Exact Closed Master Equation for Gaussian Non-Markovian Dynamics.
Ferialdi, L
2016-03-25
Non-Markovian master equations describe general open quantum systems when no approximation is made. We provide the exact closed master equation for the class of Gaussian, completely positive, trace preserving, non-Markovian dynamics. This very general result allows us to investigate a vast variety of physical systems. We show that the master equation for non-Markovian quantum Brownian motion is a particular case of our general result. Furthermore, we derive the master equation unraveled by a non-Markovian, dissipative stochastic Schrödinger equation, paving the way for the analysis of dissipative non-Markovian collapse models.
Exact non-Markovian master equation for the spin-boson and Jaynes-Cummings models
Ferialdi, L.
2017-02-01
We provide the exact non-Markovian master equation for a two-level system interacting with a thermal bosonic bath, and we write the solution of such a master equation in terms of the Bloch vector. We show that previous approximated results are particular limits of our exact master equation. We generalize these results to more complex systems involving an arbitrary number of two-level systems coupled to different thermal baths, providing the exact master equations also for these systems. As an example of this general case we derive the master equation for the Jaynes-Cummings model.
Bhattacharya, Samyadeb; Misra, Avijit; Mukhopadhyay, Chiranjib; Pati, Arun Kumar
2017-01-01
An exact canonical master equation of the Lindblad form is derived for a central spin interacting uniformly with a sea of completely unpolarized spins. The Kraus operators for the dynamical map are also derived. The non-Markovianity of the dynamics in terms of the divisibility breaking of the dynamical map and the increase of the trace distance fidelity between quantum states is shown. Moreover, it is observed that the irreversible entropy production rate is always negative (for a fixed initial state) whenever the dynamics exhibits non-Markovian behavior. In continuation with the study of witnessing non-Markovianity, it is shown that the positive rate of change of the purity of the central qubit is a faithful indicator of the non-Markovian information backflow. Given the experimental feasibility of measuring the purity of a quantum state, a possibility of experimental demonstration of non-Markovianity and the negative irreversible entropy production rate is addressed. This gives the present work considerable practical importance for detecting the non-Markovianity and the negative irreversible entropy production rate.
Using non-Markovian measures to evaluate quantum master equations for photosynthesis
Chen, Hong-Bin; Lambert, Neill; Cheng, Yuan-Chung; Chen, Yueh-Nan; Nori, Franco
2015-08-01
When dealing with system-reservoir interactions in an open quantum system, such as a photosynthetic light-harvesting complex, approximations are usually made to obtain the dynamics of the system. One question immediately arises: how good are these approximations, and in what ways can we evaluate them? Here, we propose to use entanglement and a measure of non-Markovianity as benchmarks for the deviation of approximate methods from exact results. We apply two frequently-used perturbative but non-Markovian approximations to a photosynthetic dimer model and compare their results with that of the numerically-exact hierarchy equation of motion (HEOM). This enables us to explore both entanglement and non-Markovianity measures as means to reveal how the approximations either overestimate or underestimate memory effects and quantum coherence. In addition, we show that both the approximate and exact results suggest that non-Markonivity can, counter-intuitively, increase with temperature, and with the coupling to the environment.
Using non-Markovian measures to evaluate quantum master equations for photosynthesis
Chen, Hong-Bin; Lambert, Neill; Cheng, Yuan-Chung; Chen, Yueh-Nan; Nori, Franco
2015-01-01
When dealing with system-reservoir interactions in an open quantum system, such as a photosynthetic light-harvesting complex, approximations are usually made to obtain the dynamics of the system. One question immediately arises: how good are these approximations, and in what ways can we evaluate them? Here, we propose to use entanglement and a measure of non-Markovianity as benchmarks for the deviation of approximate methods from exact results. We apply two frequently-used perturbative but non-Markovian approximations to a photosynthetic dimer model and compare their results with that of the numerically-exact hierarchy equation of motion (HEOM). This enables us to explore both entanglement and non-Markovianity measures as means to reveal how the approximations either overestimate or underestimate memory effects and quantum coherence. In addition, we show that both the approximate and exact results suggest that non-Markonivity can, counter-intuitively, increase with temperature, and with the coupling to the environment. PMID:26238479
Singh, Navinder
2011-01-01
A direct numerical algorithm for solving the time-nonlocal non-Markovian master equation in the second Born approximation is introduced and the range of utility of this approximation, and of the Markov approximation, is analyzed for the traditional dimer system that models excitation energy transfer in photosynthesis. Specifically, the coupled integro-differential equations for the reduced density matrix are solved by an efficient auxiliary function method in both the energy and site representations. In addition to giving exact results to this order, the approach allows us to computationally assess the range of the reorganization energy and decay rates of the phonon auto-correlation function for which the Markovian Redfield theory and the second order approximation is valid. For example, the use of Redfield theory for $\\lambda> 10 \\textrm{cm}^{-1}$ in systems like Fenna-Mathews-Olson (FMO) type systems is shown to be in error. In addition, analytic inequalities are obtained for the regime of validity of the M...
Non-Markovian diffusion equations and processes: analysis and simulations
Mura, Antonio; Mainardi, Francesco
2007-01-01
In this paper we introduce and analyze a class of diffusion type equations related to certain non-Markovian stochastic processes. We start from the forward drift equation which is made non-local in time by the introduction of a suitable chosen memory kernel K(t). The resulting non-Markovian equation can be interpreted in a natural way as the evolution equation of the marginal density function of a random time process l(t). We then consider the subordinated process Y(t)=X(l(t)) where X(t) is a Markovian diffusion. The corresponding time-evolution of the marginal density function of Y(t) is governed by a non-Markovian Fokker-Planck equation which involves the memory kernel K(t). We develop several applications and derive the exact solutions. We consider different stochastic models for the given equations providing path simulations.
Non- Markovian Quantum Stochastic Equation For Two Coupled Oscillators
Alpomishev, E X
2016-01-01
The system of nonlinear Langevin equations was obtained by using Hamiltonian's operator of two coupling quantum oscillators which are interacting with heat bath. By using the analytical solution of these equations, the analytical expressions for transport coefficients was found. Generalized Langevin equations and fluctuation-dissipation relations are derived for the case of a nonlinear non-Markovian noise. The explicit expressions for the time-dependent friction and diffusion coefficients are presented for the case of linear couplings in the coordinate between the collective two coupled harmonic oscillators and heat bath.
Non-Markovian dynamics for bipartite systems
2008-01-01
We analyze the appearance of non-Markovian effects in the dynamics of a bipartite system coupled to a reservoir, which can be described within a class of non-Markovian equations given by a generalized Lindblad structure. A novel master equation, which we term quantum Bloch-Boltzmann equation, is derived, describing both motional and internal states of a test particle in a quantum framework. When due to the preparation of the system or to decoherence effects one of the two degrees of freedom i...
General non-Markovian dynamics of open quantum systems.
Zhang, Wei-Min; Lo, Ping-Yuan; Xiong, Heng-Na; Tu, Matisse Wei-Yuan; Nori, Franco
2012-10-26
We present a general theory of non-Markovian dynamics for open systems of noninteracting fermions (bosons) linearly coupled to thermal environments of noninteracting fermions (bosons). We explore the non-Markovian dynamics by connecting the exact master equations with the nonequilibirum Green's functions. Environmental backactions are fully taken into account. The non-Markovian dynamics consists of nonexponential decays and dissipationless oscillations. Nonexponential decays are induced by the discontinuity in the imaginary part of the self-energy corrections. Dissipationless oscillations arise from band gaps or the finite band structure of spectral densities. The exact analytic solutions for various non-Markovian thermal environments show that non-Markovian dynamics can be largely understood from the environmental-modified spectra of open systems.
A Bohmian approach to the non-Markovian non-linear Schrödinger–Langevin equation
Energy Technology Data Exchange (ETDEWEB)
Vargas, Andrés F.; Morales-Durán, Nicolás; Bargueño, Pedro, E-mail: p.bargueno@uniandes.edu.co
2015-05-15
In this work, a non-Markovian non-linear Schrödinger–Langevin equation is derived from the system-plus-bath approach. After analyzing in detail previous Markovian cases, Bohmian mechanics is shown to be a powerful tool for obtaining the desired generalized equation.
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.
Non-Markovianity assisted Steady State Entanglement
Huelga, Susana F; Plenio, Martin B
2011-01-01
We analyze the dependence of steady state entanglement in a dimer system with a coherent exchange interaction and subject to local dephasing on the degree of Markovianity of the system-environment interaction. We demonstrate that non-Markovianity of the system-environment interaction is an essential resource that may support the formation of steady state entanglement whereas purely Markovian dynamics governed by Lindblad master equations results in separable steady states. This result illustrates possible mechanisms leading to long lived entanglement in purely decohering local environments. A feasible experimental demonstration of this non-Markovianity assisted steady state entanglement using a system of trapped ions is presented.
Non-Markovian Quantum Jumps in Excitonic Energy Transfer
Rebentrost, Patrick; Aspuru-Guzik, Alan
2009-01-01
We utilize the novel non-Markovian quantum jump (NMQJ) approach to stochastically simulate exciton dynamics derived from a time-convolutionless master equation. For relevant parameters and time scales, the time-dependent, oscillatory decoherence rates can have negative regions, a signature of non-Markovian behavior and of the revival of coherences. This can lead to non-Markovian population beatings for a dimer system at room temperature. We show that strong exciton-phonon coupling to low frequency modes can considerably modify transport properties. We observe increased exciton transport, which can be seen as an extension of recent environment-assisted quantum transport (ENAQT) concepts to the non-Markovian regime. Within the NMQJ method, the Fenna-Matthew-Olson protein is investigated as a prototype for larger photosynthetic complexes.
Non-Markovian Fermionic Stochastic Schr\\"{o}dinger Equation for Open System Dynamics
Shi, Wufu; Yu, Ting
2012-01-01
In this paper we present an exact Grassmann stochastic Schr\\"{o}dinger equation for the dynamics of an open fermionic quantum system coupled to a reservoir consisting of a finite or infinite number of fermions. We use this stochastic approach to derive the exact master equation for a fermionic system strongly coupled to electronic reservoirs. The generality and applicability of this Grassmann stochastic approach is justified and exemplified by several quantum open system problems concerning quantum decoherence and quantum transport for both vacuum and finite-temperature fermionic reservoirs. We show that the quantum coherence property of the quantum dot system can be profoundly modified by the environment memory.
Non-Markovian Dynamics of Quantum Systems
Chruściński, Dariusz; Kossakowski, Andrzej
2011-01-01
We analyze a local approach to the non-Markovian evolution of open quantum systems. It turns out that any dynamical map representing evolution of such a system may be described either by non-local master equation with memory kernel or equivalently by equation which is local in time. The price one pays for the local approach is that the corresponding generator might be highly singular and it keeps the memory about the starting point 't0'. Remarkably, singularities of generator may lead to interesting physical phenomena like revival of coherence or sudden death and revival of entanglement.
Non-Markovian Diffusive Unravellings of Entanglement
Corn, Brittany; Yu, Ting
2011-01-01
The fully quantized model of two qubits coupled to a common bath is solved using the quantum state diffusion (QSD) approach in the non-Markovian regime. We have established an explicit time-local non-Markovian QSD equation for the two-qubit dissipative model. Diffusive quantum trajectories are applied to the entanglement estimation of two-qubit systems in a non-Markovian regime. In another interesting example, we have also considered exact entanglement unravellings for a dephasing model. In both cases, non-Markovian features of entanglement evolution are revealed through quantum diffusive unravellings in the qubit state space.
Non-Markovianity-assisted steady state entanglement.
Huelga, Susana F; Rivas, Ángel; Plenio, Martin B
2012-04-20
We analyze the steady state entanglement generated in a coherently coupled dimer system subject to dephasing noise as a function of the degree of Markovianity of the evolution. By keeping fixed the effective noise strength while varying the memory time of the environment, we demonstrate that non-Markovianity is an essential, quantifiable resource that may support the formation of steady state entanglement whereas purely Markovian dynamics governed by Lindblad master equations lead to separable steady states. This result illustrates possible mechanisms leading to long-lived entanglement in purely decohering, possibly local, environments. We present a feasible experimental demonstration of this noise assisted phenomenon using a system of trapped ions.
