transfer, we show that MF-GQME provides a much higher accuracy than a direct application of mean field theory. In addition, these increases in accuracy are accompanied by computational speed-ups of between one and two orders of magnitude that become larger as the system becomes more nonadiabatic. This combination of quantum-classical theory and master equation techniques thus makes it possible to obtain the accuracy of much more computationally expensive approaches at a cost lower than even mean field dynamics, providing the ability to treat the quantum dynamics of atomistic condensed phase systems for long times.
Algebraic Bethe ansatz for the quantum group invariant open XXZ chain at roots of unity
Directory of Open Access Journals (Sweden)
Azat M. Gainutdinov
2016-08-01
Full Text Available For generic values of q, all the eigenvectors of the transfer matrix of the Uqsl(2-invariant open spin-1/2 XXZ chain with finite length N can be constructed using the algebraic Bethe ansatz (ABA formalism of Sklyanin. However, when q is a root of unity (q=eiπ/p with integer p≥2, the Bethe equations acquire continuous solutions, and the transfer matrix develops Jordan cells. Hence, there appear eigenvectors of two new types: eigenvectors corresponding to continuous solutions (exact complete p-strings, and generalized eigenvectors. We propose general ABA constructions for these two new types of eigenvectors. We present many explicit examples, and we construct complete sets of (generalized eigenvectors for various values of p and N.
Open circuit potential monitored digital photocorrosion of GaAs/AlGaAs quantum well microstructures
Aithal, Srivatsa; Dubowski, Jan J.
2018-04-01
Nanostructuring of semiconductor wafers with an atomic level depth resolution is a challenging task, primarily due to the limited availability of instruments for in situ monitoring of such processes. Conventional digital etching relies on calibration procedures and cumbersome diagnostics applied between or at the end of etching cycles. We have developed a photoluminescence (PL) based process for monitoring in situ digital photocorrosion (DPC) of GaAs/AlGaAs microstructures at rates below 0.2 nm per cycle. In this communication, we demonstrate that DPC of GaAs/AlGaAs microstructures could be monitored with open circuit potential (OCP) measured between the photocorroding surface of a microstructure and an Ag/AgCl reference electrode installed in the sample chamber. The excellent correlation between the position of both PL and OCP maxima indicates that the DPC process could be monitored in situ for materials that do not necessarily exhibit measurable PL emission.
Beyond quantum gravity and its GUT extension: Problems still open in comprehending our World
Energy Technology Data Exchange (ETDEWEB)
Birkholz, Claus
2014-07-01
QG opens totally new horizons. Its group-theoretical approach is triggering the theoretician to reconsider his aged arguments having led into the current state of stagnation in fundamental physics. A ''New Physics'' is avoiding the short-cuts of the old one. The current string models ''beyond'' the ''standard'' model are blamed to be ''irrelevant'' for physics. QG/GUT are shown to represent ''string'' models as well. but working ones, in accord with experiment. Their ''exotic'' force type is suspected to trigger the creation of black holes and, possibly, new organic structures. The Copenhagen interpretation is corrected to respect irreducibility. Then, physics will be totally deterministic, with its ''parallel-world'' scenarios becoming mere fiction. The crucial new challenge is to reconcile ''motion'' with a static, deterministic world. A key role might play the human notion of a ''memory'', which is unilaterally directed towards past events. For more information on QG and GUT see www.q-grav.com.
Dupuy, Nicolas; Casula, Michele
2018-04-01
By means of the Jastrow correlated antisymmetrized geminal power (JAGP) wave function and quantum Monte Carlo (QMC) methods, we study the ground state properties of the oligoacene series, up to the nonacene. The JAGP is the accurate variational realization of the resonating-valence-bond (RVB) ansatz proposed by Pauling and Wheland to describe aromatic compounds. We show that the long-ranged RVB correlations built in the acenes' ground state are detrimental for the occurrence of open-shell diradical or polyradical instabilities, previously found by lower-level theories. We substantiate our outcome by a direct comparison with another wave function, tailored to be an open-shell singlet (OSS) for long-enough acenes. By comparing on the same footing the RVB and OSS wave functions, both optimized at a variational QMC level and further projected by the lattice regularized diffusion Monte Carlo method, we prove that the RVB wave function has always a lower variational energy and better nodes than the OSS, for all molecular species considered in this work. The entangled multi-reference RVB state acts against the electron edge localization implied by the OSS wave function and weakens the diradical tendency for higher oligoacenes. These properties are reflected by several descriptors, including wave function parameters, bond length alternation, aromatic indices, and spin-spin correlation functions. In this context, we propose a new aromatic index estimator suitable for geminal wave functions. For the largest acenes taken into account, the long-range decay of the charge-charge correlation functions is compatible with a quasi-metallic behavior.
Zero-crossing statistics for non-Markovian time series.
Nyberg, Markus; Lizana, Ludvig; Ambjörnsson, Tobias
2018-03-01
In applications spanning from image analysis and speech recognition to energy dissipation in turbulence and time-to failure of fatigued materials, researchers and engineers want to calculate how often a stochastic observable crosses a specific level, such as zero. At first glance this problem looks simple, but it is in fact theoretically very challenging, and therefore few exact results exist. One exception is the celebrated Rice formula that gives the mean number of zero crossings in a fixed time interval of a zero-mean Gaussian stationary process. In this study we use the so-called independent interval approximation to go beyond Rice's result and derive analytic expressions for all higher-order zero-crossing cumulants and moments. Our results agree well with simulations for the non-Markovian autoregressive model.
Zero-crossing statistics for non-Markovian time series
Nyberg, Markus; Lizana, Ludvig; Ambjörnsson, Tobias
2018-03-01
In applications spanning from image analysis and speech recognition to energy dissipation in turbulence and time-to failure of fatigued materials, researchers and engineers want to calculate how often a stochastic observable crosses a specific level, such as zero. At first glance this problem looks simple, but it is in fact theoretically very challenging, and therefore few exact results exist. One exception is the celebrated Rice formula that gives the mean number of zero crossings in a fixed time interval of a zero-mean Gaussian stationary process. In this study we use the so-called independent interval approximation to go beyond Rice's result and derive analytic expressions for all higher-order zero-crossing cumulants and moments. Our results agree well with simulations for the non-Markovian autoregressive model.
Sample efficient multiagent learning in the presence of Markovian agents
Chakraborty, Doran
2014-01-01
The problem of Multiagent Learning (or MAL) is concerned with the study of how intelligent entities can learn and adapt in the presence of other such entities that are simultaneously adapting. The problem is often studied in the stylized settings provided by repeated matrix games (a.k.a. normal form games). The goal of this book is to develop MAL algorithms for such a setting that achieve a new set of objectives which have not been previously achieved. In particular this book deals with learning in the presence of a new class of agent behavior that has not been studied or modeled before in a MAL context: Markovian agent behavior. Several new challenges arise when interacting with this particular class of agents. The book takes a series of steps towards building completely autonomous learning algorithms that maximize utility while interacting with such agents. Each algorithm is meticulously specified with a thorough formal treatment that elucidates its key theoretical properties.
Reliability Analysis of Wireless Sensor Networks Using Markovian Model
Directory of Open Access Journals (Sweden)
Jin Zhu
2012-01-01
Full Text Available This paper investigates reliability analysis of wireless sensor networks whose topology is switching among possible connections which are governed by a Markovian chain. We give the quantized relations between network topology, data acquisition rate, nodes' calculation ability, and network reliability. By applying Lyapunov method, sufficient conditions of network reliability are proposed for such topology switching networks with constant or varying data acquisition rate. With the conditions satisfied, the quantity of data transported over wireless network node will not exceed node capacity such that reliability is ensured. Our theoretical work helps to provide a deeper understanding of real-world wireless sensor networks, which may find its application in the fields of network design and topology control.
Implied Stopping Rules for American Basket Options from Markovian Projection
Bayer, Christian; Hä ppö lä , Juho; Tempone, Raul
2017-01-01
This work addresses the problem of pricing American basket options in a multivariate setting, which includes among others, the Bachelier and the Black-Scholes models. In high dimensions, nonlinear partial differential equation methods for solving the problem become prohibitively costly due to the curse of dimensionality. Instead, this work proposes to use a stopping rule that depends on the dynamics of a low-dimensional Markovian projection of the given basket of assets. It is shown that the ability to approximate the original value function by a lower-dimensional approximation is a feature of the dynamics of the system and is unaffected by the path-dependent nature of the American basket option. Assuming that we know the density of the forward process and using the Laplace approximation, we first efficiently evaluate the diffusion coefficient corresponding to the low-dimensional Markovian projection of the basket. Then, we approximate the optimal early-exercise boundary of the option by solving a Hamilton-Jacobi-Bellman partial differential equation in the projected, low-dimensional space. The resulting near-optimal early-exercise boundary is used to produce an exercise strategy for the high-dimensional option, thereby providing a lower bound for the price of the American basket option. A corresponding upper bound is also provided. These bounds allow to assess the accuracy of the proposed pricing method. Indeed, our approximate early-exercise strategy provides a straightforward lower bound for the American basket option price. Following a duality argument due to Rogers, we derive a corresponding upper bound solving only the low-dimensional optimal control problem. Numerically, we show the feasibility of the method using baskets with dimensions up to fifty. In these examples, the resulting option price relative errors are only of the order of few percent.
Implied Stopping Rules for American Basket Options from Markovian Projection
Bayer, Christian
2017-05-01
This work addresses the problem of pricing American basket options in a multivariate setting, which includes among others, the Bachelier and the Black-Scholes models. In high dimensions, nonlinear partial differential equation methods for solving the problem become prohibitively costly due to the curse of dimensionality. Instead, this work proposes to use a stopping rule that depends on the dynamics of a low-dimensional Markovian projection of the given basket of assets. It is shown that the ability to approximate the original value function by a lower-dimensional approximation is a feature of the dynamics of the system and is unaffected by the path-dependent nature of the American basket option. Assuming that we know the density of the forward process and using the Laplace approximation, we first efficiently evaluate the diffusion coefficient corresponding to the low-dimensional Markovian projection of the basket. Then, we approximate the optimal early-exercise boundary of the option by solving a Hamilton-Jacobi-Bellman partial differential equation in the projected, low-dimensional space. The resulting near-optimal early-exercise boundary is used to produce an exercise strategy for the high-dimensional option, thereby providing a lower bound for the price of the American basket option. A corresponding upper bound is also provided. These bounds allow to assess the accuracy of the proposed pricing method. Indeed, our approximate early-exercise strategy provides a straightforward lower bound for the American basket option price. Following a duality argument due to Rogers, we derive a corresponding upper bound solving only the low-dimensional optimal control problem. Numerically, we show the feasibility of the method using baskets with dimensions up to fifty. In these examples, the resulting option price relative errors are only of the order of few percent.
Non-Markovian Effects on the Brownian Motion of a Free Particle
Bolivar, A. O.
2010-01-01
Non-Markovian effects upon the Brownian movement of a free particle in the presence as well as in the absence of inertial force are investigated within the framework of Fokker-Planck equations (Rayleigh and Smoluchowski equations). More specifically, it is predicted that non-Markovian features can enhance the values of the mean square displacement and momentum, thereby assuring the mathematical property of differentiability of the these physically observable quantities.
Some performance measures for vacation models with a batch Markovian arrival process
Directory of Open Access Journals (Sweden)
Sadrac K. Matendo
1994-01-01
Full Text Available We consider a single server infinite capacity queueing system, where the arrival process is a batch Markovian arrival process (BMAP. Particular BMAPs are the batch Poisson arrival process, the Markovian arrival process (MAP, many batch arrival processes with correlated interarrival times and batch sizes, and superpositions of these processes. We note that the MAP includes phase-type (PH renewal processes and non-renewal processes such as the Markov modulated Poisson process (MMPP.