Connecting two jumplike unravelings for non-Markovian open quantum systems
Luoma, Kimmo; 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 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, associate to the decay rates of time-local master equations, and consequently to the jump rates of the NMQJ method.
Non-Markovian entanglement dynamics in coupled superconducting qubit systems
Cui, Wei; Pan, Yu
2010-01-01
We theoretically analyze the entanglement generation and dynamics by coupled Josephson junction qubits. Considering a current-biased Josephson junction (CBJJ), we generate maximally entangled states. In particular, the entanglement dynamics is considered as a function of the decoherence parameters, such as the temperature, the ratio $r\\equiv\\omega_c/\\omega_0$ between the reservoir cutoff frequency $\\omega_c$ and the system oscillator frequency $\\omega_0$, % between $\\omega_0$ the characteristic frequency of the %quantum system of interest, and $\\omega_c$ the cut-off frequency of %Ohmic reservoir and the energy levels split of the superconducting circuits in the non-Markovian master equation. We analyzed the entanglement sudden death (ESD) and entanglement sudden birth (ESB) by the non-Markovian master equation. Furthermore, we find that the larger the ratio $r$ and the thermal energy $k_BT$, the shorter the decoherence. In this superconducting qubit system we find that the entanglement can be controlled and t...
Non-Markovian Quantum Dynamics: Local versus Nonlocal
Chruściński, Dariusz; Kossakowski, Andrzej
2010-02-01
We analyze non-Markovian evolution of open quantum systems. It is shown that any dynamical map representing the evolution of such a system may be described either by a nonlocal master equation with a memory kernel or equivalently by an equation which is local in time. These two descriptions are complementary: if one is simple, the other is quite involved, or even singular, and vice versa. The price one pays for the local approach is that the corresponding generator keeps the memory about the starting point “t0.” This is the very essence of non-Markovianity. Interestingly, this generator might be highly singular; nevertheless, the corresponding dynamics is perfectly regular. Remarkably, the singularities of the generator may lead to interesting physical phenomena such as the revival of coherence or sudden death and revival of entanglement.
Non-Markovian quantum dynamics: local versus non-local
Chruscinski, Dariusz
2009-01-01
We analyze non-Markovian evolution of open quantum systems. It is shown that any dynamical map representing evolution of such a system may be described either by non-local master equation with memory kernel or equivalently by equation which is local in time. Theses two descriptions are complementary: if one is simple the other is quite involved, or even singular, and vice versa. The price one pays for the local approach is that the corresponding generator keeps the memory about the starting point `t_0'. This is the very essence of non-Markovianity. Interestingly, this generator might be highly singular, nevertheless, the corresponding dynamics is perfectly regular. Remarkably, singularities of generator may lead to interesting physical phenomena like revival of coherence or sudden death and revival of entanglement.
Non-Markovian quantum Brownian motion of a harmonic oscillator
Energy Technology Data Exchange (ETDEWEB)
Tang, J.
1994-02-01
We apply the density-matrix method to the study of quantum Brownian motion of a harmonic oscillator coupled to a heat bath, a system investigated previously by Caldeira and Leggett using a different method. Unlike the earlier work, in our derivation of the master equation the non-Markovian terms are maintained. Although the same model of interaction is used, discrepancy is found between their results and our equation in the Markovian limit. We also point out that the particular interaction model used by both works cannot lead to the phenomenological generalized Langevin theory of Kubo.
Solving non-Markovian open quantum systems with multi-channel reservoir coupling
Broadbent, Curtis J; Yu, Ting; Eberly, Joseph H
2011-01-01
We extend the non-Markovian quantum state diffusion (QSD) equation to open quantum systems which exhibit multi-channel coupling to a harmonic oscillator reservoir. Open quantum systems which have multi-channel reservoir coupling are those in which canonical transformation of reservoir modes cannot reduce the number of reservoir operators appearing in the interaction Hamiltonian to one. We show that the non-Markovian QSD equation for multi-channel reservoir coupling can, in some cases, lead to an exact master equation which we derive. We then derive the exact master equation for the three-level system in a vee-type configuration which has multi-channel reservoir coupling and give the analytical solution. Finally, we examine the evolution of the three-level vee-type system with generalized Ornstein-Uhlenbeck reservoir correlations numerically.
Solving non-Markovian open quantum systems with multi-channel reservoir coupling
Broadbent, Curtis J.; Jing, Jun; Yu, Ting; Eberly, Joseph H.
2012-08-01
We extend the non-Markovian quantum state diffusion (QSD) equation to open quantum systems which exhibit multi-channel coupling to a harmonic oscillator reservoir. Open quantum systems which have multi-channel reservoir coupling are those in which canonical transformation of reservoir modes cannot reduce the number of reservoir operators appearing in the interaction Hamiltonian to one. We show that the non-Markovian QSD equation for multi-channel reservoir coupling can, in some cases, lead to an exact master equation which we derive. We then derive the exact master equation for the three-level system in a vee-type configuration which has multi-channel reservoir coupling and give the analytical solution. Finally, we examine the evolution of the three-level vee-type system with generalized Ornstein-Uhlenbeck reservoir correlations numerically.
Dynamics of non-Markovianity in the presence of a driving field
Indian Academy of Sciences (India)
Mandani Somayeh; Sarbishaei Mohsen; Javidan Kurosh
2016-03-01
We investigate a two-level system in a cavity QED by considering the effects ofamplitude damping, phase damping and driving field. We have studied the non-Markovianity in resonance and non-resonance limits in the presence of these effects using Breuer–Laine–Piilo (BLP) non-Markovianity measure ($N_{\\rm BLP}$). The evolution of the system is derived using the time convolutionless (TCL) master equation. In some conditions, it is shown that in the presence of a driving field, the $N_{\\rm BLP} increases in the resonance and non-resonance limits. We have also found the exact solution of the master equation in order to investigate the effect of temperature- and environment excited states. We have shown that the behaviour of non-Markovianity is very different from what one can see from the TCL approach. We have also presented some explanation about the behaviour of non-Markovianity in the exact solution using quantum discord (QD).
Generalized Master Equations Leading to Completely Positive Dynamics
Vacchini, Bassano
2016-12-01
We provide a general construction of quantum generalized master equations with a memory kernel leading to well-defined, that is, completely positive and trace-preserving, time evolutions. The approach builds on an operator generalization of memory kernels appearing in the description of non-Markovian classical processes and puts into evidence the nonuniqueness of the relationship arising due to the typical quantum issue of operator ordering. The approach provides a physical interpretation of the structure of the kernels, and its connection with the classical viewpoint allows for a trajectory description of the dynamics. Previous apparently unrelated results are now connected in a unified framework, which further allows us to phenomenologically construct a large class of non-Markovian evolutions taking as the starting point collections of time-dependent maps and instantaneous transformations describing the microscopic interaction dynamics.
Indian Academy of Sciences (India)
JAGHOURI HAKIMEH; SARBISHAEI MOHSEN; JAVIDAN KUROSH
2016-05-01
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. The results presented are also compared with some recently published reports.
Solving non-Markovian open quantum systems with multi-channel reservoir coupling
Energy Technology Data Exchange (ETDEWEB)
Broadbent, Curtis J., E-mail: curtis.broadbent@rochester.edu [Rochester Theory Center, and Department of Physics and Astronomy, University of Rochester, Rochester, NY 14627 (United States); Jing, Jun; Yu, Ting [Center for Controlled Quantum Systems, and the Department of Physics and Engineering Physics, Stevens Institute of Technology, Hoboken, NJ 07030 (United States); Eberly, Joseph H. [Rochester Theory Center, and Department of Physics and Astronomy, University of Rochester, Rochester, NY 14627 (United States)
2012-08-15
We extend the non-Markovian quantum state diffusion (QSD) equation to open quantum systems which exhibit multi-channel coupling to a harmonic oscillator reservoir. Open quantum systems which have multi-channel reservoir coupling are those in which canonical transformation of reservoir modes cannot reduce the number of reservoir operators appearing in the interaction Hamiltonian to one. We show that the non-Markovian QSD equation for multi-channel reservoir coupling can, in some cases, lead to an exact master equation which we derive. We then derive the exact master equation for the three-level system in a vee-type configuration which has multi-channel reservoir coupling and give the analytical solution. Finally, we examine the evolution of the three-level vee-type system with generalized Ornstein-Uhlenbeck reservoir correlations numerically. - Highlights: Black-Right-Pointing-Pointer The concept of multi-channel vs. single-channel reservoir coupling is rigorously defined. Black-Right-Pointing-Pointer The non-Markovian quantum state diffusion equation for arbitrary multi-channel reservoir coupling is derived. Black-Right-Pointing-Pointer An exact time-local master equation is derived under certain conditions. Black-Right-Pointing-Pointer The analytical solution to the three-level system in a vee-type configuration is found. Black-Right-Pointing-Pointer The evolution of the three-level system under generalized Ornstein-Uhlenbeck noise is plotted for many parameter regimes.
Witnessing non-Markovianity of quantum evolution
Chruściński, Dariusz; Kossakowski, Andrzej
2014-01-01
We provide further characterization of non-Markovian quantum dynamics based on the concept of divisible dynamical maps. In analogy to entanglement witness we propose a non-Markovianity witness and introduce the corresponding measure of non-Markovianity. We also provide characterization of non-Markovianity in terms of Wigner-Yanase-Dyson skew information.
Non-Markovian random walks and nonlinear reactions: Subdiffusion and propagating fronts
Fedotov, Sergei
2010-01-01
The main aim of the paper is to incorporate the nonlinear kinetic term into non-Markovian transport equations described by a continuous time random walk (CTRW) with nonexponential waiting time distributions. We consider three different CTRW models with reactions. We derive nonlinear Master equations for the mesoscopic density of reacting particles corresponding to CTRW with arbitrary jump and waiting time distributions. We apply these equations to the problem of front propagation in the reaction-transport systems with Kolmogorov-Petrovskii-Piskunov kinetics and anomalous diffusion. We have found an explicit expression for the speed of a propagating front in the case of subdiffusive transport.
Non-Markovian dynamics of open quantum systems
Fleming, Chris H.
An open quantum system is a quantum system that interacts with some environment whose degrees of freedom have been coarse grained away. This model describes non-equilibrium processes more general than scattering-matrix formulations. Furthermore, the microscopically-derived environment provides a model of noise, dissipation and decoherence far more general than Markovian (white noise) models. The latter are fully characterized by Lindblad equations and can be motivated phenomenologically. Non-Markovian processes consistently account for backreaction with the environment and can incorporate effects such as finite temperature and spatial correlations. We consider linear systems with bilinear coupling to the environment, or quantum Brownian motion, and nonlinear systems with weak coupling to the environment. For linear systems we provide exact solutions with analytical results for a variety of spectral densities. Furthermore, we point out an important mathematical subtlety which led to incorrect master-equation coefficients in earlier derivations, given nonlocal dissipation. For nonlinear systems we provide perturbative solutions by translating the formalism of canonical perturbation theory into the context of master equations. It is shown that unavoidable degeneracy causes an unfortunate reduction in accuracy between perturbative master equations and their solutions. We also extend the famous theorem of Lindblad, Gorini, Kossakowski and Sudarshan on completely positivity to non-Markovian master equations. Our application is primarily to model atoms interacting via a common electromagnetic field. The electromagnetic field contains correlations in both space and time, which are related to its relativistic (photon-mediated) nature. As such, atoms residing in the same field experience different environmental effects depending upon their relative position and orientation. Our more accurate solutions were necessary to assess sudden death of entanglement at zero temperature
Zeng, H. S.; Tang, N.; Zheng, Y. P.; Xu, T. T.