A framework for the direct evaluation of large deviations in non-Markovian processes
International Nuclear Information System (INIS)
Cavallaro, Massimo; Harris, Rosemary J
2016-01-01
We propose a general framework to simulate stochastic trajectories with arbitrarily long memory dependence and efficiently evaluate large deviation functions associated to time-extensive observables. This extends the ‘cloning’ procedure of Giardiná et al (2006 Phys. Rev. Lett. 96 120603) to non-Markovian systems. We demonstrate the validity of this method by testing non-Markovian variants of an ion-channel model and the totally asymmetric exclusion process, recovering results obtainable by other means. (letter)
Sandner, Raimar; Vukics, András
2014-09-01
++ libraries, GNU Scientific Library, Blitz++, FLENS, NumPy, SciPy Catalogue identifier of previous version: AELU_v1_0 Journal reference of previous version: Comput. Phys. Comm. 183 (2012) 1381 Does the new version supersede the previous version?: Yes Nature of problem: Definition of (open) composite quantum systems out of elementary building blocks [2,3]. Manipulation of such systems, with emphasis on dynamical simulations such as Master-equation evolution [4] and Monte Carlo wave-function simulation [5]. Solution method: Master equation, Monte Carlo wave-function method Reasons for new version: The new version is mainly a feature release, but it does correct some problems of the previous version, especially as regards the build system. Summary of revisions: We give an example for a typical Python script implementing the ring-cavity system presented in Sec. 3.3 of Ref. [2]: Restrictions: Total dimensionality of the system. Master equation-few thousands. Monte Carlo wave-function trajectory-several millions. Unusual features: Because of the heavy use of compile-time algorithms, compilation of programs written in the framework may take a long time and much memory (up to several GBs). Additional comments: The framework is not a program, but provides and implements an application-programming interface for developing simulations in the indicated problem domain. We use several C++11 features which limits the range of supported compilers (g++ 4.7, clang++ 3.1) Documentation, http://cppqed.sourceforge.net/ Running time: Depending on the magnitude of the problem, can vary from a few seconds to weeks. References: [1] Entry point: http://cppqed.sf.net [2] A. Vukics, C++QEDv2: The multi-array concept and compile-time algorithms in the definition of composite quantum systems, Comp. Phys. Comm. 183(2012)1381. [3] A. Vukics, H. Ritsch, C++QED: an object-oriented framework for wave-function simulations of cavity QED systems, Eur. Phys. J. D 44 (2007) 585. [4] H. J. Carmichael, An Open
Quantum capacity of Pauli channels with memory
International Nuclear Information System (INIS)
Huang Peng; He Guangqiang; Lu Yuan; Zeng Guihua
2011-01-01
The amount of coherent quantum information that can be reliably transmitted down the memory Pauli channels with Markovian correlated noise is investigated. Two methods for evaluating the quantum capacity of the memory Pauli channels are proposed to try to trace the memory effect on the transmissions of quantum information. We show that the evaluation of quantum capacity can be reduced to the calculation of the initial memory state of each successive transmission. Furthermore, we derive quantum capacities of the memory phase flip channel, bit flip channel and bit-phase flip channel. Also, a lower bound of the quantum capacity of the memory depolarizing channel is obtained. An increase of the degree of memory of the channels has a positive effect on the increase of their quantum capacities.
Achieving the Heisenberg limit in quantum metrology using quantum error correction.
Zhou, Sisi; Zhang, Mengzhen; Preskill, John; Jiang, Liang
2018-01-08
Quantum metrology has many important applications in science and technology, ranging from frequency spectroscopy to gravitational wave detection. Quantum mechanics imposes a fundamental limit on measurement precision, called the Heisenberg limit, which can be achieved for noiseless quantum systems, but is not achievable in general for systems subject to noise. Here we study how measurement precision can be enhanced through quantum error correction, a general method for protecting a quantum system from the damaging effects of noise. We find a necessary and sufficient condition for achieving the Heisenberg limit using quantum probes subject to Markovian noise, assuming that noiseless ancilla systems are available, and that fast, accurate quantum processing can be performed. When the sufficient condition is satisfied, a quantum error-correcting code can be constructed that suppresses the noise without obscuring the signal; the optimal code, achieving the best possible precision, can be found by solving a semidefinite program.
Quantum optics and fundamentals of quantum theory
International Nuclear Information System (INIS)
Dusek, M.
1997-01-01
Quantum optics has opened up new opportunities for experimental verification of the basic principles of quantum mechanics, particularly in the field of quantum interference and so-called non-local phenomena. The results of the experiments described provide unambiguous support to quantum mechanics. (Z.J.)
Approximate zero-variance Monte Carlo estimation of Markovian unreliability
International Nuclear Information System (INIS)
Delcoux, J.L.; Labeau, P.E.; Devooght, J.
1997-01-01
Monte Carlo simulation has become an important tool for the estimation of reliability characteristics, since conventional numerical methods are no more efficient when the size of the system to solve increases. However, evaluating by a simulation the probability of occurrence of very rare events means playing a very large number of histories of the system, which leads to unacceptable computation times. Acceleration and variance reduction techniques have to be worked out. We show in this paper how to write the equations of Markovian reliability as a transport problem, and how the well known zero-variance scheme can be adapted to this application. But such a method is always specific to the estimation of one quality, while a Monte Carlo simulation allows to perform simultaneously estimations of diverse quantities. Therefore, the estimation of one of them could be made more accurate while degrading at the same time the variance of other estimations. We propound here a method to reduce simultaneously the variance for several quantities, by using probability laws that would lead to zero-variance in the estimation of a mean of these quantities. Just like the zero-variance one, the method we propound is impossible to perform exactly. However, we show that simple approximations of it may be very efficient. (author)
Two parallel finite queues with simultaneous services and Markovian arrivals
Directory of Open Access Journals (Sweden)
S. R. Chakravarthy
1997-01-01
Full Text Available In this paper, we consider a finite capacity single server queueing model with two buffers, A and B, of sizes K and N respectively. Messages arrive one at a time according to a Markovian arrival process. Messages that arrive at buffer A are of a different type from the messages that arrive at buffer B. Messages are processed according to the following rules: 1. When buffer A(B has a message and buffer B(A is empty, then one message from A(B is processed by the server. 2. When both buffers, A and B, have messages, then two messages, one from A and one from B, are processed simultaneously by the server. The service times are assumed to be exponentially distributed with parameters that may depend on the type of service. This queueing model is studied as a Markov process with a large state space and efficient algorithmic procedures for computing various system performance measures are given. Some numerical examples are discussed.
Measuring the effective phonon density of states of a quantum dot in cavity quantum electrodynamics
DEFF Research Database (Denmark)
Madsen, Kristian Høeg; Nielsen, Per Kær; Kreiner-Møller, Asger
2013-01-01
We employ detuning-dependent decay-rate measurements of a quantum dot in a photonic-crystal cavity to study the influence of phonon dephasing in a solid-state quantum-electrodynamics experiment. The experimental data agree with a microscopic non-Markovian model accounting for dephasing from...... longitudinal acoustic phonons, and the analysis explains the difference between nonresonant cavity feeding in different nanocavities. From the comparison between experiment and theory we extract the effective phonon density of states experienced by the quantum dot in the nanocavity. This quantity determines...
Song, Ya-Ju; Tan, Qing-Shou; Kuang, Le-Man
2017-03-08
We investigate the possibility to control quantum evolution speed of a single dephasing qubit for arbitrary initial states by the use of periodic dynamical decoupling (PDD) pulses. It is indicated that the quantum speed limit time (QSLT) is determined by initial and final quantum coherence of the qubit, as well as the non-Markovianity of the system under consideration during the evolution when the qubit is subjected to a zero-temperature Ohmic-like dephasing reservoir. It is shown that final quantum coherence of the qubit and the non-Markovianity of the system can be modulated by PDD pulses. Our results show that for arbitrary initial states of the dephasing qubit with non-vanishing quantum coherence, PDD pulses can be used to induce potential acceleration of the quantum evolution in the short-time regime, while PDD pulses can lead to potential speedup and slow down in the long-time regime. We demonstrate that the effect of PDD on the QSLT for the Ohmic or sub-Ohmic spectrum (Markovian reservoir) is much different from that for the super-Ohmic spectrum (non-Markovian reservoir).
Markovian robots: Minimal navigation strategies for active particles
Nava, Luis Gómez; Großmann, Robert; Peruani, Fernando
2018-04-01
We explore minimal navigation strategies for active particles in complex, dynamical, external fields, introducing a class of autonomous, self-propelled particles which we call Markovian robots (MR). These machines are equipped with a navigation control system (NCS) that triggers random changes in the direction of self-propulsion of the robots. The internal state of the NCS is described by a Boolean variable that adopts two values. The temporal dynamics of this Boolean variable is dictated by a closed Markov chain—ensuring the absence of fixed points in the dynamics—with transition rates that may depend exclusively on the instantaneous, local value of the external field. Importantly, the NCS does not store past measurements of this value in continuous, internal variables. We show that despite the strong constraints, it is possible to conceive closed Markov chain motifs that lead to nontrivial motility behaviors of the MR in one, two, and three dimensions. By analytically reducing the complexity of the NCS dynamics, we obtain an effective description of the long-time motility behavior of the MR that allows us to identify the minimum requirements in the design of NCS motifs and transition rates to perform complex navigation tasks such as adaptive gradient following, detection of minima or maxima, or selection of a desired value in a dynamical, external field. We put these ideas in practice by assembling a robot that operates by the proposed minimalistic NCS to evaluate the robustness of MR, providing a proof of concept that is possible to navigate through complex information landscapes with such a simple NCS whose internal state can be stored in one bit. These ideas may prove useful for the engineering of miniaturized robots.
Efficiency versus speed in quantum heat engines: Rigorous constraint from Lieb-Robinson bound
Shiraishi, Naoto; Tajima, Hiroyasu
2017-08-01
A long-standing open problem whether a heat engine with finite power achieves the Carnot efficiency is investgated. We rigorously prove a general trade-off inequality on thermodynamic efficiency and time interval of a cyclic process with quantum heat engines. In a first step, employing the Lieb-Robinson bound we establish an inequality on the change in a local observable caused by an operation far from support of the local observable. This inequality provides a rigorous characterization of the following intuitive picture that most of the energy emitted from the engine to the cold bath remains near the engine when the cyclic process is finished. Using this description, we prove an upper bound on efficiency with the aid of quantum information geometry. Our result generally excludes the possibility of a process with finite speed at the Carnot efficiency in quantum heat engines. In particular, the obtained constraint covers engines evolving with non-Markovian dynamics, which almost all previous studies on this topic fail to address.
Mixed H2/H∞ Pitch Control of Wind Turbine with a Markovian Jump Model
DEFF Research Database (Denmark)
Lin, Zhongwei; Liu, Jizhen; Wu, Qiuwei
2016-01-01
This paper proposes a Markovian jump model and the corresponding H2 /H∞ control strategy for the wind turbine driven by the stochastic switching wind speed, which can be used to regulate the generator speed in order to harvest the rated power while reducing the fatigue loads on the mechanical side...... operating points of wind turbine can be divided into separate subregions correspondingly, where the model parameters and the control mode can be fixed in each mode. Then, the mixed H2 /H∞ control problem is discussed for such a class of Markovian jump wind turbine working above the rated wind speed...
Sojourn time distributions in a Markovian G-queue with batch arrival and batch removal
Directory of Open Access Journals (Sweden)
Yang Woo Shin
1999-01-01
Full Text Available We consider a single server Markovian queue with two types of customers; positive and negative, where positive customers arrive in batches and arrivals of negative customers remove positive customers in batches. Only positive customers form a queue and negative customers just reduce the system congestion by removing positive ones upon their arrivals. We derive the LSTs of sojourn time distributions for a single server Markovian queue with positive customers and negative customers by using the first passage time arguments for Markov chains.