2012-10-01
By use of the recently presented two measures, the indivisibility and the backflow of information, we study the non-Markovianity of the dynamics for a two-level system interacting with a zero-temperature structured environment without using rotating wave approximation (RWA). In the limit of weak coupling between the system and its reservoir, and by expanding the time-convolutionless (TCL) generator to the forth order with respect to the coupling strength, the time-local non-Markovian master equation for the reduced state of the system is derived. Under the secular approximation, the exact analytic solution is obtained and the sufficient and necessary conditions for the indivisibility and the backflow of information for the system dynamics are presented. In the more general case, we investigate numerically the properties of the two measures for the case of Lorentzian reservoir. Our results show the importance of the counter-rotating terms to the short-time-scale non-Markovian behavior of the system dynamics, further expose the relation between the two measures and their rationality as non-Markovian measures. Finally, the complete positivity of the dynamics of the considered system is discussed.
Chen, Yu; Zou, Jian; Yang, Zi-Yi; Li, Longwu; Li, Hai; Shao, Bin
2016-08-01
The dynamics of N-qubit GHZ state quantum Fisher information (QFI) under phase noise lasers (PNLs) driving is investigated in terms of non-Markovian master equation. We first investigate the non-Markovian dynamics of the QFI of N-qubit GHZ state and show that when the ratio of the PNL rate and the system-environment coupling strength is very small, the oscillations of the QFIs decay slower which corresponds to the non-Markovian region; yet when it becomes large, the QFIs monotonously decay which corresponds to the Markovian region. When the atom number N increases, QFIs in both regions decay faster. We further find that the QFI flow disappears suddenly followed by a sudden birth depending on the ratio of the PNL rate and the system-environment coupling strength and the atom number N, which unveil a fundamental connection between the non-Markovian behaviors and the parameters of system-environment couplings. We discuss two optimal positive operator-valued measures (POVMs) for two different strategies of our model and find the condition of the optimal measurement. At last, we consider the QFI of two atoms with qubit-qubit interaction under random telegraph noises (RTNs).
Quantum molecular master equations
Brechet, Sylvain D.; Reuse, Francois A.; Maschke, Klaus; Ansermet, Jean-Philippe
2016-10-01
We present the quantum master equations for midsize molecules in the presence of an external magnetic field. The Hamiltonian describing the dynamics of a molecule accounts for the molecular deformation and orientation properties, as well as for the electronic properties. In order to establish the master equations governing the relaxation of free-standing molecules, we have to split the molecule into two weakly interacting parts, a bath and a bathed system. The adequate choice of these systems depends on the specific physical system under consideration. Here we consider a first system consisting of the molecular deformation and orientation properties and the electronic spin properties and a second system composed of the remaining electronic spatial properties. If the characteristic time scale associated with the second system is small with respect to that of the first, the second may be considered as a bath for the first. Assuming that both systems are weakly coupled and initially weakly correlated, we obtain the corresponding master equations. They describe notably the relaxation of magnetic properties of midsize molecules, where the change of the statistical properties of the electronic orbitals is expected to be slow with respect to the evolution time scale of the bathed system.
DEFF Research Database (Denmark)
Dyre, Jeppe
1995-01-01
energies chosen randomly according to a Gaussian. The random-walk model is here derived from Newton's laws by making a number of simplifying assumptions. In the second part of the paper an approximate low-temperature description of energy fluctuations in the random-walk modelthe energy master equation...... (EME)is arrived at. The EME is one dimensional and involves only energy; it is derived by arguing that percolation dominates the relaxational properties of the random-walk model at low temperatures. The approximate EME description of the random-walk model is expected to be valid at low temperatures...... of the random-walk model. The EME allows a calculation of the energy probability distribution at realistic laboratory time scales for an arbitrarily varying temperature as function of time. The EME is probably the only realistic equation available today with this property that is also explicitly consistent...
Non-Markovian Quantum State Diffusion
Diósi, L; Strunz, W T
1998-01-01
We present a nonlinear stochastic Schroedinger equation for pure states describing non-Markovian diffusion of quantum trajectories. It provides an unravelling of the evolution of a quantum system coupled to a finite or infinite number of harmonic oscillators, without any approximation. Its power is illustrated by several examples, including measurement-like situations, dissipation, and quantum Brownian motion. In some examples, we treat the environment phenomenologically as an infinite reservoir with fluctuations of arbitrary correlation. In other examples the environment consists of a finite number of oscillators. In these quasi-periodic cases we see the reversible decay of a `Schroedinger cat' state. Finally, our description of open systems is compatible with different positions of the `Heisenberg cut' between system and environment.
Non-Markovianity during quantum Zeno effect
Thilagam, A
2013-01-01
We examine the Zeno and anti-Zeno effects in the context of non-Markovian dynamics in entangled spin-boson systems in contact with noninteracting reservoirs. We identify enhanced non-Markovian signatures in specific two-qubit partitions of a Bell-like initial state, with results showing that the intra-qubit Zeno effect or anti-Zeno effect occurs in conjunction with inter-qubit non-Markovian dynamics for a range of system parameters. The time domain of effective Zeno or anti-Zeno dynamics is about the same order of magnitude as the non-Markovian time scale of the reservoir correlation dynamics, and changes in decay rate due to the Zeno mechanism appears coordinated with information flow between specific two-qubit partitions. We extend our analysis to examine the Zeno mechanism-non-Markovianity link using the tripartite states arising from a donor-acceptor-sink model of photosynthetic biosystems.
Non-Markovian time evolution of an accelerated qubit
Moustos, Dimitris
2016-01-01
We present a new method for evaluating the response of a moving qubit detector interacting with a scalar field in Minkowski spacetime. We treat the detector as an open quantum system, but we do not invoke the Markov approximation. The evolution equations for the qubit density matrix are valid at all times, for all qubit trajectories and they incorporate non-Markovian effects. We analyze in detail the case of uniform acceleration, providing a detailed characterization of all regimes where non-Markovian effects are significant. We argue that the most stable characterization of acceleration temperature refers to the late time behavior of the detector, because interaction with the field vacuum brings the qubit to a thermal state at the Unruh temperature. In contrast, the early-time transition rate, that is invoked in most discussions of acceleration temperature, does not exhibit a thermal behavior when non-Markovian effects are taken into account. Finally, we note that the non-Markovian evolution derived here als...
Dynamics of open quantum spin systems: An assessment of the quantum master equation approach.
Zhao, P; De Raedt, H; Miyashita, S; Jin, F; Michielsen, K
2016-08-01
Data of the numerical solution of the time-dependent Schrödinger equation of a system containing one spin-1/2 particle interacting with a bath of up to 32 spin-1/2 particles is used to construct a Markovian quantum master equation describing the dynamics of the system spin. The procedure of obtaining this quantum master equation, which takes the form of a Bloch equation with time-independent coefficients, accounts for all non-Markovian effects inasmuch the general structure of the quantum master equation allows. Our simulation results show that, with a few rather exotic exceptions, the Bloch-type equation with time-independent coefficients provides a simple and accurate description of the dynamics of a spin-1/2 particle in contact with a thermal bath. A calculation of the coefficients that appear in the Redfield master equation in the Markovian limit shows that this perturbatively derived equation quantitatively differs from the numerically estimated Markovian master equation, the results of which agree very well with the solution of the time-dependent Schrödinger equation.
Non-Markovian Dynamics in Chiral Quantum Networks with Spins and Photons
Ramos, Tomás; Hauke, Philipp; Pichler, Hannes; Zoller, Peter
2016-01-01
We study the dynamics of chiral quantum networks consisting of nodes coupled by unidirectional or asymmetric bidirectional quantum channels. In contrast to the familiar photonic networks consisting of driven two-level atoms exchanging photons via 1D photonic nanostructures, we propose and study a setup where interactions between the atoms are mediated by spin excitations (magnons) in 1D XX-spin chains representing a spin waveguide. While Markovian quantum network theory eliminates quantum channels as structureless reservoirs in a Born-Markov approximation to obtain a master equation for the nodes, we are interested in non-Markovian dynamics. This arises from the nonlinear character of the dispersion with band-edge effects, and from finite spin propagation velocities leading to time delays in interactions. To account for the non-Markovian dynamics we treat the quantum degrees of freedom of the nodes and connecting channel as a composite spin system with the surrounding of the quantum network as a Markovian bat...
Open system dynamics with non-Markovian quantum trajectories
Strunz, W T; Gisin, Nicolas; Strunz, Walter T; Diosi, Lajos; Gisin, Nicolas
1999-01-01
A non-Markovian stochastic Schroedinger equation for a quantum system coupled to an environment of harmonic oscillators is presented. Its solutions, when averaged over the noise, reproduce the standard reduced density operator without any approximation. We illustrate the power of this approach with several examples, including exponentially decaying bath correlations and extreme non-Markovian cases, where the `environment' consists of only a single oscillator. The latter case shows the decay and revival of a `Schroedinger cat' state. For strong coupling to a dissipative environment with memory, the asymptotic state can be reached in a finite time. Our description of open systems is compatible with different positions of the `Heisenberg cut' between system and environment.
The Entropy Production Distribution in Non-Markovian Thermal Baths
Directory of Open Access Journals (Sweden)
José Inés Jiménez-Aquino
2014-03-01
Full Text Available In this work we study the distribution function for the total entropy production of a Brownian particle embedded in a non-Markovian thermal bath. The problem is studied in the overdamped approximation of the generalized Langevin equation, which accounts for a friction memory kernel characteristic of a Gaussian colored noise. The problem is studied in two physical situations: (i when the particle in the harmonic trap is subjected to an arbitrary time-dependent driving force; and (ii when the minimum of the harmonic trap is arbitrarily dragged out of equilibrium by an external force. By assuming a natural non Markovian canonical distribution for the initial conditions, the distribution function for the total entropy production becomes a non Gaussian one. Its characterization is then given through the first three cumulants.
Comparisons of different witnesses of non-Markovianity
Zuo, Wei; Qian, Xiao-Qing; Liang, Xian-Ting
2017-01-01
In this paper, the evolutions of two kinds of witnesses of the non-Markovianity and their rates of changes with time are investigated and compared. Four definitions, the trace distance, fidelity, quantum relative entropy, and quantum Fisher information are used for the first kind of witnesses which are based on the completely positive maps (CPM). Three definitions, the quantum entanglement, quantum mutual information, and quantum discord are used for the second kind of witnesses, and they are based on the local completely positive maps (LCPM). An open two-level quantum system model and a numerically quantum dissipative dynamics method, hierarchy equation of motion (HEM) are used in the investigations. It is shown that the evolutions of the witnesses and their rates of the changes calculated with different definitions clearly show the characteristics of the non-Markovianity and they are in agreement with each other.
Multi-qubit joint measurements in circuit QED: stochastic master equation analysis
Energy Technology Data Exchange (ETDEWEB)
Criger, Ben; Ciani, Alessandro [RWTH, JARA Institut fuer Quanteninformation, Aachen (Germany); DiVincenzo, David P. [RWTH, JARA Institut fuer Quanteninformation, Aachen (Germany); Forschungszentrum Juelich, Juelich (Germany)
2016-12-15
We derive a family of stochastic master equations describing homodyne measurement of multi-qubit diagonal observables in circuit quantum electrodynamics. In the regime where qubit decay can be neglected, our approach replaces the polaron-like transformation of previous work, which required a lengthy calculation for the physically interesting case of three qubits and two resonator modes. The technique introduced here makes this calculation straightforward and manifestly correct. Using this technique, we are able to show that registers larger than one qubit evolve under a non-Markovian master equation. We perform numerical simulations of the three-qubit, two-mode case from previous work, obtaining an average post-measurement state fidelity of ∝94%, limited by measurement-induced decoherence and dephasing. (orig.)
Quantum Metrology in Non-Markovian Environments
Chin, Alex W; Plenio, Martin B
2011-01-01
We analyze optimal bounds for precision spectroscopy in the presence of general, non-Markovian phase noise. We demonstrate that the metrological equivalence of product and maximally entangled states that holds under Markovian dephasing fails in the non-Markovian case. Using an exactly solvable model of a physically realistic finite band-width dephasing environment, we show that the ensuing non-Markovian dynamics enables quantum correlated states to outperform metrological strategies based on uncorrelated states but otherwise identical resources. We show that this conclusion is a direct result of the coherent dynamics of the global state of the system and environment and, as a result, possesses general validity that goes beyond specific models.