Non-markovian effects in semiconductor cavity QED: Role of phonon-mediated processes
DEFF Research Database (Denmark)
Nielsen, Per Kær; Nielsen, Torben Roland; Lodahl, Peter
We show theoretically that the non-Markovian nature of the carrier-phonon interaction influences the dynamical properties of a semiconductor cavity QED system considerably, leading to asymmetries with respect to detuning in carrier lifetimes. This pronounced phonon effect originates from the pola......We show theoretically that the non-Markovian nature of the carrier-phonon interaction influences the dynamical properties of a semiconductor cavity QED system considerably, leading to asymmetries with respect to detuning in carrier lifetimes. This pronounced phonon effect originates from...... the polaritonic quasi-particle nature of the carrier-photon system interacting with the phonon reservoir....
Joint probability distributions for a class of non-Markovian processes.
Baule, A; Friedrich, R
2005-02-01
We consider joint probability distributions for the class of coupled Langevin equations introduced by Fogedby [H. C. Fogedby, Phys. Rev. E 50, 1657 (1994)]. We generalize well-known results for the single-time probability distributions to the case of N -time joint probability distributions. It is shown that these probability distribution functions can be obtained by an integral transform from distributions of a Markovian process. The integral kernel obeys a partial differential equation with fractional time derivatives reflecting the non-Markovian character of the process.
International Nuclear Information System (INIS)
Lou Xuyang; Cui Baotong
2009-01-01
In this paper, the problem of stochastic stability for a class of delayed neural networks of neutral type with Markovian jump parameters is investigated. The jumping parameters are modelled as a continuous-time, discrete-state Markov process. A sufficient condition guaranteeing the stochastic stability of the equilibrium point is derived for the Markovian jumping delayed neural networks (MJDNNs) with neutral type. The stability criterion not only eliminates the differences between excitatory and inhibitory effects on the neural networks, but also can be conveniently checked. The sufficient condition obtained can be essentially solved in terms of linear matrix inequality. A numerical example is given to show the effectiveness of the obtained results.
Le Gouët, Jean-Louis; Moiseev, Sergey
2012-06-01
Interaction of quantum radiation with multi-particle ensembles has sparked off intense research efforts during the past decade. Emblematic of this field is the quantum memory scheme, where a quantum state of light is mapped onto an ensemble of atoms and then recovered in its original shape. While opening new access to the basics of light-atom interaction, quantum memory also appears as a key element for information processing applications, such as linear optics quantum computation and long-distance quantum communication via quantum repeaters. Not surprisingly, it is far from trivial to practically recover a stored quantum state of light and, although impressive progress has already been accomplished, researchers are still struggling to reach this ambitious objective. This special issue provides an account of the state-of-the-art in a fast-moving research area that makes physicists, engineers and chemists work together at the forefront of their discipline, involving quantum fields and atoms in different media, magnetic resonance techniques and material science. Various strategies have been considered to store and retrieve quantum light. The explored designs belong to three main—while still overlapping—classes. In architectures derived from photon echo, information is mapped over the spectral components of inhomogeneously broadened absorption bands, such as those encountered in rare earth ion doped crystals and atomic gases in external gradient magnetic field. Protocols based on electromagnetic induced transparency also rely on resonant excitation and are ideally suited to the homogeneous absorption lines offered by laser cooled atomic clouds or ion Coulomb crystals. Finally off-resonance approaches are illustrated by Faraday and Raman processes. Coupling with an optical cavity may enhance the storage process, even for negligibly small atom number. Multiple scattering is also proposed as a way to enlarge the quantum interaction distance of light with matter. The
Network geometry with flavor: From complexity to quantum geometry
Bianconi, Ginestra; Rahmede, Christoph
2016-03-01
Network geometry is attracting increasing attention because it has a wide range of applications, ranging from data mining to routing protocols in the Internet. At the same time advances in the understanding of the geometrical properties of networks are essential for further progress in quantum gravity. In network geometry, simplicial complexes describing the interaction between two or more nodes play a special role. In fact these structures can be used to discretize a geometrical d -dimensional space, and for this reason they have already been widely used in quantum gravity. Here we introduce the network geometry with flavor s =-1 ,0 ,1 (NGF) describing simplicial complexes defined in arbitrary dimension d and evolving by a nonequilibrium dynamics. The NGF can generate discrete geometries of different natures, ranging from chains and higher-dimensional manifolds to scale-free networks with small-world properties, scale-free degree distribution, and nontrivial community structure. The NGF admits as limiting cases both the Bianconi-Barabási models for complex networks, the stochastic Apollonian network, and the recently introduced model for complex quantum network manifolds. The thermodynamic properties of NGF reveal that NGF obeys a generalized area law opening a new scenario for formulating its coarse-grained limit. The structure of NGF is strongly dependent on the dimensionality d . In d =1 NGFs grow complex networks for which the preferential attachment mechanism is necessary in order to obtain a scale-free degree distribution. Instead, for NGF with dimension d >1 it is not necessary to have an explicit preferential attachment rule to generate scale-free topologies. We also show that NGF admits a quantum mechanical description in terms of associated quantum network states. Quantum network states evolve by a Markovian dynamics and a quantum network state at time t encodes all possible NGF evolutions up to time t . Interestingly the NGF remains fully classical but
Energy Technology Data Exchange (ETDEWEB)
Sidles, John A; Jacky, Jonathan P [Department of Orthopaedics and Sports Medicine, Box 356500, School of Medicine, University of Washington, Seattle, WA, 98195 (United States); Garbini, Joseph L; Malcomb, Joseph R; Williamson, Austin M [Department of Mechanical Engineering, University of Washington, Seattle, WA 98195 (United States); Harrell, Lee E [Department of Physics, US Military Academy, West Point, NY 10996 (United States); Hero, Alfred O [Department of Electrical Engineering, University of Michigan, MI 49931 (United States); Norman, Anthony G [Department of Bioengineering, University of Washington, Seattle, WA 98195 (United States)], E-mail: sidles@u.washington.edu
2009-06-15
Practical recipes are presented for simulating high-temperature and nonequilibrium quantum spin systems that are continuously measured and controlled. The notion of a spin system is broadly conceived, in order to encompass macroscopic test masses as the limiting case of large-j spins. The simulation technique has three stages: first the deliberate introduction of noise into the simulation, then the conversion of that noise into an equivalent continuous measurement and control process, and finally, projection of the trajectory onto state-space manifolds having reduced dimensionality and possessing a Kaehler potential of multilinear algebraic form. These state-spaces can be regarded as ruled algebraic varieties upon which a projective quantum model order reduction (MOR) is performed. The Riemannian sectional curvature of ruled Kaehlerian varieties is analyzed, and proved to be non-positive upon all sections that contain a rule. These manifolds are shown to contain Slater determinants as a special case and their identity with Grassmannian varieties is demonstrated. The resulting simulation formalism is used to construct a positive P-representation for the thermal density matrix. Single-spin detection by magnetic resonance force microscopy (MRFM) is simulated, and the data statistics are shown to be those of a random telegraph signal with additive white noise. Larger-scale spin-dust models are simulated, having no spatial symmetry and no spatial ordering; the high-fidelity projection of numerically computed quantum trajectories onto low dimensionality Kaehler state-space manifolds is demonstrated. The reconstruction of quantum trajectories from sparse random projections is demonstrated, the onset of Donoho-Stodden breakdown at the Candes-Tao sparsity limit is observed, a deterministic construction for sampling matrices is given and methods for quantum state optimization by Dantzig selection are given.
International Nuclear Information System (INIS)
Sidles, John A; Jacky, Jonathan P; Garbini, Joseph L; Malcomb, Joseph R; Williamson, Austin M; Harrell, Lee E; Hero, Alfred O; Norman, Anthony G
2009-01-01
Practical recipes are presented for simulating high-temperature and nonequilibrium quantum spin systems that are continuously measured and controlled. The notion of a spin system is broadly conceived, in order to encompass macroscopic test masses as the limiting case of large-j spins. The simulation technique has three stages: first the deliberate introduction of noise into the simulation, then the conversion of that noise into an equivalent continuous measurement and control process, and finally, projection of the trajectory onto state-space manifolds having reduced dimensionality and possessing a Kaehler potential of multilinear algebraic form. These state-spaces can be regarded as ruled algebraic varieties upon which a projective quantum model order reduction (MOR) is performed. The Riemannian sectional curvature of ruled Kaehlerian varieties is analyzed, and proved to be non-positive upon all sections that contain a rule. These manifolds are shown to contain Slater determinants as a special case and their identity with Grassmannian varieties is demonstrated. The resulting simulation formalism is used to construct a positive P-representation for the thermal density matrix. Single-spin detection by magnetic resonance force microscopy (MRFM) is simulated, and the data statistics are shown to be those of a random telegraph signal with additive white noise. Larger-scale spin-dust models are simulated, having no spatial symmetry and no spatial ordering; the high-fidelity projection of numerically computed quantum trajectories onto low dimensionality Kaehler state-space manifolds is demonstrated. The reconstruction of quantum trajectories from sparse random projections is demonstrated, the onset of Donoho-Stodden breakdown at the Candes-Tao sparsity limit is observed, a deterministic construction for sampling matrices is given and methods for quantum state optimization by Dantzig selection are given.
Sidles, John A.; Garbini, Joseph L.; Harrell, Lee E.; Hero, Alfred O.; Jacky, Jonathan P.; Malcomb, Joseph R.; Norman, Anthony G.; Williamson, Austin M.
2009-06-01
Practical recipes are presented for simulating high-temperature and nonequilibrium quantum spin systems that are continuously measured and controlled. The notion of a spin system is broadly conceived, in order to encompass macroscopic test masses as the limiting case of large-j spins. The simulation technique has three stages: first the deliberate introduction of noise into the simulation, then the conversion of that noise into an equivalent continuous measurement and control process, and finally, projection of the trajectory onto state-space manifolds having reduced dimensionality and possessing a Kähler potential of multilinear algebraic form. These state-spaces can be regarded as ruled algebraic varieties upon which a projective quantum model order reduction (MOR) is performed. The Riemannian sectional curvature of ruled Kählerian varieties is analyzed, and proved to be non-positive upon all sections that contain a rule. These manifolds are shown to contain Slater determinants as a special case and their identity with Grassmannian varieties is demonstrated. The resulting simulation formalism is used to construct a positive P-representation for the thermal density matrix. Single-spin detection by magnetic resonance force microscopy (MRFM) is simulated, and the data statistics are shown to be those of a random telegraph signal with additive white noise. Larger-scale spin-dust models are simulated, having no spatial symmetry and no spatial ordering; the high-fidelity projection of numerically computed quantum trajectories onto low dimensionality Kähler state-space manifolds is demonstrated. The reconstruction of quantum trajectories from sparse random projections is demonstrated, the onset of Donoho-Stodden breakdown at the Candès-Tao sparsity limit is observed, a deterministic construction for sampling matrices is given and methods for quantum state optimization by Dantzig selection are given.
Liu, Peng; Wang, Qiong; Niu, Meixing; Wang, Dunyou
2017-08-10
Combining multi-level quantum mechanics theories and molecular mechanics with an explicit water model, we investigated the ring opening process of guanine damage by hydroxyl radical in aqueous solution. The detailed, atomic-level ring-opening mechanism along the reaction pathway was revealed in aqueous solution at the CCSD(T)/MM levels of theory. The potentials of mean force in aqueous solution were calculated at both the DFT/MM and CCSD(T)/MM levels of the theory. Our study found that the aqueous solution has a significant effect on this reaction in solution. In particular, by comparing the geometries of the stationary points between in gas phase and in aqueous solution, we found that the aqueous solution has a tremendous impact on the torsion angles much more than on the bond lengths and bending angles. Our calculated free-energy barrier height 31.6 kcal/mol at the CCSD(T)/MM level of theory agrees well with the one obtained based on gas-phase reaction profile and free energies of solvation. In addition, the reaction path in gas phase was also mapped using multi-level quantum mechanics theories, which shows a reaction barrier at 19.2 kcal/mol at the CCSD(T) level of theory, agreeing very well with a recent ab initio calculation result at 20.8 kcal/mol.