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.
Shi, Pengqin; Hu, Menghan; Ying, Yaofeng; Jin, Jinshuang
2016-09-01
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.
On Non-Markovian Quantum Evolution
Chruściński, Dariusz; Kossakowski, Andrzej
2013-01-01
We analyze two measures of non-Markovianity: one based on the mathematical concept of divisibility of the dynamical map and the other one based on distinguishability of quantum states. We provide a simple example of qubit dynamic to show that these two measures need not agree. In addition, we discuss possible generalizations and intricate relations between these measures.
Iles-Smith, Jake; Lambert, Neill; Nazir, Ahsan
2015-01-01
We explore excitonic energy transfer dynamics in a molecular dimer system coupled to both structured and unstructured oscillator environments. By extending the reaction coordinate master equation technique developed in [J. Iles-Smith, N. Lambert, and A. Nazir, Phys. Rev. A 90, 032114 (2014)], we go beyond the commonly used Born-Markov approximations to incorporate system-environment correlations and the resultant non-Markovian dynamical effects. We obtain energy transfer dynamics for both underdamped and overdamped oscillator environments that are in perfect agreement with the numerical hierarchical equations of motion over a wide range of parameters. Furthermore, we show that the Zusman equations, which may be obtained in a semiclassical limit of the reaction coordinate model, are often incapable of describing the correct dynamical behaviour. This demonstrates the necessity of properly accounting for quantum correlations generated between the system and its environment when the Born-Markov approximations no ...
Zhao, Xinyu; Corn, Brittany; Yu, Ting; 10.1103/PhysRevA.84.032101
2011-01-01
Non-Markovian dynamics is studied for two interacting quibts strongly coupled to a dissipative bosonic environment. For the first time, we have derived the 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 studied the residual entanglement in the steady state by analyzing the steady state solution of the QSD equation. Finally, we have discussed an approximate QSD equation.
Non-Markovian Reactivation of Quantum Relays
Pirandola, Stefano; Jacobsen, Christian S; Spedalieri, Gaetana; Braunstein, Samuel L; Gehring, Tobias; Andersen, Ulrik L
2015-01-01
We consider a quantum relay which is used by two parties to perform several continuous-variable protocols: Entanglement swapping, distillation, quantum teleportation, and quantum key distribution. The theory of these protocols is extended to a non-Markovian model of decoherence characterized by correlated Gaussian noise. Even if bipartite entanglement is completely lost at the relay, we show that the various protocols can progressively be reactivated by the separable noise-correlations of the environment. In fact, above a critical amount, these correlations are able to restore the distribution of quadripartite entanglement, which can be localized into an exploitable bipartite form by the action of the relay. Our findings are confirmed by a proof-of-principle experiment and show the potential advantages of non-Markovian effects in a quantum network architecture.
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.
Quantum metrology in non-Markovian environments.
Chin, Alex W; Huelga, Susana F; Plenio, Martin B
2012-12-07
We analyze precision bounds for a local phase estimation in the presence of general, non-Markovian phase noise. We demonstrate that the metrological equivalence of product and maximally entangled states that holds under strictly Markovian dephasing fails in the non-Markovian case. Using an exactly solvable model of a physically realistic finite bandwidth dephasing environment, we demonstrate that the ensuing non-Markovian dynamics enables quantum correlated states to outperform metrological strategies based on uncorrelated states using otherwise identical resources. We show that this conclusion is a direct result of the coherent dynamics of the global state of the system and environment and therefore the obtained scaling with the number of particles, which surpasses the standard quantum limit but does not achieve Heisenberg resolution, possesses general validity that goes beyond specific models. This is in marked contrast with the situation encountered under general Markovian noise, where an arbitrarily small amount of noise is enough to restore the scaling dictated by the standard quantum limit.
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......We derive an extension to the quantum regression theorem which facilitates the calculation of two-time correlation functions and emission spectra for systems undergoing non-Markovian evolution. The derivation exploits projection operator techniques, with which we obtain explicit equations of motion...
Non-Markovian dynamics in pulsed and continuous wave atom lasers
Breuer, H P; Kappler, B; Petruccione, F
1999-01-01
The dynamics of atom lasers with a continuous output coupler based on two-photon Raman transitions is investigated. With the help of the time-convolutionless projection operator technique the quantum master equations for pulsed and continuous wave (cw) atom lasers are derived. In the case of the pulsed atom laser the power of the time-convolutionless projection operator technique is demonstrated through comparison with the exact solution. It is shown that in an intermediate coupling regime where the Born-Markov approximation fails the results of this algorithm agree with the exact solution. To study the dynamics of a continuous wave atom laser a pump mechanism is included in the model. Whereas the pump mechanism is treated within the Born-Markov approximation, the output coupling leads to non-Markovian effects. The solution of the master equation resulting from the time-convolutionless projection operator technique exhibits strong oscillations in the occupation number of the Bose-Einstein condensate. These os...
Long-time memory in non-Markovian evolutions
Chruściński, Dariusz; Kossakowski, Andrzej; Pascazio, Saverio
2010-03-01
If the dynamics of an open quantum system is non-Markovian, its asymptotic state strongly depends on the initial conditions, even if the dynamics possesses an invariant state. This is the very essence of memory effects. In particular, the asymptotic state can remember and partially preserve its initial entanglement. Interestingly, even if the non-Markovian evolution relaxes to an equilibrium state, this state needs not be invariant. Therefore, the noninvariance of equilibrium becomes a clear sign of non-Markovianity.
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.
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....
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
Entanglement and non-markovianity of quantum evolutions.
Rivas, Angel; Huelga, Susana F; Plenio, Martin B
2010-07-30
We address the problem of quantifying the non-markovian character of quantum time evolutions of general systems in contact with an environment. We introduce two different measures of non-markovianity that exploit the specific traits of quantum correlations and are suitable for opposite experimental contexts. When complete tomographic knowledge about the evolution is available, our measure provides a necessary and sufficient condition to quantify strictly the non-markovianity. In the opposite case, when no information whatsoever is available, we propose a sufficient condition for non-markovianity. Remarkably, no optimization procedure underlies our derivation, which greatly enhances the practical relevance of the proposed criteria.
Closing the hierarchy for non-Markovian magnetization dynamics
Energy Technology Data Exchange (ETDEWEB)
Tranchida, J., E-mail: julien.tranchida@cea.fr [CEA/DAM/Le Ripault, BP 16, F-37260 Monts (France); CNRS-Laboratoire de Mathématiques et Physique Théorique (UMR 7350), Fédération de Recherche “Denis Poisson” (FR2964), Département de Physique, Université de Tours, Parc de Grandmont, F-37200 Tours (France); Thibaudeau, P., E-mail: pascal.thibaudeau@cea.fr [CEA/DAM/Le Ripault, BP 16, F-37260 Monts (France); Nicolis, S., E-mail: stam.nicolis@lmpt.univ-tours.fr [CNRS-Laboratoire de Mathématiques et Physique Théorique (UMR 7350), Fédération de Recherche “Denis Poisson” (FR2964), Département de Physique, Université de Tours, Parc de Grandmont, F-37200 Tours (France)
2016-04-01
We propose a stochastic approach for the description of the time evolution of the magnetization of nanomagnets, that interpolates between the Landau–Lifshitz–Gilbert and the Landau–Lifshitz–Bloch approximations, by varying the strength of the noise. In addition, we take into account the autocorrelation time of the noise and explore the consequences, when it is finite, on the scale of the response of the magnetization, i.e. when it may be described as colored, rather than white, noise and non-Markovian features become relevant. We close the hierarchy for the moments of the magnetization, by introducing a suitable truncation scheme, whose validity is tested by direct numerical solution of the moment equations and compared to the average deduced from a numerical solution of the corresponding stochastic Langevin equation. In this way we establish a general framework that allows both coarse-graining simulations and faster calculations beyond the truncation approximation used here.
Light with Tunable Non-Markovian Phase Imprint
Fischer, Robert; Vidal, Itamar; Gilboa, Doron; Correia, Ricardo R. B.; Ribeiro-Teixeira, Ana C.; Prado, Sandra D.; Hickman, Jandir; Silberberg, Yaron
2015-08-01
We introduce a simple and flexible method to generate spatially non-Markovian light with tunable coherence properties in one and two dimensions. The unusual behavior of this light is demonstrated experimentally by probing the far field and by recording its diffraction pattern after a double slit: In both cases we observe, instead of a central intensity maximum, a line- or cross-shaped dark region, whose width and profile depend on the non-Markovian coherence properties. Because these properties can be controlled and easily reproduced in experiment, the presented approach lends itself to serving as a test bed to study and gain a deeper understanding of non-Markovian processes.
Light with tunable non-Markovian phase imprint
Fischer, Robert; Gilboa, Doron; Correia, Ricardo R B; Ribeiro-Teixeira, Ana C; Prado, Sandra D; Hickman, Jandir; Silberberg, Yaron
2015-01-01
We introduce a simple and flexible method to generate spatially non-Markovian light with tunable coherence properties in one and two dimensions. The unusual behavior of this light is demonstrated experimentally by probing the far field and recording its diffraction pattern after a double slit: In both cases we observe instead of a central intensity maximum a line or cross shaped dark region, whose width and profile depend on the non-Markovian coherence properties. Since these properties can be controlled and easily reproduced in experiment, the presented approach lends itself to serve as a testbed to gain a deeper understanding of non-Markovian processes.
On Non-Markovian Time Evolution in Open Quantum Systems
Kossakowski, Andrzej; Rebolledo, Rolando
2008-03-01
Non-Markovian reduced dynamics of an open system is investigated. In the case the initial state of the reservoir is the vacuum state, an approximation is introduced which makes possible to construct a reduced dynamics which is completely positive.
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.
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....
Decision-Theoretic Planning with non-Markovian Rewards
Gretton, C; Price, D; Slaney, J; Thiebaux, S
2011-01-01
A decision process in which rewards depend on history rather than merely on the current state is called a decision process with non-Markovian rewards (NMRDP). In decision-theoretic planning, where many desirable behaviours are more naturally expressed as properties of execution sequences rather than as properties of states, NMRDPs form a more natural model than the commonly adopted fully Markovian decision process (MDP) model. While the more tractable solution methods developed for MDPs do not directly apply in the presence of non-Markovian rewards, a number of solution methods for NMRDPs have been proposed in the literature. These all exploit a compact specification of the non-Markovian reward function in temporal logic, to automatically translate the NMRDP into an equivalent MDP which is solved using efficient MDP solution methods. This paper presents NMRDPP (Non-Markovian Reward Decision Process Planner), a software platform for the development and experimentation of methods for decision-theoretic planning...
Entanglement and non-Markovianity of quantum evolutions
Rivas, Ángel; Plenio, Martin B
2009-01-01
We address the problem of quantifying the non-Markovian character of quantum time-evolutions of general systems in contact with an environment. We introduce two different measures of non-Markovianity that exploit the specific traits of quantum correlations and are suitable for opposite experimental contexts, one requiring complete tomographic knowledge about the evolution and the other one requiring no knowledge at all. Remarkably, no optimization procedure underlies our derivation, which greatly enhances the practical relevance of the proposed criteria.