Diaz, Adrian; Thomas, Benjamin; Castillo, Paulo; Gross, Barry; Moshary, Fred
2016-05-01
Fugitive gas emissions from agricultural or industrial plants and gas pipelines are an important environmental concern as they contribute to the global increase of greenhouse gas concentrations. Moreover, they are also a security and safety concern because of possible risk of fire/explosion or toxicity. This study presents standoff detection of CH4 and N2O leaks using a quantum cascade laser open-path system that retrieves path-averaged concentrations by collecting the backscattered light from a remote hard target. It is a true standoff system and differs from other open-path systems that are deployed as point samplers or long-path transmission systems that use retroreflectors. The measured absorption spectra are obtained using a thermal intra-pulse frequency chirped DFB quantum cascade laser at ~7.7 µm wavelength range with ~200 ns pulse width. Making fast time resolved observations, the system simultaneously realizes high spectral resolution and range to the target, resulting in path-averaged concentration retrieval. The system performs measurements at high speed ~15 Hz and sufficient range (up to 45 m, ~148 feet) achieving an uncertainty of 3.1 % and normalized sensitivity of 3.3 ppm m Hz-1/2 for N2O and 9.3 % and normalized sensitivity of 30 ppm m Hz-1/2 for CH4 with a 0.31 mW average power QCL. Given these characteristics, this system is promising for mobile or multidirectional search and remote detection of gas leaks.
International Nuclear Information System (INIS)
Mineo, H.; Lin, S. H.; Fujimura, Y.; Xu, J.; Xu, R. X.; Yan, Y. J.
2013-01-01
Results of a theoretical study on non-Markov response for femtosecond laser-driven coherent ring currents in chiral aromatic molecules embedded in a condensed phase are presented. Coherent ring currents are generated by coherent excitation of a pair of quasi-degenerated π-electronic excited states. The coherent electronic dynamical behaviors are strongly influenced by interactions between the electronic system and phonon bath in a condensed phase. Here, the bath correlation time is not instantaneous but should be taken to be a finite time in ultrashort time-resolved experiments. In such a case, Markov approximation breaks down. A hierarchical master equation approach for an improved semiclassical Drude dissipation model was adopted to examine the non-Markov effects on ultrafast coherent electronic ring currents of (P)-2,2 ′ -biphenol in a condensed phase. Time evolution of the coherent ring current derived in the hierarchical master equation approach was calculated and compared with those in the Drude model in the Markov approximation and in the static limit. The results show how non-Markovian behaviors in quantum beat signals of ring currents depend on the Drude bath damping constant. Effects of temperatures on ultrafast coherent electronic ring currents are also clarified
Data-based Non-Markovian Model Inference
Ghil, Michael
2015-04-01
This talk concentrates on obtaining stable and efficient data-based models for simulation and prediction in the geosciences and life sciences. The proposed model derivation relies on using a multivariate time series of partial observations from a large-dimensional system, and the resulting low-order models are compared with the optimal closures predicted by the non-Markovian Mori-Zwanzig formalism of statistical physics. Multilayer stochastic models (MSMs) are introduced as both a very broad generalization and a time-continuous limit of existing multilevel, regression-based approaches to data-based closure, in particular of empirical model reduction (EMR). We show that the multilayer structure of MSMs can provide a natural Markov approximation to the generalized Langevin equation (GLE) of the Mori-Zwanzig formalism. A simple correlation-based stopping criterion for an EMR-MSM model is derived to assess how well it approximates the GLE solution. Sufficient conditions are given for the nonlinear cross-interactions between the constitutive layers of a given MSM to guarantee the existence of a global random attractor. This existence ensures that no blow-up can occur for a very broad class of MSM applications. The EMR-MSM methodology is first applied to a conceptual, nonlinear, stochastic climate model of coupled slow and fast variables, in which only slow variables are observed. The resulting reduced model with energy-conserving nonlinearities captures the main statistical features of the slow variables, even when there is no formal scale separation and the fast variables are quite energetic. Second, an MSM is shown to successfully reproduce the statistics of a partially observed, generalized Lokta-Volterra model of population dynamics in its chaotic regime. The positivity constraint on the solutions' components replaces here the quadratic-energy-preserving constraint of fluid-flow problems and it successfully prevents blow-up. This work is based on a close
Evolution of entropy in different types of non-Markovian three-level ...
Indian Academy of Sciences (India)
We solve the Nakajima–Zwanzig (NZ) non-Markovian master equation to study the dynamics of different types of three-level atomic systems interacting with bosonic Lorentzian reservoirs at zero temperature. Von Neumann entropy (S) is used to show the evolution of the degree of entanglement of the subsystems.
Stability of the Markov operator and synchronization of Markovian random products
Díaz, Lorenzo J.; Matias, Edgar
2018-05-01
We study Markovian random products on a large class of ‘m-dimensional’ connected compact metric spaces (including products of closed intervals and trees). We introduce a splitting condition, generalizing the classical one by Dubins and Freedman, and prove that this condition implies the asymptotic stability of the corresponding Markov operator and (exponentially fast) synchronization.
Large deviation estimates for a Non-Markovian Lévy generator of big order
International Nuclear Information System (INIS)
Léandre, Rémi
2015-01-01
We give large deviation estimates for a non-markovian convolution semi-group with a non-local generator of Lévy type of big order and with the standard normalisation of semi-classical analysis. No stochastic process is associated to this semi-group. (paper)
Evolution of entropy in different types of non-Markovian three-level ...
Indian Academy of Sciences (India)
Home; Journals; Pramana – Journal of Physics; Volume 86; Issue 5. Evolution of entropy in different types of non-Markovian three-level systems: Single reservoir vs. two independent reservoirs. JAGHOURI HAKIMEH SARBISHAEI MOHSEN JAVIDAN KUROSH. Regular Volume 86 Issue 5 May 2016 pp 997-1008 ...
Sidles, John A.; Garbini, Joseph L.; Harrell, Lee E.; Hero, Alfred O.; Jacky, Jonathan P.; Malcomb, Joseph R.; Norman, Anthony G.; Williamson, Austin M.
2008-01-01
This article presents numerical recipes for simulating high-temperature and non-equilibrium quantum spin systems that are continuously measured and controlled. The notion of a spin system is broadly conceived, in order to encompass macroscopic test masses as the limiting case of large-j spins. The simulation technique has three stages: first the deliberate introduction of noise into the simulation, then the conversion of that noise into an equivalent continuous measurement and control process...
Yan, YiJing
2014-02-07
This work establishes a strongly correlated system-and-bath dynamics theory, the many-dissipaton density operators formalism. It puts forward a quasi-particle picture for environmental influences. This picture unifies the physical descriptions and algebraic treatments on three distinct classes of quantum environments, electron bath, phonon bath, and two-level spin or exciton bath, as their participating in quantum dissipation processes. Dynamical variables for theoretical description are no longer just the reduced density matrix for system, but remarkably also those for quasi-particles of bath. The present theoretical formalism offers efficient and accurate means for the study of steady-state (nonequilibrium and equilibrium) and real-time dynamical properties of both systems and hybridizing environments. It further provides universal evaluations, exact in principle, on various correlation functions, including even those of environmental degrees of freedom in coupling with systems. Induced environmental dynamics could be reflected directly in experimentally measurable quantities, such as Fano resonances and quantum transport current shot noise statistics.
Schmidt number for quantum operations
International Nuclear Information System (INIS)
Huang Siendong
2006-01-01
To understand how entangled states behave under local quantum operations is an open problem in quantum-information theory. The Jamiolkowski isomorphism provides a natural way to study this problem in terms of quantum states. We introduce the Schmidt number for quantum operations by this duality and clarify how the Schmidt number of a quantum state changes under a local quantum operation. Some characterizations of quantum operations with Schmidt number k are also provided
A characterization of Markovian homogeneous multicomponent Gaussian fields
International Nuclear Information System (INIS)
Ekhaguere, G.O.S.
1980-01-01
Necessary and sufficient conditions are given for a certain class of homogeneous multicomponent Gaussian generalized stochastic fields to possess a Markov property equivalent to Nelson's. The class of Markov fields so characterized has a as a cubclass the class of Markov fields which lead by Nelson's Reconstruction Theorem to some covariant (free) quantum fields. (orig.)
2012-09-27
ultralong lifetimes and their tomographic state analysis Phys. Rev. Lett. 92 220402 [7] Resch K J, Walther P and Zeilinger A 2005 Full characterization...of a three-photon Greenberger– Horne– Zeilinger state using quantum state tomography Phys. Rev. Lett. 94 070402 [8] Häffner H et al 2005 Scalable...Iterative algorithm for reconstruction of entangled states Phys. Rev. A 63 040303 [74] Molina-Terriza G, Vaziri A, Řeháček J, Hradil Z and Zeilinger
Cendagorta, Joseph R; Bačić, Zlatko; Tuckerman, Mark E
2018-03-14
We introduce a scheme for approximating quantum time correlation functions numerically within the Feynman path integral formulation. Starting with the symmetrized version of the correlation function expressed as a discretized path integral, we introduce a change of integration variables often used in the derivation of trajectory-based semiclassical methods. In particular, we transform to sum and difference variables between forward and backward complex-time propagation paths. Once the transformation is performed, the potential energy is expanded in powers of the difference variables, which allows us to perform the integrals over these variables analytically. The manner in which this procedure is carried out results in an open-chain path integral (in the remaining sum variables) with a modified potential that is evaluated using imaginary-time path-integral sampling rather than requiring the generation of a large ensemble of trajectories. Consequently, any number of path integral sampling schemes can be employed to compute the remaining path integral, including Monte Carlo, path-integral molecular dynamics, or enhanced path-integral molecular dynamics. We believe that this approach constitutes a different perspective in semiclassical-type approximations to quantum time correlation functions. Importantly, we argue that our approximation can be systematically improved within a cumulant expansion formalism. We test this approximation on a set of one-dimensional problems that are commonly used to benchmark approximate quantum dynamical schemes. We show that the method is at least as accurate as the popular ring-polymer molecular dynamics technique and linearized semiclassical initial value representation for correlation functions of linear operators in most of these examples and improves the accuracy of correlation functions of nonlinear operators.
Cendagorta, Joseph R.; Bačić, Zlatko; Tuckerman, Mark E.
2018-03-01
We introduce a scheme for approximating quantum time correlation functions numerically within the Feynman path integral formulation. Starting with the symmetrized version of the correlation function expressed as a discretized path integral, we introduce a change of integration variables often used in the derivation of trajectory-based semiclassical methods. In particular, we transform to sum and difference variables between forward and backward complex-time propagation paths. Once the transformation is performed, the potential energy is expanded in powers of the difference variables, which allows us to perform the integrals over these variables analytically. The manner in which this procedure is carried out results in an open-chain path integral (in the remaining sum variables) with a modified potential that is evaluated using imaginary-time path-integral sampling rather than requiring the generation of a large ensemble of trajectories. Consequently, any number of path integral sampling schemes can be employed to compute the remaining path integral, including Monte Carlo, path-integral molecular dynamics, or enhanced path-integral molecular dynamics. We believe that this approach constitutes a different perspective in semiclassical-type approximations to quantum time correlation functions. Importantly, we argue that our approximation can be systematically improved within a cumulant expansion formalism. We test this approximation on a set of one-dimensional problems that are commonly used to benchmark approximate quantum dynamical schemes. We show that the method is at least as accurate as the popular ring-polymer molecular dynamics technique and linearized semiclassical initial value representation for correlation functions of linear operators in most of these examples and improves the accuracy of correlation functions of nonlinear operators.
International Nuclear Information System (INIS)
Piecuch, Piotr; Wloch, Marta; Gour, Jeffrey R.; Dean, David J.; Papenbrock, Thomas; Hjorth-Jensen, Morten
2005-01-01
We review basic elements of the single-reference coupled-cluster theory and discuss large scale ab initio calculations of ground and excited states of 15O, 16O, and 17O using coupled-cluster methods and algorithms developed in quantum chemistry. By using realistic two-body interactions and the renormalized form of the Hamiltonian obtained with a no-core G-matrix approach, we obtain the converged results for 16O and promising preliminary results for 15O and 17O at the level of two-body interactions. The calculated properties other than energies include matter density, charge radius, and charge form factor. The relatively low costs of coupled-cluster calculations, which are characterized by the low-order polynomial scaling with the system size, enable us to probe large model spaces with up to 7 or 8 major oscillator shells, for which non-truncated shell-model calculations for nuclei with A = 15 17 active particles are presently not possible. We argue that the use of coupled-cluster methods and computer algorithms developed by quantum chemists to calculate properties of nuclei is an important step toward the development of accurate and affordable many-body theories that cross the boundaries of various physical sciences
Khrennikova, Polina; Haven, Emmanuel; Khrennikov, Andrei
2014-04-01
The Gorini-Kossakowski-Sudarshan-Lindblad equation allows us to model the process of decision making in US elections. The crucial point we attempt to make is that the voter's mental state can be represented as a superposition of two possible choices for either republicans or democrats. However, reality dictates a more complicated situation: typically a voter participates in two elections, i.e. the congress and the presidential elections. In both elections the voter has to decide between two choices. This very feature of the US election system requires that the mental state is represented by a 2-qubit state corresponding to the superposition of 4 different choices. The main issue is to describe the dynamics of the voters' mental states taking into account the mental and political environment. What is novel in this paper is that we apply the theory of open quantum systems to social science. The quantum master equation describes the resolution of uncertainty (represented in the form of superposition) to a definite choice.
Natural approach to quantum dissipation
Taj, David; Öttinger, Hans Christian
2015-12-01
The dissipative dynamics of a quantum system weakly coupled to one or several reservoirs is usually described in terms of a Lindblad generator. The popularity of this approach is certainly due to the linear character of the latter. However, while such linearity finds justification from an underlying Hamiltonian evolution in some scaling limit, it does not rely on solid physical motivations at small but finite values of the coupling constants, where the generator is typically used for applications. The Markovian quantum master equations we propose are instead supported by very natural thermodynamic arguments. They themselves arise from Markovian master equations for the system and the environment which preserve factorized states and mean energy and generate entropy at a non-negative rate. The dissipative structure is driven by an entropic map, called modular, which introduces nonlinearity. The generated modular dynamical semigroup (MDS) guarantees for the positivity of the time evolved state the correct steady state properties, the positivity of the entropy production, and a positive Onsager matrix with symmetry relations arising from Green-Kubo formulas. We show that the celebrated Davies Lindblad generator, obtained through the Born and the secular approximations, generates a MDS. In doing so we also provide a nonlinear MDS which is supported by a weak coupling argument and is free from the limitations of the Davies generator.
Quantum tight-binding chains with dissipative coupling
International Nuclear Information System (INIS)
Mogilevtsev, D; Slepyan, G Ya; Garusov, E; Kilin, S Ya; Korolkova, N
2015-01-01
We present a one-dimensional tight-binding chain of two-level systems coupled only through common dissipative Markovian reservoirs. This quantum chain can demonstrate anomalous thermodynamic behavior contradicting Fourier law. Population dynamics of individual systems of the chain is polynomial with the order determined by the initial state of the chain. The chain can simulate classically hard problems, such as multi-dimensional random walks. (paper)
Heat flux and quantum correlations in dissipative cascaded systems
Lorenzo, Salvatore; Farace, Alessandro; Ciccarello, Francesco; Palma, G. Massimo; Giovannetti, Vittorio
2015-02-01
We study the dynamics of heat flux in the thermalization process of a pair of identical quantum systems that interact dissipatively with a reservoir in a cascaded fashion. Despite that the open dynamics of the bipartite system S is globally Lindbladian, one of the subsystems "sees" the reservoir in a state modified by the interaction with the other subsystem and hence it undergoes a non-Markovian dynamics. As a consequence, the heat flow exhibits a nonexponential time behavior which can greatly deviate from the case where each party is independently coupled to the reservoir. We investigate both thermal and correlated initial states of S and show that the presence of correlations at the beginning can considerably affect the heat-flux rate. We carry out our study in two paradigmatic cases—a pair of harmonic oscillators with a reservoir of bosonic modes and two qubits with a reservoir of fermionic modes—and compare the corresponding behaviors. In the case of qubits and for initial thermal states, we find that the trace distance discord is at any time interpretable as the correlated contribution to the total heat flux.
DEFF Research Database (Denmark)
Settnes, Mikkel; Nielsen, Per Kær; Lund, Anders Mølbjerg
2013-01-01
perform microscopic calculations of the effect treating the wetting layer as a non-Markovian reservoir interacting with the coupled quantum dot-cavity system through Coulomb interactions. Experimentally, cavity feeding has been observed in the asymmetric detuning range of -10 to +45 meV. We show...
Chin, Alex
Singlet fission (SF) is an ultrafast process in which a singlet exciton spontaneously converts into a pair of entangled triplet excitons on neighbouring organic molecules. As a mechanism of multiple exciton generation, it has been suggested as a way to increase the efficiency of organic photovoltaic devices, and its underlying photophysics across a wide range of molecules and materials has attracted significant theoretical attention. Recently, a number of studies using ultrafast nonlinear optics have underscored the importance of intramolecular vibrational dynamics in efficient SF systems, prompting a need for methods capable of simulating open quantum dynamics in the presence of highly structured and strongly coupled environments. Here, a combination of ab initio electronic structure techniques and a new tensor-network methodology for simulating open vibronic dynamics is presented and applied to a recently synthesised dimer of pentacene (DP-Mes). We show that ultrafast (300 fs) SF in this system is driven entirely by symmetry breaking vibrations, and our many-body approach enables the real-time identification and tracking of the ''functional' vibrational dynamics and the role of the ''bath''-like parts of the environment. Deeper analysis of the emerging wave functions points to interesting links between the time at which parts of the environment become relevant to the SF process and the optimal topology of the tensor networks, highlighting the additional insight provided by moving the problem into the natural language of correlated quantum states and how this could lead to simulations of much larger multichromophore systems Supported by The Winton Programme for the Physics of Sustainability.
Non-Markovian phonon dephasing of a quantum dot in a photonic-crystal nanocavity
DEFF Research Database (Denmark)
Madsen, Kristian Høeg; Nielsen, Per Kær; Kreiner-Møller, Asger
2012-01-01
this model, we are able to explain the broadband enhancement in an L3 cavity, and the quantitative difference compared to the AL-cavity arises from a larger background decay rate in the AL-cavity due to the presence of leaky radiation modes. The concept of the effective phonon density of states (DOS...
Quantum coherence and non-Markovianity of an atom in a dissipative cavity under weak measurement
Liu, Yu; Zou, Hong-Mei; Fang, Mao-Fa
2018-01-01
Not Available Project supported by the Scientific Research Project of Hunan Provincial Education Department, China (Grant No. 16C0949), the Hunan Provincial Innovation Foundation for Postgraduate, China (Grant No. CX2017B177), the National Natural Science Foundation of China (Grant No. 11374096), and the Doctoral Science Foundation of Hunan Normal University, China.
Tao, Lei; Sun, Kang; Khan, M Amir; Miller, David J; Zondlo, Mark A
2012-12-17
A compact and portable open-path sensor for simultaneous detection of atmospheric N(2)O and CO has been developed with a 4.5 μm quantum cascade laser (QCL). An in-line acetylene (C(2)H(2)) gas reference cell allows for continuous monitoring of the sensor drift and calibration in rapidly changing field environments and thereby allows for open-path detection at high precision and stability. Wavelength modulation spectroscopy (WMS) is used to detect simultaneously both the second and fourth harmonic absorption spectra with an optimized dual modulation amplitude scheme. Multi-harmonic spectra containing atmospheric N(2)O, CO, and the reference C(2)H(2) signals are fit in real-time (10 Hz) by combining a software-based lock-in amplifier with a computationally fast numerical model for WMS. The sensor consumes ~50 W of power and has a mass of ~15 kg. Precision of 0.15 ppbv N(2)O and 0.36 ppbv CO at 10 Hz under laboratory conditions was demonstrated. The sensor has been deployed for extended periods in the field. Simultaneous N(2)O and CO measurements distinguished between natural and fossil fuel combustion sources of N(2)O, an important greenhouse gas with poorly quantified emissions in space and time.
Sufficient conditions for positivity of non-Markovian master equations with Hermitian generators
International Nuclear Information System (INIS)
Wilkie, Joshua; Wong Yinmei
2009-01-01
We use basic physical motivations to develop sufficient conditions for positive semidefiniteness of the reduced density matrix for generalized non-Markovian integrodifferential Lindblad-Kossakowski master equations with Hermitian generators. We show that it is sufficient for the memory function to be the Fourier transform of a real positive symmetric frequency density function with certain properties. These requirements are physically motivated, and are more general and more easily checked than previously stated sufficient conditions. We also explore the decoherence dynamics numerically for some simple models using the Hadamard representation of the propagator. We show that the sufficient conditions are not necessary conditions. We also show that models exist in which the long time limit is in part determined by non-Markovian effects
Population dynamics of excited atoms in non-Markovian environments at zero and finite temperature
International Nuclear Information System (INIS)
Zou Hong-Mei; Fang Mao-Fa
2015-01-01
The population dynamics of a two-atom system, which is in two independent Lorentzian reservoirs or in two independent Ohmic reservoirs respectively, where the reservoirs are at zero temperature or finite temperature, is studied by using the time-convolutionless master-equation method. The influences of the characteristics and temperature of a non-Markovian environment on the population of the excited atoms are analyzed. We find that the population trapping of the excited atoms is related to the characteristics and the temperature of the non-Markovian environment. The results show that, at zero temperature, the two atoms can be effectively trapped in the excited state both in the Lorentzian reservoirs and in the Ohmic reservoirs. At finite temperature, the population of the excited atoms will quickly decay to a nonzero value. (paper)
Kinetics of subdiffusion-assisted reactions: non-Markovian stochastic Liouville equation approach
International Nuclear Information System (INIS)
Shushin, A I
2005-01-01
Anomalous specific features of the kinetics of subdiffusion-assisted bimolecular reactions (time-dependence, dependence on parameters of systems, etc) are analysed in detail with the use of the non-Markovian stochastic Liouville equation (SLE), which has been recently derived within the continuous-time random-walk (CTRW) approach. In the CTRW approach, subdiffusive motion of particles is modelled by jumps whose onset probability distribution function is of a long-tailed form. The non-Markovian SLE allows for rigorous describing of some peculiarities of these reactions; for example, very slow long-time behaviour of the kinetics, non-analytical dependence of the reaction rate on the reactivity of particles, strong manifestation of fluctuation kinetics showing itself in very slowly decreasing behaviour of the kinetics at very long times, etc
Bulk-mediated surface diffusion: non-Markovian desorption and biased behaviour in an infinite system
International Nuclear Information System (INIS)
Revelli, Jorge A; Budde, Carlos E; Wio, Horacio S
2005-01-01
We analyse the dynamics of adsorbed molecules within the bulk-mediated surface diffusion framework. We consider that the particle's desorption mechanism is characterized by a non-Markovian process, while the particle's adsorption and its motion in the bulk are governed by Markovian dynamics, and include the effect of an external field in the form of a bias in the normal motion to the surface. We study this system for the diffusion of particles in a semi-infinite lattice, analysing the conditional probability to find the system on the reference absorptive plane as well as the surface dispersion as functions of time. The agreement between numerical and analytical asymptotic results is discussed
Robust extended Kalman filter of discrete-time Markovian jump nonlinear system under uncertain noise
International Nuclear Information System (INIS)
Zhu, Jin; Park, Jun Hong; Lee, Kwan Soo; Spiryagin, Maksym
2008-01-01
This paper examines the problem of robust extended Kalman filter design for discrete -time Markovian jump nonlinear systems with noise uncertainty. Because of the existence of stochastic Markovian switching, the state and measurement equations of underlying system are subject to uncertain noise whose covariance matrices are time-varying or un-measurable instead of stationary. First, based on the expression of filtering performance deviation, admissible uncertainty of noise covariance matrix is given. Secondly, two forms of noise uncertainty are taken into account: Non- Structural and Structural. It is proved by applying game theory that this filter design is a robust mini-max filter. A numerical example shows the validity of the method
Joint Probability Distributions for a Class of Non-Markovian Processes
Baule, A.; Friedrich, R.