Energy Technology Data Exchange (ETDEWEB)
Iles-Smith, Jake, E-mail: Jakeilessmith@gmail.com [Controlled Quantum Dynamics Theory, Imperial College London, London SW7 2PG (United Kingdom); Photon Science Institute and School of Physics and Astronomy, The University of Manchester, Oxford Road, Manchester M13 9PL (United Kingdom); Department of Photonics Engineering, DTU Fotonik, Ørsteds Plads, 2800 Kongens Lyngby (Denmark); Dijkstra, Arend G. [Max Planck Institute for the Structure and Dynamics of Matter, Luruper Chaussee 149, 22761 Hamburg (Germany); Lambert, Neill [CEMS, RIKEN, Saitama 351-0198 (Japan); Nazir, Ahsan, E-mail: ahsan.nazir@manchester.ac.uk [Photon Science Institute and School of Physics and Astronomy, The University of Manchester, Oxford Road, Manchester M13 9PL (United Kingdom)
2016-01-28
We explore excitonic energy transfer dynamics in a molecular dimer system coupled to both structured and unstructured oscillator environments. By extending the reaction coordinate master equation technique developed by Iles-Smith et al. [Phys. Rev. A 90, 032114 (2014)], we go beyond the commonly used Born-Markov approximations to incorporate system-environment correlations and the resultant non-Markovian dynamical effects. We obtain energy transfer dynamics for both underdamped and overdamped oscillator environments that are in perfect agreement with the numerical hierarchical equations of motion over a wide range of parameters. Furthermore, we show that the Zusman equations, which may be obtained in a semiclassical limit of the reaction coordinate model, are often incapable of describing the correct dynamical behaviour. This demonstrates the necessity of properly accounting for quantum correlations generated between the system and its environment when the Born-Markov approximations no longer hold. Finally, we apply the reaction coordinate formalism to the case of a structured environment comprising of both underdamped (i.e., sharply peaked) and overdamped (broad) components simultaneously. We find that though an enhancement of the dimer energy transfer rate can be obtained when compared to an unstructured environment, its magnitude is rather sensitive to both the dimer-peak resonance conditions and the relative strengths of the underdamped and overdamped contributions.
Markovian Master Equations: A Critical Study
Rivas, Ángel; Huelga, Susana F; Plenio, Martin B
2010-01-01
We derive Markovian master equations of single and interacting harmonic systems in different scenarios, including strong internal coupling. By comparing the dynamics resulting from the corresponding Markovian master equations with exact numerical simulations of the evolution of the global system, we precisely delimit their validity regimes and assess the robustness of the assumptions usually made in the process of deriving the reduced dynamics. The proposed method is sufficiently general to suggest that the conclusions made here are widely applicable to a large class of settings involving interacting chains subject to a weak interaction with an environment.
Markovian master equations: a critical study
Energy Technology Data Exchange (ETDEWEB)
Rivas, Angel; Huelga, Susana F; B Plenio, Martin [Institut fuer Theoretische Physik, Universitaet Ulm, Albert-Einstein-Allee 11, D-89069 Ulm (Germany); K Plato, A Douglas, E-mail: angel.rivas@uni-ulm.d [Institute for Mathematical Sciences, Imperial College London, London SW7 2PG (United Kingdom)
2010-11-15
We derive Markovian master equations for single and interacting harmonic systems in different scenarios, including strong internal coupling. By comparing the dynamics resulting from the corresponding master equations with numerical simulations of the global system's evolution, we delimit their validity regimes and assess the robustness of the assumptions usually made in the process of deriving the reduced Markovian dynamics. The results of these illustrative examples serve to clarify the general properties of other open quantum system scenarios subject to treatment within a Markovian approximation.
Kato, Akihito; Tanimura, Yoshitaka
2016-12-01
We consider a quantum system strongly coupled to multiple heat baths at different temperatures. Quantum heat transport phenomena in this system are investigated using two definitions of the heat current: one in terms of the system energy and the other in terms of the bath energy. When we consider correlations among system-bath interactions (CASBIs)—which have a purely quantum mechanical origin—the definition in terms of the bath energy becomes different. We found that CASBIs are necessary to maintain the consistency of the heat current with thermodynamic laws in the case of strong system-bath coupling. However, within the context of the quantum master equation approach, both of these definitions are identical. Through a numerical investigation, we demonstrate this point for a non-equilibrium spin-boson model and a three-level heat engine model using the reduced hierarchal equations of motion approach under the strongly coupled and non-Markovian conditions. We observe the cyclic behavior of the heat currents and the work performed by the heat engine, and we find that their phases depend on the system-bath coupling strength. Through consideration of the bath heat current, we show that the efficiency of the heat engine decreases as the strength of the system-bath coupling increases, due to the CASBI contribution. In the case of a large system-bath coupling, the efficiency decreases further if the bath temperature is increased, even if the ratio of the bath temperatures is fixed, due to the discretized nature of energy eigenstates. This is also considered to be a unique feature of quantum heat engines.
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.
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.
Non-Markovian expansion in quantum Brownian motion
Fraga, Eduardo S.; Krein, Gastão; Palhares, Letícia F.
2014-01-01
We consider the non-Markovian Langevin evolution of a dissipative dynamical system in quantum mechanics in the path integral formalism. After discussing the role of the frequency cutoff for the interaction of the system with the heat bath and the kernel and noise correlator that follow from the most common choices, we derive an analytic expansion for the exact non-Markovian dissipation kernel and the corresponding colored noise in the general case that is consistent with the fluctuation-dissipation theorem and incorporates systematically non-local corrections. We illustrate the modifications to results obtained using the traditional (Markovian) Langevin approach in the case of the exponential kernel and analyze the case of the non-Markovian Brownian motion. We present detailed results for the free and the quadratic cases, which can be compared to exact solutions to test the convergence of the method, and discuss potentials of a general nonlinear form.
Non-Markovian expansion in quantum dissipative systems
Fraga, E S; Palhares, L F
2009-01-01
We consider the non-Markovian Langevin evolution of a dissipative dynamical system in quantum mechanics in the path integral formalism. After discussing the role of the frequency cutoff for the interaction of the system with the heat bath and the kernel and noise correlator that follow from the most common choices, we derive an analytic expansion for the exact non-Markovian dissipation kernel and the corresponding colored noise in the general case that is consistent with the fluctuation-dissipation theorem and incorporates systematically non-local corrections. We illustrate the modifications to results obtained using the traditional (Markovian) Langevin approach in the case of the exponential kernel and analyze the case of the non-Markovian Brownian motion.
Effect of memory in non-Markovian Boolean networks
Ebadi, Haleh; Ausloos, Marcel; Jafari, GholamReza
2016-01-01
One successful model of interacting biological systems is the Boolean network. The dynamics of a Boolean network, controlled with Boolean functions, is usually considered to be a Markovian (memory-less) process. However, both self organizing features of biological phenomena and their intelligent nature should raise some doubt about ignoring the history of their time evolution. Here, we extend the Boolean network Markovian approach: we involve the effect of memory on the dynamics. This can be explored by modifying Boolean functions into non-Markovian functions, for example, by investigating the usual non-Markovian threshold function, - one of the most applied Boolean functions. By applying the non-Markovian threshold function on the dynamical process of a cell cycle network, we discover a power law memory with a more robust dynamics than the Markovian dynamics.
Decoherence of Josephson charge qubit in non-Markovian environment
Energy Technology Data Exchange (ETDEWEB)
Qiu, Qing-Qian; Zhou, Xing-Fei; Liang, Xian-Ting, E-mail: liangxianting@nbu.edu.cn
2016-05-15
In this paper we investigate the decoherence of Josephson charge qubit (JCQ) by using a time-nonlocal (TNL) dynamical method. Three kinds of environmental models, described with Ohmic, super-Ohmic, and sub-Ohmic spectral density functions are considered. It is shown that the TNL method can effectively include the non-Markovian effects in the dynamical solutions. In particular, it is shown that the sub-Ohmic environment has longer correlation time than the Ohmic and super-Ohmic ones. And the Markovian and non-Markovian dynamics are obviously different for the qubit in sub-Ohmic environment.
Programmable entanglement oscillations in a non Markovian channel
Cialdi, Simone; Tesio, Enrico; Paris, Matteo G A
2010-01-01
We suggest and demonstrate an all-optical experimental setup to observe and engineer entanglement oscillations of a pair of polarization qubits in a non-Markovian channel. We generate entangled photon pairs by spontaneous parametric downconversion (SPDC), and then insert a programmable spatial light modulator in order to impose a polarization dependent phase-shift on the spatial domain of the SPDC output and to create an effective non-Markovian environment. Modulation of the enviroment spectrum is obtained by inserting a spatial grating on the signal arm. In our experiment, programmable oscillations of entanglement are achieved, with the maximally revived state that violates Bell's inequality by 17 standard deviations.
Kolli, Avinash; Nazir, Ahsan; Olaya-Castro, Alexandra
2011-10-21
We derive a many-site version of the non-Markovian time-convolutionless polaron master equation [Jang et al., J. Chem Phys. 129, 101104 (2008)] to describe electronic excitation dynamics in multichromophoric systems. By treating electronic and vibrational degrees of freedom in a combined frame (polaron frame), this theory is capable of interpolating between weak and strong exciton-phonon coupling and is able to account for initial non-equilibrium bath states and spatially correlated environments. Besides outlining a general expression for the expected value of any electronic system observable in the original frame, we also discuss implications of the Markovian and Secular approximations highlighting that they need not hold in the untransformed frame despite being strictly satisfied in the polaron frame. The key features of the theory are illustrated using as an example a four-site subsystem of the Fenna-Mathews-Olson light-harvesting complex. For a spectral density including a localised mode, we show that oscillations of site populations may only be observed when non-equilibrium bath effects are taken into account. Furthermore, we illustrate how this formalism allows us to identify the electronic and vibrational components of the oscillatory dynamics.
Novel dissipative properties of the master equation
Hong, Liu; Jia, Chen; Zhu, Yi; Yong, Wen-An
2016-10-01
Recent studies have shown that the entropy production rate for the master equation consists of two non-negative terms: the adiabatic and non-adiabatic parts, where the non-adiabatic part is also known as the free energy dissipation rate. In this paper, we present some nonzero lower bounds for the free energy, the entropy production rate, and its adiabatic and non-adiabatic parts. These nonzero lower bounds not only reveal some novel dissipative properties for nonequilibrium dynamics which are much stronger than the second law of thermodynamics, but also impose some new constraints on thermodynamic constitutive relations. Moreover, we also give a mathematical application of the nonzero lower bounds by studying the long-time behavior of the master equation. Extensions to the Tsallis statistics are also discussed, including the nonzero lower bounds for the Tsallis-type free energy and its dissipation rate.
Master-equation approach to stochastic neurodynamics
Ohira, Toru; Cowan, Jack D.
1993-09-01
A master-equation approach to the stochastic neurodynamics proposed by Cowan [in Advances in Neural Information Processing Systems 3, edited by R. P. Lippman, J. E. Moody, and D. S. Touretzky (Morgan Kaufmann, San Mateo, 1991), p. 62] is investigated in this paper. We deal with a model neural network that is composed of two-state neurons obeying elementary stochastic transition rates. We show that such an approach yields concise expressions for multipoint moments and an equation of motion. We apply the formalism to a (1+1)-dimensional system. Exact and approximate expressions for various statistical parameters are obtained and compared with Monte Carlo simulations.
Solve the Master Equation in Python
Fan, Wei; Chen, Bing; Ye, Qianqian
2011-01-01
A brief introduction to the Python computing environment is given. By solving the master equation encountered in quantum transport, we give an example of how to solve the ODE problems in Python. The ODE solvers used are the ZVODE routine in Scipy and the bsimp solver in GSL. For the former, the equation can be in its complex-valued form, while for the latter, it has to be rewritten to a real-valued form. The focus is on the detailed workflow of the implementation process, rather than on the syntax of the python language, with the hope to help readers simulate their own models in Python.
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
Long-time memory in non-Markovian evolutions
Chruściński, Dariusz; Pascazio, Saverio
2009-01-01
If the dynamics of an open quantum systems is non-Markovian, its asymptotic state strongly depends on the initial conditions, even if the dynamics possesses an invariant state. This is the very essence of memory effects. In particular, the asymptotic state can remember and partially preserve its initial entanglement.
On measures of non-Markovianity: divisibility vs. Markovianity
Chruściński, Dariusz
2011-01-01
We analyze two recently proposed measure of non-Markovianity: one based on the concept of divisibility of the dynamical map and the other one based on distinguishability of quantum states. We provide a toy model to show that these two measures need not agree. Finally, we discuss possible generalizations and intricate relations between these measures.