2004-01-01
We consider joint probability distributions for the class of coupled Langevin equations introduced by Fogedby [H.C. Fogedby, Phys. Rev. E 50, 1657 (1994)]. We generalize well-known results for the single time probability distributions to the case of N-time joint probability distributions. It is shown that these probability distribution functions can be obtained by an integral transform from distributions of a Markovian process. The integral kernel obeys a partial differential equation with fr...
Directory of Open Access Journals (Sweden)
Hua Yang
2012-01-01
Full Text Available We are concerned with the stochastic differential delay equations with Poisson jump and Markovian switching (SDDEsPJMSs. Most SDDEsPJMSs cannot be solved explicitly as stochastic differential equations. Therefore, numerical solutions have become an important issue in the study of SDDEsPJMSs. The key contribution of this paper is to investigate the strong convergence between the true solutions and the numerical solutions to SDDEsPJMSs when the drift and diffusion coefficients are Taylor approximations.
Nelson's stochastic quantization of free linearized gravitational field and its Markovian structure
International Nuclear Information System (INIS)
Lim, S.C.
1983-05-01
It is shown that by applying Nelson's stochastic quantization scheme to free linearized gravitational field tensor one can associate with the resulting stochastic system a stochastic tensor field which coincides with the ''space'' part of the Riemannian tensor in Euclidean space-time. However, such a stochastic field fails to satisfy the Markov property. Instead, it satisfies the reflection positivity. The Markovian structure of the stochastic fields associated with the electromagnetic field is also discussed. (author)
Directory of Open Access Journals (Sweden)
Xueling Jiang
2014-01-01
Full Text Available The problem of adaptive asymptotical synchronization is discussed for the stochastic complex dynamical networks with time-delay and Markovian switching. By applying the stochastic analysis approach and the M-matrix method for stochastic complex networks, several sufficient conditions to ensure adaptive asymptotical synchronization for stochastic complex networks are derived. Through the adaptive feedback control techniques, some suitable parameters update laws are obtained. Simulation result is provided to substantiate the effectiveness and characteristics of the proposed approach.
The simulation of the non-Markovian behaviour of a two-level system
Semina, I.; Petruccione, F.
2016-05-01
Non-Markovian relaxation dynamics of a two-level system is studied with the help of the non-linear stochastic Schrödinger equation with coloured Ornstein-Uhlenbeck noise. This stochastic Schrödinger equation is investigated numerically with an adapted Platen scheme. It is shown, that the memory effects have a significant impact to the dynamics of the system.
Description of quantum-mechanical motion by using the formalism of non-Markov stochastic process
International Nuclear Information System (INIS)
Skorobogatov, G.A.; Svertilov, S.I.
1999-01-01
The principle possibilities of mathematical modeling of quantum mechanical motion by the theory of a real stochastic processes is considered. The set of equations corresponding to the simplest case of a two-level system undergoing transitions under the influence of electromagnetic field are obtained. It is shown that quantum-mechanical processes are purely discrete processes of non-Markovian type. They are continuous processes in the space of probability amplitudes and posses the properties of quantum Markovity. The formulation of quantum mechanics in terms of the theory of stochastic processes is necessary for its generalization on small space-time intervals [ru
A Markovian Entropy Measure for the Analysis of Calcium Activity Time Series.
Marken, John P; Halleran, Andrew D; Rahman, Atiqur; Odorizzi, Laura; LeFew, Michael C; Golino, Caroline A; Kemper, Peter; Saha, Margaret S
2016-01-01
Methods to analyze the dynamics of calcium activity often rely on visually distinguishable features in time series data such as spikes, waves, or oscillations. However, systems such as the developing nervous system display a complex, irregular type of calcium activity which makes the use of such methods less appropriate. Instead, for such systems there exists a class of methods (including information theoretic, power spectral, and fractal analysis approaches) which use more fundamental properties of the time series to analyze the observed calcium dynamics. We present a new analysis method in this class, the Markovian Entropy measure, which is an easily implementable calcium time series analysis method which represents the observed calcium activity as a realization of a Markov Process and describes its dynamics in terms of the level of predictability underlying the transitions between the states of the process. We applied our and other commonly used calcium analysis methods on a dataset from Xenopus laevis neural progenitors which displays irregular calcium activity and a dataset from murine synaptic neurons which displays activity time series that are well-described by visually-distinguishable features. We find that the Markovian Entropy measure is able to distinguish between biologically distinct populations in both datasets, and that it can separate biologically distinct populations to a greater extent than other methods in the dataset exhibiting irregular calcium activity. These results support the benefit of using the Markovian Entropy measure to analyze calcium dynamics, particularly for studies using time series data which do not exhibit easily distinguishable features.
A Markovian Entropy Measure for the Analysis of Calcium Activity Time Series.
Directory of Open Access Journals (Sweden)
John P Marken
Full Text Available Methods to analyze the dynamics of calcium activity often rely on visually distinguishable features in time series data such as spikes, waves, or oscillations. However, systems such as the developing nervous system display a complex, irregular type of calcium activity which makes the use of such methods less appropriate. Instead, for such systems there exists a class of methods (including information theoretic, power spectral, and fractal analysis approaches which use more fundamental properties of the time series to analyze the observed calcium dynamics. We present a new analysis method in this class, the Markovian Entropy measure, which is an easily implementable calcium time series analysis method which represents the observed calcium activity as a realization of a Markov Process and describes its dynamics in terms of the level of predictability underlying the transitions between the states of the process. We applied our and other commonly used calcium analysis methods on a dataset from Xenopus laevis neural progenitors which displays irregular calcium activity and a dataset from murine synaptic neurons which displays activity time series that are well-described by visually-distinguishable features. We find that the Markovian Entropy measure is able to distinguish between biologically distinct populations in both datasets, and that it can separate biologically distinct populations to a greater extent than other methods in the dataset exhibiting irregular calcium activity. These results support the benefit of using the Markovian Entropy measure to analyze calcium dynamics, particularly for studies using time series data which do not exhibit easily distinguishable features.
Bilayer graphene lattice-layer entanglement in the presence of non-Markovian phase noise
Bittencourt, Victor A. S. V.; Blasone, Massimo; Bernardini, Alex E.
2018-03-01
The evolution of single particle excitations of bilayer graphene under effects of non-Markovian noise is described with focus on the decoherence process of lattice-layer (LL) maximally entangled states. Once the noiseless dynamics of an arbitrary initial state is identified by the correspondence between the tight-binding Hamiltonian for the AB-stacked bilayer graphene and the Dirac equation—which includes pseudovectorlike and tensorlike field interactions—the noisy environment is described as random fluctuations on bias voltage and mass terms. The inclusion of noisy dynamics reproduces the Ornstein-Uhlenbeck processes: A non-Markovian noise model with a well-defined Markovian limit. Considering that an initial amount of entanglement shall be dissipated by the noise, two profiles of dissipation are identified. On one hand, for eigenstates of the noiseless Hamiltonian, deaths and revivals of entanglement are identified along the oscillation pattern for long interaction periods. On the other hand, for departing LL Werner and Cat states, the entanglement is suppressed although, for both cases, some identified memory effects compete with the pure noise-induced decoherence in order to preserve the the overall profile of a given initial state.
Quantum measurement and entanglement of spin quantum bits in diamond
Pfaff, W.
2013-01-01
This thesis presents a set of experiments that explore the possible realisation of a macroscopic quantum network based on solid-state quantum bits. Such a quantum network would allow for studying quantum mechanics on large scales (meters, or even kilometers), and can open new possibilities for
Iliopoulos, Nikos; Thanopulos, Ioannis; Yannopapas, Vassilios; Paspalakis, Emmanuel
2018-03-01
We study the spontaneous emission of a two-level quantum emitter next to a plasmonic nanoparticle beyond the Markovian approximation and the rotating-wave approximation (RWA) by combining quantum dynamics and classical electromagnetic calculations. For emitters with decay times in the picosecond to nanosecond time regime, as well as located at distances from the nanoparticle up to its radius, the dynamics with and without the RWA and the transition from the non-Markovian to the Markovian regime are investigated. For emitters with longer decay times, the Markov approximation proves to be adequate for distances larger than half the nanoparticle radius. However, the RWA is correct for all distances of the emitter from the nanoparticle. For short decay time emitters, the Markov approximation and RWA are both inadequate, with only the RWA becoming valid again at a distance larger than half the nanoparticle radius. We also show that the entanglement dynamics of two initially entangled qubits interacting independently with the nanoparticle may have a strong non-Markovian character when counter-rotating effects are included. Interesting effects such as entanglement sudden death, periodic entanglement revival, entanglement oscillations, and entanglement trapping are further observed when different initial two-qubit states and different distances between the qubit and the nanoparticle are considered.
International Nuclear Information System (INIS)
Faraggi, A.E.; Matone, M.
1998-01-01
We show that the quantum Hamilton-Jacobi equation can be written in the classical form with the spatial derivative ∂ q replaced by ∂ q with dq = dq/√1-β 2 (q), where β 2 (q) is strictly related to the quantum potential. This can be seen as the opposite of the problem of finding the wave function representation of classical mechanics as formulated by Schiller and Rosen. The structure of the above open-quotes quantum transformationclose quotes, related to the recently formulated equivalence principle, indicates that the potential deforms space geometry. In particular, a result by Flanders implies that both W(q) = V(q) - E and the quantum potential Q are proportional to the curvatures κ W and κ Q which arise as natural invariants in an equivalence problem for curves in the projective line. In this formulation the Schroedinger equation takes the geometrical form (∂ q 2 + κ W )ψ = 0
Quantum Internet: from Communication to Distributed Computing!
Caleffi, Marcello; Cacciapuoti, Angela Sara; Bianchi, Giuseppe
2018-01-01
In this invited paper, the authors discuss the exponential computing speed-up achievable by interconnecting quantum computers through a quantum internet. They also identify key future research challenges and open problems for quantum internet design and deployment.
A quantum CISC compiler and scalable assembler for quantum computing on large systems
Energy Technology Data Exchange (ETDEWEB)
Schulte-Herbrueggen, Thomas; Spoerl, Andreas; Glaser, Steffen [Dept. Chemistry, Technical University of Munich (TUM), 85747 Garching (Germany)
2008-07-01
Using the cutting edge high-speed parallel cluster HLRB-II (with a total LINPACK performance of 63.3 TFlops/s) we present a quantum CISC compiler into time-optimised or decoherence-protected complex instruction sets. They comprise effective multi-qubit interactions with up to 10 qubits. We show how to assemble these medium-sized CISC-modules in a scalable way for quantum computation on large systems. Extending the toolbox of universal gates by optimised complex multi-qubit instruction sets paves the way to fight decoherence in realistic Markovian and non-Markovian settings. The advantage of quantum CISC compilation over standard RISC compilations into one- and two-qubit universal gates is demonstrated inter alia for the quantum Fourier transform (QFT) and for multiply-controlled NOT gates. The speed-up is up to factor of six thus giving significantly better performance under decoherence. - Implications for upper limits to time complexities are also derived.
LDRD final report on theory and exploration of quantum-dot optical nonlinearities and coherences
International Nuclear Information System (INIS)
Chow, Weng Wah
2008-01-01
A microscopic theory for investigating quantum-dot optical properties was developed. The theory incorporated advances on various aspects of quantum-dot physics developed at Sandia and elsewhere. Important components are a non-Markovian treatment of polarization dephasing due to carrier-carrier scattering (developed at Sandia) and a nonperturbative treatment within a polaron picture of the scattering of carriers by longitudinal-optical phonons (developed at Bremen University). A computer code was also developed that provides a detailed accounting of electronic structure influences and a consistent treatment of many-body effects, the latter via the incorporation of results from the microscopic theory. This code was used to explore quantum coherence physics in a quantum-dot system. The investigation furthers the understanding of the underlying differences between atomic quantum coherence and semiconductor quantum coherence, and helps improve the potential of using quantum coherences in quantum computing, coherent control and high-resolution spectroscopy
Stabilizing strongly correlated photon fluids with non-Markovian reservoirs
Lebreuilly, José; Biella, Alberto; Storme, Florent; Rossini, Davide; Fazio, Rosario; Ciuti, Cristiano; Carusotto, Iacopo
2017-09-01
We introduce a frequency-dependent incoherent pump scheme with a square-shaped spectrum as a way to study strongly correlated photons in arrays of coupled nonlinear resonators. This scheme can be implemented via a reservoir of population-inverted two-level emitters with a broad distribution of transition frequencies. Our proposal is predicted to stabilize a nonequilibrium steady state sharing important features with a zero-temperature equilibrium state with a tunable chemical potential. We confirm the efficiency of our proposal for the Bose-Hubbard model by computing numerically the steady state for finite system sizes: first, we predict the occurrence of a sequence of incompressible Mott-insulator-like states with arbitrary integer densities presenting strong robustness against tunneling and losses. Secondly, for stronger tunneling amplitudes or noninteger densities, the system enters a coherent regime analogous to the superfluid state. In addition to an overall agreement with the zero-temperature equilibrium state, exotic nonequilibrium processes leading to a finite entropy generation are pointed out in specific regions of parameter space. The equilibrium ground state is shown to be recovered by adding frequency-dependent losses. The promise of this improved scheme in view of quantum simulation of the zero-temperature many-body physics is highlighted.
Linear entropy in quantum phase space
International Nuclear Information System (INIS)
Rosales-Zarate, Laura E. C.; Drummond, P. D.
2011-01-01
We calculate the quantum Renyi entropy in a phase-space representation for either fermions or bosons. This can also be used to calculate purity and fidelity, or the entanglement between two systems. We show that it is possible to calculate the entropy from sampled phase-space distributions in normally ordered representations, although this is not possible for all quantum states. We give an example of the use of this method in an exactly soluble thermal case. The quantum entropy cannot be calculated at all using sampling methods in classical symmetric (Wigner) or antinormally ordered (Husimi) phase spaces, due to inner-product divergences. The preferred method is to use generalized Gaussian phase-space methods, which utilize a distribution over stochastic Green's functions. We illustrate this approach by calculating the reduced entropy and entanglement of bosonic or fermionic modes coupled to a time-evolving, non-Markovian reservoir.
Strong Coupling Corrections in Quantum Thermodynamics
Perarnau-Llobet, M.; Wilming, H.; Riera, A.; Gallego, R.; Eisert, J.
2018-03-01
Quantum systems strongly coupled to many-body systems equilibrate to the reduced state of a global thermal state, deviating from the local thermal state of the system as it occurs in the weak-coupling limit. Taking this insight as a starting point, we study the thermodynamics of systems strongly coupled to thermal baths. First, we provide strong-coupling corrections to the second law applicable to general systems in three of its different readings: As a statement of maximal extractable work, on heat dissipation, and bound to the Carnot efficiency. These corrections become relevant for small quantum systems and vanish in first order in the interaction strength. We then move to the question of power of heat engines, obtaining a bound on the power enhancement due to strong coupling. Our results are exemplified on the paradigmatic non-Markovian quantum Brownian motion.
Linear entropy in quantum phase space
Energy Technology Data Exchange (ETDEWEB)
Rosales-Zarate, Laura E. C.; Drummond, P. D. [Centre for Atom Optics and Ultrafast Spectroscopy, Swinburne University of Technology, Melbourne 3122 (Australia)
2011-10-15
We calculate the quantum Renyi entropy in a phase-space representation for either fermions or bosons. This can also be used to calculate purity and fidelity, or the entanglement between two systems. We show that it is possible to calculate the entropy from sampled phase-space distributions in normally ordered representations, although this is not possible for all quantum states. We give an example of the use of this method in an exactly soluble thermal case. The quantum entropy cannot be calculated at all using sampling methods in classical symmetric (Wigner) or antinormally ordered (Husimi) phase spaces, due to inner-product divergences. The preferred method is to use generalized Gaussian phase-space methods, which utilize a distribution over stochastic Green's functions. We illustrate this approach by calculating the reduced entropy and entanglement of bosonic or fermionic modes coupled to a time-evolving, non-Markovian reservoir.
Aihara, Taketo; Tayagaki, Takeshi; Nagato, Yuki; Okano, Yoshinobu; Sugaya, Takeyoshi
2018-04-01
To analyze the open-circuit voltage (V oc) in intermediate-band solar cells, we investigated the current-voltage characteristics in wide-bandgap InGaP-based InP quantum dot (QD) solar cells. From the temperature dependence of the current-voltage curves, we show that the V oc in InP QD solar cells increases with decreasing temperature. We use a simple diode model to extract V oc at the zero-temperature limit, V 0, and the temperature coefficient C of the solar cells. Our results show that, while the C of InP QD solar cells is slightly larger than that of the reference InGaP solar cells, V 0 significantly decreases and coincides with the bandgap energy of the InP QDs rather than that of the InGaP host. This V 0 indicates that the V oc reduction in the InP QD solar cells is primarily caused by the breaking of the Fermi energy separation between the QDs and the host semiconductor in intermediate-band solar cells, rather than by enhanced carrier recombination.
Veeraraghavan, Srikant; Mazziotti, David A
2014-03-28
We present a density matrix approach for computing global solutions of restricted open-shell Hartree-Fock theory, based on semidefinite programming (SDP), that gives upper and lower bounds on the Hartree-Fock energy of quantum systems. While wave function approaches to Hartree-Fock theory yield an upper bound to the Hartree-Fock energy, we derive a semidefinite relaxation of Hartree-Fock theory that yields a rigorous lower bound on the Hartree-Fock energy. We also develop an upper-bound algorithm in which Hartree-Fock theory is cast as a SDP with a nonconvex constraint on the rank of the matrix variable. Equality of the upper- and lower-bound energies guarantees that the computed solution is the globally optimal solution of Hartree-Fock theory. The work extends a previously presented method for closed-shell systems [S. Veeraraghavan and D. A. Mazziotti, Phys. Rev. A 89, 010502-R (2014)]. For strongly correlated systems the SDP approach provides an alternative to the locally optimized Hartree-Fock energies and densities with a certificate of global optimality. Applications are made to the potential energy curves of C2, CN, Cr2, and NO2.
Kishi, Ryohei; Nakano, Masayoshi
2011-04-21
A novel method for the calculation of the dynamic polarizability (α) of open-shell molecular systems is developed based on the quantum master equation combined with the broken-symmetry (BS) time-dependent density functional theory within the Tamm-Dancoff approximation, referred to as the BS-DFTQME method. We investigate the dynamic α density distribution obtained from BS-DFTQME calculations in order to analyze the spatial contributions of electrons to the field-induced polarization and clarify the contributions of the frontier orbital pair to α and its density. To demonstrate the performance of this method, we examine the real part of dynamic α of singlet 1,3-dipole systems having a variety of diradical characters (y). The frequency dispersion of α, in particular in the resonant region, is shown to strongly depend on the exchange-correlation functional as well as on the diradical character. Under sufficiently off-resonant condition, the dynamic α is found to decrease with increasing y and/or the fraction of Hartree-Fock exchange in the exchange-correlation functional, which enhances the spin polarization, due to the decrease in the delocalization effects of π-diradical electrons in the frontier orbital pair. The BS-DFTQME method with the BHandHLYP exchange-correlation functional also turns out to semiquantitatively reproduce the α spectra calculated by a strongly correlated ab initio molecular orbital method, i.e., the spin-unrestricted coupled-cluster singles and doubles.
Energy Technology Data Exchange (ETDEWEB)
Vatansever, Fatma, E-mail: vatansever.fatma@mgh.harvard.edu; Hamblin, Michael R., E-mail: hamblin@helix.mgh.harvard.edu [Massachusetts General Hospital, Wellman Center for Photomedicine (United States)
2016-10-15
Core–shell CdSe/ZnS quantum dots (QDs) are useful as tunable photostable fluorophores for multiple applications in industry, biology, and medicine. However, to achieve the optimum optical properties, the surface of the QDs must be passivated to remove charged sites that might bind extraneous substances and allow aggregation. Here we describe a method of growing an organic polymer corona onto the QD surface using the bottom-up approach of surface-initiated ring-opening metathesis polymerization (SI-ROMP) with Grubbs catalyst. CdSe/ZnS QDs were first coated with mercaptopropionic acid by displacing the original tri-octylphosphine oxide layer, and then reacted with 7-octenyl dimethyl chlorosilane. The resulting octenyl double bonds allowed the attachment of ruthenium alkylidene groups as a catalyst. A subsequent metathesis reaction with strained bicyclic monomers (norbornene-dicarbonyl chloride (NDC), and a mixture of NDC and norbornenylethylisobutyl-polyhedral oligomeric silsesquioxane (norbornoPOSS)) allowed the construction of tethered organic homo-polymer or co-polymer layers onto the QD. Compounds were characterized by FT-IR, 1H-NMR, X-ray photoelectron spectroscopy, differential scanning calorimetry, and transmission electron microscopy. Atomic force microscopy showed that the coated QDs were separate and non-aggregated with a range of diameter of 48–53 nm.
Liu, Qiang; Van Mieghem, Piet
2018-02-01
Since a real epidemic process is not necessarily Markovian, the epidemic threshold obtained under the Markovian assumption may be not realistic. To understand general non-Markovian epidemic processes on networks, we study the Weibullian susceptible-infected-susceptible (SIS) process in which the infection process is a renewal process with a Weibull time distribution. We find that, if the infection rate exceeds 1 /ln(λ1+1 ) , where λ1 is the largest eigenvalue of the network's adjacency matrix, then the infection will persist on the network under the mean-field approximation. Thus, 1 /ln(λ1+1 ) is possibly the largest epidemic threshold for a general non-Markovian SIS process with a Poisson curing process under the mean-field approximation. Furthermore, non-Markovian SIS processes may result in a multimodal prevalence. As a byproduct, we show that a limiting Weibullian SIS process has the potential to model bursts of a synchronized infection.
What is quantum in quantum randomness?
Grangier, P; Auffèves, A
2018-07-13
It is often said that quantum and classical randomness are of different nature, the former being ontological and the latter epistemological. However, so far the question of 'What is quantum in quantum randomness?', i.e. what is the impact of quantization and discreteness on the nature of randomness, remains to be answered. In a first part, we make explicit the differences between quantum and classical randomness within a recently proposed ontology for quantum mechanics based on contextual objectivity. In this view, quantum randomness is the result of contextuality and quantization. We show that this approach strongly impacts the purposes of quantum theory as well as its areas of application. In particular, it challenges current programmes inspired by classical reductionism, aiming at the emergence of the classical world from a large number of quantum systems. In a second part, we analyse quantum physics and thermodynamics as theories of randomness, unveiling their mutual influences. We finally consider new technological applications of quantum randomness that have opened up in the emerging field of quantum thermodynamics.This article is part of a discussion meeting issue 'Foundations of quantum mechanics and their impact on contemporary society'. © 2018 The Author(s).