Measures of non-Markovianity: Divisibility versus backflow of information
Chruściński, Dariusz; Kossakowski, Andrzej; Rivas, Ángel
2011-05-01
We analyze two recently proposed measures of non-Markovianity: one based on the concept of divisibility of the dynamical map and the other one based on distinguishability of quantum states. We provide a model to show that these two measures need not agree. In addition, we discuss possible generalizations and intricate relations between these measures.
Non-Markovian character in human mobility: Online and offline
Zhao, Zhi-Dan; Cai, Shi-Min; Lu, Yang
2015-06-01
The dynamics of human mobility characterizes the trajectories that humans follow during their daily activities and is the foundation of processes from epidemic spreading to traffic prediction and information recommendation. In this paper, we investigate a massive data set of human activity, including both online behavior of browsing websites and offline one of visiting towers based mobile terminations. The non-Markovian character observed from both online and offline cases is suggested by the scaling law in the distribution of dwelling time at individual and collective levels, respectively. Furthermore, we argue that the lower entropy and higher predictability in human mobility for both online and offline cases may originate from this non-Markovian character. However, the distributions of individual entropy and predictability show the different degrees of non-Markovian character between online and offline cases. To account for non-Markovian character in human mobility, we apply a protype model with three basic ingredients, namely, preferential return, inertial effect, and exploration to reproduce the dynamic process of online and offline human mobilities. The simulations show that the model has an ability to obtain characters much closer to empirical observations.
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 of t...
Quantum non-Markovianity induced by Anderson localization
Lorenzo, Salvatore; Lombardo, Federico; Ciccarello, Francesco; Palma, G. Massimo
2017-02-01
As discovered by P. W. Anderson, excitations do not propagate freely in a disordered lattice, but, due to destructive interference, they localise. As a consequence, when an atom interacts with a disordered lattice, one indeed observes a non-trivial excitation exchange between atom and lattice. Such non-trivial atomic dynamics will in general be characterised also by a non-trivial quantum information backflow, a clear signature of non-Markovian dynamics. To investigate the above scenario, we consider a quantum emitter, or atom, weakly coupled to a uniform coupled-cavity array (CCA). If initially excited, in the absence of disorder, the emitter undergoes a Markovian spontaneous emission by releasing all its excitation into the CCA (initially in its vacuum state). By introducing static disorder in the CCA the field normal modes become Anderson-localized, giving rise to a non-Markovian atomic dynamics. We show the existence of a functional relationship between a rigorous measure of quantum non-Markovianity and the CCA localization. We furthermore show that the average non-Markovianity of the atomic dynamics is well-described by a phenomenological model in which the atom is coupled, at the same time, to a single mode and to a standard - Markovian - dissipative bath.
Quantum non-Markovianity induced by Anderson localization
Lorenzo, Salvatore; Lombardo, Federico; Ciccarello, Francesco; Palma, G. Massimo
2017-01-01
As discovered by P. W. Anderson, excitations do not propagate freely in a disordered lattice, but, due to destructive interference, they localise. As a consequence, when an atom interacts with a disordered lattice, one indeed observes a non-trivial excitation exchange between atom and lattice. Such non-trivial atomic dynamics will in general be characterised also by a non-trivial quantum information backflow, a clear signature of non-Markovian dynamics. To investigate the above scenario, we consider a quantum emitter, or atom, weakly coupled to a uniform coupled-cavity array (CCA). If initially excited, in the absence of disorder, the emitter undergoes a Markovian spontaneous emission by releasing all its excitation into the CCA (initially in its vacuum state). By introducing static disorder in the CCA the field normal modes become Anderson-localized, giving rise to a non-Markovian atomic dynamics. We show the existence of a functional relationship between a rigorous measure of quantum non-Markovianity and the CCA localization. We furthermore show that the average non-Markovianity of the atomic dynamics is well-described by a phenomenological model in which the atom is coupled, at the same time, to a single mode and to a standard - Markovian - dissipative bath. PMID:28205542
Strasberg, Philipp; Schaller, Gernot; Lambert, Neill; Brandes, Tobias
2016-07-01
We propose a method to study the thermodynamic behaviour of small systems beyond the weak coupling and Markovian approximation, which is different in spirit from conventional approaches. The idea is to redefine the system and environment such that the effective, redefined system is again coupled weakly to Markovian residual baths and thus, allows to derive a consistent thermodynamic framework for this new system-environment partition. To achieve this goal we make use of the reaction coordinate (RC) mapping, which is a general method in the sense that it can be applied to an arbitrary (quantum or classical and even time-dependent) system coupled linearly to an arbitrary number of harmonic oscillator reservoirs. The core of the method relies on an appropriate identification of a part of the environment (the RC), which is subsequently included as a part of the system. We demonstrate the power of this concept by showing that non-Markovian effects can significantly enhance the steady state efficiency of a three-level-maser heat engine, even in the regime of weak system-bath coupling. Furthermore, we show for a single electron transistor coupled to vibrations that our method allows one to justify master equations derived in a polaron transformed reference frame.
Quantifying uncertainty in the chemical master equation
Bayati, Basil S.
2017-06-01
We describe a novel approach to quantifying the uncertainty inherent in the chemical kinetic master equation with stochastic coefficients. A stochastic collocation method is coupled to an analytical expansion of the master equation to analyze the effects of both extrinsic and intrinsic noise. The method consists of an analytical moment-closure method resulting in a large set of differential equations with stochastic coefficients that are in turn solved via a Smolyak sparse grid collocation method. We discuss the error of the method relative to the dimension of the model and clarify which methods are most suitable for the problem. We apply the method to two typical problems arising in chemical kinetics with time-independent extrinsic noise. Additionally, we show agreement with classical Monte Carlo simulations and calculate the variance over time as the sum of two expectations. The method presented here has better convergence properties for low to moderate dimensions than standard Monte Carlo methods and is therefore a superior alternative in this regime.
Markovian quantum master equation beyond adiabatic regime
Yamaguchi, Makoto; Yuge, Tatsuro; Ogawa, Tetsuo
2017-01-01
By introducing a temporal change time scale τA(t ) for the time-dependent system Hamiltonian, a general formulation of the Markovian quantum master equation is given to go well beyond the adiabatic regime. In appropriate situations, the framework is well justified even if τA(t ) is faster than the decay time scale of the bath correlation function. An application to the dissipative Landau-Zener model demonstrates this general result. The findings are applicable to a wide range of fields, providing a basis for quantum control beyond the adiabatic regime.
Li, Zhen; Lee, Hee Sun; Darve, Eric; Karniadakis, George Em
2017-01-07
Memory effects are often introduced during coarse-graining of a complex dynamical system. In particular, a generalized Langevin equation (GLE) for the coarse-grained (CG) system arises in the context of Mori-Zwanzig formalism. Upon a pairwise decomposition, GLE can be reformulated into its pairwise version, i.e., non-Markovian dissipative particle dynamics (DPD). GLE models the dynamics of a single coarse particle, while DPD considers the dynamics of many interacting CG particles, with both CG systems governed by non-Markovian interactions. We compare two different methods for the practical implementation of the non-Markovian interactions in GLE and DPD systems. More specifically, a direct evaluation of the non-Markovian (NM) terms is performed in LE-NM and DPD-NM models, which requires the storage of historical information that significantly increases computational complexity. Alternatively, we use a few auxiliary variables in LE-AUX and DPD-AUX models to replace the non-Markovian dynamics with a Markovian dynamics in a higher dimensional space, leading to a much reduced memory footprint and computational cost. In our numerical benchmarks, the GLE and non-Markovian DPD models are constructed from molecular dynamics (MD) simulations of star-polymer melts. Results show that a Markovian dynamics with auxiliary variables successfully generates equivalent non-Markovian dynamics consistent with the reference MD system, while maintaining a tractable computational cost. Also, transient subdiffusion of the star-polymers observed in the MD system can be reproduced by the coarse-grained models. The non-interacting particle models, LE-NM/AUX, are computationally much cheaper than the interacting particle models, DPD-NM/AUX. However, the pairwise models with momentum conservation are more appropriate for correctly reproducing the long-time hydrodynamics characterised by an algebraic decay in the velocity autocorrelation function.
Epidemics in networks: A master equation approach
Cotacallapa, M
2016-01-01
A problem closely related to epidemiology, where a subgraph of 'infected' links is defined inside a larger network, is investigated. This subgraph is generated from the underlying network by a random variable, which decides whether a link is able to propagate a disease/information. The relaxation timescale of this random variable is examined in both annealed and quenched limits, and the effectiveness of propagation of disease/information is analyzed. The dynamics of the model is governed by a master equation and two types of underlying network are considered: one is scale-free and the other has exponential degree distribution. We have shown that the relaxation timescale of the contagion variable has a major influence on the topology of the subgraph of infected links, which determines the efficiency of spreading of disease/information over the network.
Tunneling through molecules and quantum dots: master-equation approaches
Timm, Carsten
2008-01-01
An important class of approaches to the description of electronic transport through molecules and quantum dots is based on the master equation. We discuss various formalisms for deriving a master equation and their interrelations. It is shown that the master equations derived by Wangsness, Bloch, and Redfield and by Koenig et al. are equivalent. The roles of the large-reservoir and Markov approximations are clarified. The Markov approximation is traced back to nonzero bias voltage and tempera...
Wang, Hao-Tian; Zou, Yang; Ge, Rong-Chun; Guo, Guang-Can
2010-01-01
We present a detailed study of the entanglement dynamics of a two-qubit system coupled to independent non-Markovian environments, employing hierarchy equations. This recently developed theoretical treatment can conveniently solve non-Markovian problems and take into consideration the correlation between the system and bath in an initial state. We concentrate on calculating the death and rebirth time points of the entanglement to obtain a general view of the concurrence curve and explore the behavior of entanglement dynamics with respect to the coupling strength, the characteristic frequency of the noise bath and the environment temperature.
Kinetics of self-induced aggregation of Brownian particles: non-Markovian and non-Gaussian features
Ghosh, Pulak Kumar; Bag, Bidhan Chandra
2012-01-01
In this paper we have studied a model for self-induced aggregation in Brownian particle incorporating the non-Markovian and non-Gaussian character of the associated random noise process. In this model the time evolution of each individual is guided by an over-damped Langevin equation of motion with a non-local drift resulting from the local unbalance distributions of the other individuals. Our simulation result shows that colored nose can induce the cluster formation even at large noise strength. Another observation is that critical noise strength grows very rapidly with increase of noise correlation time for Gaussian noise than non Gaussian one. However, at long time limit the cluster number in aggregation process decreases with time following a power law. The exponent in the power law increases remarkable for switching from Markovian to non Markovian noise process.
Non-Markovian transmission through two quantum dots connected by a continuum
Energy Technology Data Exchange (ETDEWEB)
Cao, Yunshan [School of Physics, Peking University, Beijing 100871 (China); Department of Physics, Beijing Normal University, Beijing 100875 (China); Xu, Luting; Meng, Jianyu [Department of Physics, Beijing Normal University, Beijing 100875 (China); Li, Xin-Qi, E-mail: lixinqi@bnu.edu.cn [Department of Physics, Beijing Normal University, Beijing 100875 (China)
2012-10-01
We consider a transport setup that contains a double-dot connected by a continuum. Via an exact solution of the time-dependent Schrödinger equation, we demonstrate a highly non-Markovian quantum-coherence-mediated transport through this dot–continuum–dot (DCD) system, which is in contrast with the common premise since in typical case a quantum particle does not reenter the system of interest once it irreversibly decayed into a continuum (such as the spontaneous emission of a photon). We also find that this DCD system supports an unusual steady state with unequal source and drain currents, owing to electrons irreversibly entering the continuum and floating there. -- Highlights: ► We analyze the non-Markovian transmission through a double-dot connected by a continuum. ► We convert the many-electron problem into a single-particle approach and find an exact solution. ► We reveal some interesting behaviors associated with quantum-coherence-assisted transmission through a continuum.
Non-Markovian Brownian motion in a magnetic field and time-dependent force fields
Hidalgo-Gonzalez, J. C.; Jiménez-Aquino, J. I.; Romero-Bastida, M.
2016-11-01
This work focuses on the derivation of the velocity and phase-space generalized Fokker-Planck equations for a Brownian charged particle embedded in a memory thermal bath and under the action of force fields: a constant magnetic field and arbitrary time-dependent force fields. To achieve the aforementioned goal we use a Gaussian but non-Markovian generalized Langevin equation with an arbitrary friction memory kernel. In a similar way, the generalized diffusion equation in the zero inertia limit is also derived. Additionally we show, in the absence of the time-dependent external forces, that, if the fluctuation-dissipation relation of the second kind is valid, then the generalized Langevin dynamics associated with the charged particle reaches a stationary state in the large-time limit. The consistency of our theoretical results is also verified when they are compared with those derived in the absence of the force fields and in the Markovian case.
From Markovian semigroup to non-Markovian quantum evolution
Chruscinski, Dariusz
2010-01-01
We provided a class of legitimate memory kernels leading to completely positive trace preserving dynamical maps. Our construction is based on a simple normalization procedure. Interestingly, when applied to the celebrated Wigner-Weisskopf theory it gives the standard Markovian evolution governed by the local master equation.
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
Efficient simulation of non-Markovian system-environment interaction
Rosenbach, Robert; Huelga, Susana F; Cao, Jianshu; Plenio, Martin Bodo
2015-01-01
In this work, we combine an established method for open quantum systems -- the time evolving density matrix using orthogonal polynomials algorithm (TEDOPA) -- with the transfer tensors formalism (TTM), a new tool for the analysis, compression and propagation of non-Markovian processes. This enables the investigation of previously inaccessible long-time dynamics, such as those ensuing from low temperature regimes with arbitrary, possibly highly structured, spectral densities. We briefly introduce both methods, followed by a benchmark to prove viability and combination synergies. Subsequently we illustrate the capabilities of this approach at the hand of specific examples and conclude our analysis by highlighting possible further applications of our method.
Characterization of the degree of Musical non-Markovianity
Mannone, Maria
2013-01-01
Musical compositions could be characterized by a certain degree of memory, that takes into account repetitions and similarity of sequences of pitches, durations and intensities (the patterns). The higher the quantity of variations, the lower the degree of memory. This degree has never quantitatively been defined and measured. In physics, mathematical tools to quantify memory (defined as non-Markovianity) in quantum systems have been developed. The aim of this paper is to extend these mathematical tools to music, defining a general method to measure the degree of memory in musical compositions. Applications to some musical scores give results that agree with the expectations.
Non-Markovian dynamics of a superconducting qubit in an open multimode resonator
Malekakhlagh, Moein; Petrescu, Alexandru; Türeci, Hakan E.
2016-12-01
We study the dynamics of a transmon qubit that is capacitively coupled to an open multimode superconducting resonator. Our effective equations are derived by eliminating resonator degrees of freedom while encoding their effect in the Green's function of the electromagnetic background. We account for the dissipation of the resonator exactly by employing a spectral representation for the Green's function in terms of a set of non-Hermitian modes and show that it is possible to derive effective Heisenberg-Langevin equations without resorting to the rotating-wave, two-level, Born, or Markov approximations. A well-behaved time-domain perturbation theory is derived to systematically account for the nonlinearity of the transmon. We apply this method to the problem of spontaneous emission, capturing accurately the non-Markovian features of the qubit dynamics, valid for any qubit-resonator coupling strength.
Alonso, D; Alonso, Daniel; Vega, In\\'es de
2004-01-01
Multiple time correlation functions are found in the dynamical description of different phenomena. They encode and describe the fluctuations of the dynamical variables of a system. In this paper we formulate a theory of non-Markovian multiple-time correlation functions (MTCF) for a wide class of systems. We derive the dynamical equation of the {\\it reduced propagator}, an object that evolve state vectors of the system conditioned to the dynamics of its environment, which is not necessarily at the vacuum state at the initial time. Such reduced propagator is the essential piece to obtain multiple-time correlation functions. An average over the different environmental histories of the reduced propagator permits us to obtain the evolution equations of the multiple-time correlation functions. We also study the evolution of MTCF within the weak coupling limit and it is shown that the multiple-time correlation function of some observables satisfy the Quantum Regression Theorem (QRT), whereas other correlations do no...
Jiménez-Aquino, J. I.; Romero-Bastida, M.
2016-09-01
In this paper we derive the non-Markovian barotropic-type and Hall-type fluctuation relations for noninteracting charged Brownian particles embedded in a memory heat bath and under the action of crossed electric and magnetic fields. We first obtain a more general non-Markovian fluctuation relation formulated within the context of a generalized Langevin equation with arbitrary friction memory kernel and under the action of a constant magnetic field and an arbitrary time-dependent electric field. It is shown that this fluctuation relation is related to the total amount of an effective work done on the charged particle as it is driven out of equilibrium by the applied time-dependent electric field. Both non-Markovian barotropic- and Hall-type fluctuation relations are then derived when the electric field is assumed to be also a constant vector pointing along just one axis. In the Markovian limit, we show explicitly that they reduce to the same results reported in the literature.
Objectivity in the non-Markovian spin-boson model
Lampo, Aniello; Tuziemski, Jan; Lewenstein, Maciej; Korbicz, Jarosław K.
2017-07-01
Objectivity constitutes one of the main features of the macroscopic classical world. An important aspect of the quantum-to-classical transition issue is to explain how such a property arises from the microscopic quantum theory. Recently, within the framework of open quantum systems, there has been proposed such a mechanism in terms of the so-called spectrum broadcast structures. These are multipartite quantum states of the system of interest and a part of its environment, assumed to be under an observation. This approach requires a departure from the standard open quantum systems methods, as the environment cannot be completely neglected. In the present paper we study the emergence of such a state structure in one of the canonical models of the condensed-matter theory: the spin-boson model, describing the dynamics of a two-level system coupled to an environment made up by a large number of harmonic oscillators. We pay much attention to the behavior of the model in the non-Markovian regime, in order to provide a testbed to analyze how the non-Markovian nature of the evolution affects the surfacing of a spectrum broadcast structure.
Staying positive: going beyond Lindblad with perturbative master equations
Energy Technology Data Exchange (ETDEWEB)
Whitney, Robert S [Institut Laue-Langevin, 6 rue Jules Horowitz, BP 156, 38042 Grenoble (France)
2008-05-02
The perturbative master equation (Bloch-Redfield) is used extensively to study dissipative quantum mechanics-particularly for qubits-despite the 25-year-old criticism that it violates positivity (generating negative probabilities). We take an arbitrary system coupled to an environment containing many degrees-of-freedom and cast its perturbative master equation (derived from a perturbative treatment of Nakajima-Zwanzig or Schoeller-Schoen equations) in the form of a Lindblad master equation. We find that the equation's parameters are time dependent. This time dependence is rarely accounted for and invalidates Lindblad's dynamical semigroup analysis. We analyse one such Bloch-Redfield master equation (for a two-level system coupled to an environment with a short but non-vanishing memory time), which apparently violates positivity. We analytically show that, once the time dependence of the parameters is accounted for, positivity is preserved.
Ritschel, Gerhard; Möbius, Sebastian; Strunz, Walter T; Eisfeld, Alexander
2014-01-01
Non-Markovian Quantum State Diffusion (NMQSD) has turned out to be an effective method to calculate excitonic properties of aggregates composed of organic chromophores, taking into account the strong coupling of electronic transitions to vibrational modes of the chromophores. In this paper we show how to calculate linear optical spectra at finite temperatures in an efficient way. To this end we map a finite temperature environment to the zero temperature case using the so-called thermofield method. The zero temperature case equations can then be solved efficiently by standard integrators. As an example we calculate absorption and circular dichroism spectra of a linear aggregate. The formalism developed can be applied to calculate arbitrary correlation functions.
Extending the applicability of Redfield theories into highly non-Markovian regimes
Montoya-Castillo, Andrés; Reichman, David R
2015-01-01
We present a new, computationally inexpensive method for the calculation of reduced density matrix dynamics for systems with a potentially large number of subsystem degrees of freedom coupled to a generic bath. The approach consists of propagation of weak-coupling Redfield-like equations for the high frequency bath degrees of freedom only, while the low frequency bath modes are dynamically arrested but statistically sampled. We examine the improvements afforded by this approximation by comparing with exact results for the spin-boson model over a wide range of parameter space. The results from the method are found to dramatically improve Redfield dynamics in highly non--Markovian regimes, at a similar computational cost. Relaxation of the mode-freezing approximation via classical (Ehrenfest) evolution of the low frequency modes results in a dynamical hybrid method. We find that this Redfield-based dynamical hybrid approach, which is computationally more expensive than bare Redfield dynamics, yields only a marg...
Solvent fluctuations induce non-Markovian kinetics in hydrophobic pocket-ligand binding
Weiß, R Gregor; Dzubiella, Joachim
2016-01-01
We investigate the impact of water fluctuations on the key-lock association kinetics of a hydrophobic ligand (key) binding to a hydrophobic pocket (lock) by means of a minimalistic stochastic model system. It describes the collective hydration behavior of the pocket by bimodal fluctuations of a water-pocket interface that dynamically couples to the diffusive motion of the approaching ligand via the hydrophobic interaction. This leads to a set of overdamped Langevin equations in 2D-coordinate-space, that is Markovian in each dimension. Numerical simulations demonstrate locally increased friction of the ligand, decelerated binding kinetics, and local non-Markovian (memory) effects in the ligand's reaction coordinate as found previously in explicit-water molecular dynamics studies of model hydrophobic pocket-ligand binding [1,2]. Our minimalistic model elucidates the origin of effectively enhanced friction in the process that can be traced back to long-time decays in the force-autocorrelation function induced by...
Ritschel, Gerhard; Suess, Daniel; Möbius, Sebastian; Strunz, Walter T.; Eisfeld, Alexander
2015-01-01
Non-Markovian Quantum State Diffusion (NMQSD) has turned out to be an efficient method to calculate excitonic properties of aggregates composed of organic chromophores, taking into account the coupling of electronic transitions to vibrational modes of the chromophores. NMQSD is an open quantum system approach that incorporates environmental degrees of freedom (the vibrations in our case) in a stochastic way. We show in this paper that for linear optical spectra (absorption, circular dichroism), no stochastics is needed, even for finite temperatures. Thus, the spectra can be obtained by propagating a single trajectory. To this end, we map a finite temperature environment to the zero temperature case using the so-called thermofield method. The resulting equations can then be solved efficiently by standard integrators.
Non-Markovian Model for Transport and Reactions of Particles in Spiny Dendrites
Fedotov, Sergei; Méndez, Vicenç
2008-11-01
Motivated by the experiments [Santamaria , Neuron 52, 635 (2006)NERNET0896-627310.1016/j.neuron.2006.10.025] that indicated the possibility of subdiffusive transport of molecules along dendrites of cerebellar Purkinje cells, we develop a mesoscopic model for transport and chemical reactions of particles in spiny dendrites. The communication between spines and a parent dendrite is described by a non-Markovian random process and, as a result, the overall movement of particles can be subdiffusive. A system of integrodifferential equations is derived for the particles densities in dendrites and spines. This system involves the spine-dendrite interaction term which describes the memory effects and nonlocality in space. We consider the impact of power-law waiting time distributions on the transport of biochemical signals and mechanism of the accumulation of plasticity-inducing signals inside spines.
Master equations and the theory of stochastic path integrals
Weber, Markus F
2016-01-01
This review provides a pedagogic and self-contained introduction to master equations and to their representation by path integrals. We discuss analytical and numerical methods for the solution of master equations, keeping our focus on methods that are applicable even when stochastic fluctuations are strong. The reviewed methods include the generating function technique and the Poisson representation, as well as novel ways of mapping the forward and backward master equations onto linear partial differential equations (PDEs). Spectral methods, WKB approximations, and a variational approach have been proposed for the analysis of the PDE obeyed by the generating function. After outlining these methods, we solve the derived PDEs in terms of two path integrals. The path integrals provide distinct exact representations of the conditional probability distribution solving the master equations. We exemplify both path integrals in analysing elementary chemical reactions. Furthermore, we review a method for the approxima...
General-dyne unravelling of a thermal master equation
Genoni, M. G.; Mancini, S.; Serafini, A.