EDITORIAL: Focus on Quantum Information and Many-Body Theory
Eisert, Jens; Plenio, Martin B.
2010-02-01
and F Verstraete SIMULATION AND DYNAMICS A quantum differentiation of k-SAT instances B Tamir and G Ortiz Classical Ising model test for quantum circuits Joseph Geraci and Daniel A Lidar Exact matrix product solutions in the Heisenberg picture of an open quantum spin chain S R Clark, J Prior, M J Hartmann, D Jaksch and M B Plenio Exact solution of Markovian master equations for quadratic Fermi systems: thermal baths, open XY spin chains and non-equilibrium phase transition Tomaž Prosen and Bojan Žunkovič Quantum kinetic Ising models R Augusiak, F M Cucchietti, F Haake and M Lewenstein ENTANGLEMENT AND SPECTRAL PROPERTIES Ground states of unfrustrated spin Hamiltonians satisfy an area law Niel de Beaudrap, Tobias J Osborne and Jens Eisert Correlation density matrices for one-dimensional quantum chains based on the density matrix renormalization group W Münder, A Weichselbaum, A Holzner, Jan von Delft and C L Henley The invariant-comb approach and its relation to the balancedness of multipartite entangled states Andreas Osterloh and Jens Siewert Entanglement scaling of fractional quantum Hall states through geometric deformations Andreas M Läuchli, Emil J Bergholtz and Masudul Haque Entanglement versus gap for one-dimensional spin systems Daniel Gottesman and M B Hastings Entanglement spectra of critical and near-critical systems in one dimension F Pollmann and J E Moore Macroscopic bound entanglement in thermal graph states D Cavalcanti, L Aolita, A Ferraro, A García-Saez and A Acín Entanglement at the quantum phase transition in a harmonic lattice Elisabeth Rieper, Janet Anders and Vlatko Vedral Multipartite entanglement and frustration P Facchi, G Florio, U Marzolino, G Parisi and S Pascazio Entropic uncertainty relations—a survey Stephanie Wehner and Andreas Winter Entanglement in a spin system with inverse square statistical interaction D Giuliano, A Sindona, G Falcone, F Plastina and L Amico APPLICATIONS Time-dependent currents of one-dimensional bosons
International Nuclear Information System (INIS)
Beenakker, C W J
2005-01-01
Quantum Noise is advertised as a handbook, and this is indeed how it functions for me these days: it is a book that I keep within hand's reach, ready to be consulted on the proper use of quantum stochastic methods in the course of my research on quantum dots. I should point out that quantum optics, the target field for this book, is not my field by training. So I have much to learn, and find this handbook to be a reliable and helpful guide. Crispin Gardiner previously wrote the Handbook of Stochastic Methods (also published by Springer), which provides an overview of methods in classical statistical physics. Quantum Noise, written jointly with Peter Zoller, is the counterpart for quantum statistical physics, and indeed the two books rely on each other by frequent cross referencing. The fundamental problem addressed by Quantum Noise is how the quantum dynamics of an open system can be described statistically by treating the environment as a source of noise. This is a general problem in condensed matter physics (in particular in the context of Josephson junctions) and in quantum optics. The emphasis in this book in on the optical applications (for condensed matter applications one could consult Quantum Dissipative Systems by Ulrich Weiss, published by World Scientific). The optical applications centre around the interaction of light with atoms, where the atoms represent the open system and the light is the noisy environment. A complete description of the production and detection of non-classical states of radiation (such as squeezed states) can be obtained using one of the equivalent quantum stochastic formulations: the quantum Langevin equation for the field operators (in either the Ito or the Stratonovich form), the Master equation for the density matrix, or the stochastic Schroedinger equation for the wave functions. Each formulation is fully developed here (as one would expect from a handbook), with detailed instructions on how to go from one to the other. The
Spherical particle Brownian motion in viscous medium as non-Markovian random process
International Nuclear Information System (INIS)
Morozov, Andrey N.; Skripkin, Alexey V.
2011-01-01
The Brownian motion of a spherical particle in an infinite medium is described by the conventional methods and integral transforms considering the entrainment of surrounding particles of the medium by the Brownian particle. It is demonstrated that fluctuations of the Brownian particle velocity represent a non-Markovian random process. The features of Brownian motion in short time intervals and in small displacements are considered. -- Highlights: → Description of Brownian motion considering the entrainment of medium is developed. → We find the equations for statistical characteristics of impulse fluctuations. → Brownian motion at small time intervals is considered. → Theoretical results and experimental data are compared.
Synchronization of stochastic delayed neural networks with markovian switching and its application.
Tang, Yang; Fang, Jian-An; Miao, Qing-Ying
2009-02-01
In this paper, the problem of adaptive synchronization for a class of stochastic neural networks (SNNs) which involve both mixed delays and Markovian jumping parameters is investigated. The mixed delays comprise the time-varying delays and distributed delays, both of which are mode-dependent. The stochastic perturbations are described in terms of Browian motion. By the adaptive feedback technique, several sufficient criteria have been proposed to ensure the synchronization of SNNs in mean square. Moreover, the proposed adaptive feedback scheme is applied to the secure communication. Finally, the corresponding simulation results are given to demonstrate the usefulness of the main results obtained.
Replacement policy in a system under shocks following a Markovian arrival process
International Nuclear Information System (INIS)
Montoro-Cazorla, Delia; Perez-Ocon, Rafael; Carmen Segovia, Maria del
2009-01-01
We present a system subject to shocks that arrive following a Markovian arrival process. The system is minimally repaired. It is replaced when a certain number of shocks arrive. A general model where the replacements are governed by a discrete phase-type distribution is studied. For this system, the Markov process governing the system is constructed, and the interarrival times between replacements and the number of replacements are calculated. A special case of this system is when it can stand a prefixed number of shocks. For this new system, the same performance measures are calculated. The systems are considered in transient and stationary regime
Replacement policy in a system under shocks following a Markovian arrival process
Energy Technology Data Exchange (ETDEWEB)
Montoro-Cazorla, Delia [Department of Statistics and Operational Research, University of Jaen (Spain); Perez-Ocon, Rafael [Department of Statistics and Operational Research, University of Granada, Granada (Spain)], E-mail: rperezo@ugr.es; Carmen Segovia, Maria del [Departamento de Estadistica e I.O., University of Granada, Granada (Spain)
2009-02-15
We present a system subject to shocks that arrive following a Markovian arrival process. The system is minimally repaired. It is replaced when a certain number of shocks arrive. A general model where the replacements are governed by a discrete phase-type distribution is studied. For this system, the Markov process governing the system is constructed, and the interarrival times between replacements and the number of replacements are calculated. A special case of this system is when it can stand a prefixed number of shocks. For this new system, the same performance measures are calculated. The systems are considered in transient and stationary regime.
International Nuclear Information System (INIS)
Wang Linshan; Zhang Zhe; Wang Yangfan
2008-01-01
Some criteria for the global stochastic exponential stability of the delayed reaction-diffusion recurrent neural networks with Markovian jumping parameters are presented. The jumping parameters considered here are generated from a continuous-time discrete-state homogeneous Markov process, which are governed by a Markov process with discrete and finite state space. By employing a new Lyapunov-Krasovskii functional, a linear matrix inequality (LMI) approach is developed to establish some easy-to-test criteria of global exponential stability in the mean square for the stochastic neural networks. The criteria are computationally efficient, since they are in the forms of some linear matrix inequalities
Directory of Open Access Journals (Sweden)
Yajun Li
2015-01-01
Full Text Available This paper deals with the robust H∞ filter design problem for a class of uncertain neutral stochastic systems with Markovian jumping parameters and time delay. Based on the Lyapunov-Krasovskii theory and generalized Finsler Lemma, a delay-dependent stability condition is proposed to ensure not only that the filter error system is robustly stochastically stable but also that a prescribed H∞ performance level is satisfied for all admissible uncertainties. All obtained results are expressed in terms of linear matrix inequalities which can be easily solved by MATLAB LMI toolbox. Numerical examples are given to show that the results obtained are both less conservative and less complicated in computation.
Environment-Assisted Speed-up of the Field Evolution in Cavity Quantum Electrodynamics.
Cimmarusti, A D; Yan, Z; Patterson, B D; Corcos, L P; Orozco, L A; Deffner, S
2015-06-12
We measure the quantum speed of the state evolution of the field in a weakly driven optical cavity QED system. To this end, the mode of the electromagnetic field is considered as a quantum system of interest with a preferential coupling to a tunable environment: the atoms. By controlling the environment, i.e., changing the number of atoms coupled to the optical cavity mode, an environment-assisted speed-up is realized: the quantum speed of the state repopulation in the optical cavity increases with the coupling strength between the optical cavity mode and this non-Markovian environment (the number of atoms).
Environment-Assisted Speed-up of the Field Evolution in Cavity Quantum Electrodynamics
International Nuclear Information System (INIS)
Cimmarusti, A. D.; Yan, Z.; Patterson, B. D.; Corcos, L. P.; Orozco, L. A.; Deffner, S.
2015-01-01
We measure the quantum speed of the state evolution of the field in a weakly-driven optical cavity QED system. To this end, the mode of the electromagnetic field is considered as a quantum system of interest with a preferential coupling to a tunable environment: the atoms. By controlling the environment, i.e., changing the number of atoms coupled to the optical cavity mode, an environment assisted speed-up is realized: the quantum speed of the state re-population in the optical cavity increases with the coupling strength between the optical cavity mode and this non-Markovian environment (the number of atoms)
Decoherence dynamics of two charge qubits in vertically coupled quantum dots
International Nuclear Information System (INIS)
Ben Chouikha, W.; Bennaceur, R.; Jaziri, S.
2007-01-01
The decoherence dynamics of two charge qubits in a double quantum dot is investigated theoretically. We consider the quantum dynamics of two interacting electrons in a vertically coupled quantum dot driven by an external electric field. We derive the equations of motion for the density matrix, in which the presence of an electron confined in the double dot represents one qubit. A Markovian approach to the dynamical evolution of the reduced density matrix is adopted. We evaluate the concurrence of two qubits in order to study the effect of acoustic phonons on the entanglement. We also show that the disentanglement effect depends on the double dot parameters and increases with the temperature
Reducing dephasing in coupled quantum dot-cavity systems by engineering the carrier wavefunctions
DEFF Research Database (Denmark)
Nysteen, Anders; Nielsen, Per Kær; Mørk, Jesper
2012-01-01
We demonstrate theoretically how photon-assisted dephasing by the electron-phonon interaction in a coupled cavity-quantum dot system can be significantly reduced for specific QD-cavity detunings. Our starting point is a recently published theory,1 which considers longitudinal acoustic phonons......, described by a non-Markovian model, interacting with a coupled quantum dot-cavity system. The reduction of phonon-induced dephasing is obtained by placing the cavity-quantum dot system inside an infinite slab, assuming spherical electronic wavefunctions. Based on our calculations, we expect this to have...
National Research Council Canada - National Science Library
Agarwal, G. S
2013-01-01
.... Focusing on applications of quantum optics, the textbook covers recent developments such as engineering of quantum states, quantum optics on a chip, nano-mechanical mirrors, quantum entanglement...
Quantum neuromorphic hardware for quantum artificial intelligence
Prati, Enrico
2017-08-01
The development of machine learning methods based on deep learning boosted the field of artificial intelligence towards unprecedented achievements and application in several fields. Such prominent results were made in parallel with the first successful demonstrations of fault tolerant hardware for quantum information processing. To which extent deep learning can take advantage of the existence of a hardware based on qubits behaving as a universal quantum computer is an open question under investigation. Here I review the convergence between the two fields towards implementation of advanced quantum algorithms, including quantum deep learning.