2014-07-01
We analyze the unravelling of the quantum optical master equation at finite temperature due to direct, continuous, general-dyne detection of the environment. We first express the general-dyne Positive Operator Valued Measure (POVM) in terms of the eigenstates of a non-Hermitian operator associated to the general-dyne measurement. Then we derive the stochastic master equation obtained by considering the interaction between the system and a reservoir at thermal equilibrium, which is measured according to the POVM previously determined. Finally, we present a feasible measurement scheme, which reproduces general-dyne detection for any value of the parameter characterizing the stochastic master equation.
Reveal non-Markovianity of open quantum systems via local operations
Yang, Huan; Chen, Yanbei
2011-01-01
Non-Markovianity, as an important feature of general open quantum systems, is usually difficult to quantify with limited knowledge of how the plant that we are interested in interacts with its environment-the bath. It often happens that the reduced dynamics of the plant attached to a non-Markovian bath becomes indistinguishable from the one with a Markovian bath, if we left the entire system freely evolve. Here we show that non-Markovianity can be revealed via applying local unitary operations on the plant-they will influence the plant evolution at later times due to memory of the bath. This not only provides a new criterion for non-Markovianity, but also sheds light on protecting and recovering quantum coherence in non-Markovian systems, which will be useful for quantum-information processing.
Markovian and non-Markovian dynamics in quantum and classical systems
Vacchini, Bassano; 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 for 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 is constructed which allow to study the basic features of the classical and the quantum definitions and to evaluate explicitly the me...
Random phase wave: a soluble non-Markovian system
Energy Technology Data Exchange (ETDEWEB)
Dewar, R.L.
1977-12-01
The averaged propagator and the corresponding mass operator (non-Markovian particle-wave collision operator) of a particle being accelerated by a random potential are constructed explicitly in a model system. The model consists of an ensemble of monochromatic waves of random phase, such as arises in narrow-bandwidth plasma turbulence, and is particularly interesting as a system exhibiting strong trapping. An essential simplifying feature is that the propagator is evaluated in oscillation-center picture, which greatly simplifies the momentum-space operators occurring in the problem, and leads to a remarkable factorization of the mass operator. General analyticity and symmetry properties are derived using a projection-operator method, and verified for the solution of the model system. The nature of the memory exhibited by the mass operator is briefly examined.
Quantum correlations dynamics under different non-markovian environmental models
Zhang, Ying-Jie; Shan, Chuan-Jia; Xia, Yun-Jie
2011-01-01
We investigate the roles of different environmental models on quantum correlation dynamics of two-qubit composite system interacting with two independent environments. The most common environmental models (the single-Lorentzian model, the squared-Lorentzian model, the two-Lorentzian model and band-gap model) are analyzed. First, we note that for the weak coupling regime, the monotonous decay speed of the quantum correlation is mainly determined by the spectral density functions of these different environments. Then, by considering the strong coupling regime we find that, contrary to what is stated in the weak coupling regime, the dynamics of quantum correlation depends on the non-Markovianity of the environmental models, and is independent of the environmental spectrum density functions.
Linear Optics Simulation of Non-Markovian Quantum Dynamics
Chiuri, Andrea; Mazzola, Laura; Paternostro, Mauro; Mataloni, Paolo
2012-01-01
The simulation of quantum processes is a key goal for the grand programme aiming at grounding quantum technologies as the way to explore complex phenomena that are inaccessible through standard, classical calculators. Some interesting steps have been performed in this direction and this scenario has recently been extended to open quantum evolutions, marking the possibility to investigate important features of the way a quantum system interacts with its environment. Here we demonstrate experimentally the (non-)Markovianity of a process where system and environment are coupled through a simulated transverse Ising model. By engineering the evolution in a fully controlled photonic quantum simulator, we assess and demonstrate the role that system-environment correlations have in the emergence of memory effects.
Fermionic-mode entanglement in non-Markovian environment
Cheng, Jiong; Han, Yan; An, Qing-zhi; Zhou, Ling
2015-03-01
We evaluate the non-Markovian effects on the entanglement dynamics of a fermionic system interacting with two dissipative vacuum reservoirs. The exact solution of density matrix is derived by utilizing the Feynman-Vernon influence functional theory in the fermionic coherent state representation and the Grassmann calculus, which are valid for both the fermionic and bosonic baths, and their difference lies in the dependence of the parity of the initial states. The fermionic entanglement dynamics is presented by adding an additional restriction to the density matrix known as the superselection rules. Our analysis shows that the usual decoherence suppression schemes implemented in qubits systems can also be achieved for systems of identical fermions, and the initial state proves its importance in the evolution of fermionic entanglement. Our results provide a potential way to decoherence controlling of identical fermions.
Catchment residence and travel time distributions: The master equation
National Research Council Canada - National Science Library
Gianluca Botter; Enrico Bertuzzo; Andrea Rinaldo
2011-01-01
Travel/residence time pdf's are related objects with different physical meaning A Master Equation for the residence time pdf is derived and solved analytically We develop a mathematical framework...
Counting master integrals. Integration by parts vs. functional equations
Energy Technology Data Exchange (ETDEWEB)
Kniehl, Bernd A.; Tarasov, Oleg V. [Hamburg Univ. (Germany). II. Inst. fuer Theoretische Physik
2016-01-15
We illustrate the usefulness of functional equations in establishing relationships between master integrals under the integration-by-parts reduction procedure by considering a certain two-loop propagator-type diagram as an example.
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
Dynamics of non-Markovian open quantum systems
de Vega, Inés; Alonso, Daniel
2017-01-01
Open quantum systems (OQSs) cannot always be described with the Markov approximation, which requires a large separation of system and environment time scales. An overview is given of some of the most important techniques available to tackle the dynamics of an OQS beyond the Markov approximation. Some of these techniques, such as master equations, Heisenberg equations, and stochastic methods, are based on solving the reduced OQS dynamics, while others, such as path integral Monte Carlo or chain mapping approaches, are based on solving the dynamics of the full system. The physical interpretation and derivation of the various approaches are emphasized, how they are connected is explored, and how different methods may be suitable for solving different problems is examined.
Non-Markovianity and reservoir memory of quantum channels: a quantum information theory perspective.
Bylicka, B; Chruściński, D; Maniscalco, S
2014-07-21
Quantum technologies rely on the ability to coherently transfer information encoded in quantum states along quantum channels. Decoherence induced by the environment sets limits on the efficiency of any quantum-enhanced protocol. Generally, the longer a quantum channel is the worse its capacity is. We show that for non-Markovian quantum channels this is not always true: surprisingly the capacity of a longer channel can be greater than of a shorter one. We introduce a general theoretical framework linking non-Markovianity to the capacities of quantum channels and demonstrate how harnessing non-Markovianity may improve the efficiency of quantum information processing and communication.
Dynamical role of system-environment correlations in non-Markovian dynamics
Mazzola, Laura; Modi, Kavan; Paternostro, Mauro
2012-01-01
We analyse the role played by system-environment correlations in the emergence of non-Markovian dynamics. By working within the framework developed in Breuer et al., Phys. Rev. Lett. 103, 210401 (2009), we unveil a fundamental connection between non-Markovian behaviour and dynamics of system-environment correlations. We derive an upper bound to the derivative of rate of change of the distinguishability between different states of the system that explicitly depends on the development and establishment of correlations between system and environment. We illustrate our results using a fully solvable spin-chain model, which allows us to gain insight on the mechanisms triggering non-Markovian evolution.
Non-Markovianity and reservoir memory of quantum channels: a quantum information theory perspective
Bylicka, B.; Chruściński, D.; Maniscalco, S.
2014-01-01
Quantum technologies rely on the ability to coherently transfer information encoded in quantum states along quantum channels. Decoherence induced by the environment sets limits on the efficiency of any quantum-enhanced protocol. Generally, the longer a quantum channel is the worse its capacity is. We show that for non-Markovian quantum channels this is not always true: surprisingly the capacity of a longer channel can be greater than of a shorter one. We introduce a general theoretical framework linking non-Markovianity to the capacities of quantum channels and demonstrate how harnessing non-Markovianity may improve the efficiency of quantum information processing and communication. PMID:25043763
The Approach to Equilibrium: Detailed Balance and the Master Equation
Alexander, Millard H.; Hall, Gregory E.; Dagdigian, Paul J.
2011-01-01
The approach to the equilibrium (Boltzmann) distribution of populations of internal states of a molecule is governed by inelastic collisions in the gas phase and with surfaces. The set of differential equations governing the time evolution of the internal state populations is commonly called the master equation. An analytic solution to the master…
Master Equation Analysis of Thermal and Nonthermal Microwave Effects.
Ma, Jianyi
2016-10-11
Master equation is a successful model to describe the conventional heating reaction, it is expanded to capture the "microwave effect" in this work. The work equation of "microwave effect" included master equation presents the direct heating, indirect heating, and nonthermal effect about the microwave field. The modified master equation provides a clear physics picture to the nonthermal microwave effect: (1) The absorption and the emission of the microwave, which is dominated by the transition dipole moment between two corresponding states and the intensity of the microwave field, provides a new path to change the reaction rate constants. (2) In the strong microwave field, the distribution of internal states of the molecules will deviate from the equilibrium distribution, and the system temperature defined in the conventional heating reaction is no longer available. According to the general form of "microwave effect" included master equation, a two states model for unimolecular dissociation is proposed and is used to discuss the microwave nonthermal effect particularly. The average rate constants can be increased up to 2400 times for some given cases without the temperature changed in the two states model. Additionally, the simulation of a model system was executed using our State Specified Master Equation package. Three important conclusions can be obtained in present work: (1) A reasonable definition of the nonthermal microwave effect is given in the work equation of "microwave effect" included master equation. (2) Nonthermal microwave effect possibly exists theoretically. (3) The reaction rate constants perhaps can be changed obviously by the microwave field for the non-RRKM and the mode-specified reactions.
The Pentabox Master Integrals with the Simplified Differential Equations approach
Papadopoulos, Costas G; Wever, Christopher
2015-01-01
We present the calculation of massless two-loop Master Integrals relevant to five-point amplitudes with one off-shell external leg and derive the complete set of planar Master Integrals with five on-mass-shell legs, that contribute to many $2\\to 3$ amplitudes of interest at the LHC, as for instance three jet production, $\\gamma, V, H +2$ jets etc., based on the Simplified Differential Equations approach.
Entanglement and non-Markovianity of a multi-level atom decaying in a cavity
Zi-Long, Fan; Yu-Kun, Ren; Hao-Sheng, Zeng
2016-01-01
We present a paradigmatic method for exactly studying non-Markovian dynamics of a multi-level V-type atom interacting with a zero-temperature bosonic bath. Special attention is paid to the entanglement evolution and the dynamical non-Markovianity of a three-level V-type atom. We find that the entanglement negativity decays faster and non-Markovianity is smaller in the resonance regions than those in the non-resonance regions. More importantly, the quantum interference between the dynamical non-Markovianities induced by different transition channels is manifested, and the frequency domains for constructive and destructive interferences are found. Project supported by the National Natural Science Foundation of China (Grant Nos. 11275064 and 11075050), the Specialized Research Fund for the Doctoral Program of Higher Education, China (Grant No. 20124306110003), and the Construct Program of the National Key Discipline, China.
A framework for the direct evaluation of large deviations in non-Markovian processes
Cavallaro, Massimo; Harris, Rosemary J.
2016-11-01
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.
Gauge Poisson representations for birth/death master equations
Drummond, P D
2002-01-01
Poisson representation techniques provide a powerful method for mapping master equations for birth/death processes - found in many fields of physics, chemistry and biology - into more tractable stochastic differential equations. However, the usual expansion is not exact in the presence of boundary terms, which commonly occur when the differential equations are nonlinear. In this paper, a stochastic gauge technique is introduced that eliminates boundary terms, to give an exact representation as a weighted rate equation with stochastic terms. These methods provide novel techniques for calculating and understanding the effects of number correlations in systems that have a master equation description. As examples, correlations induced by strong mutations in genetics, and the astrophysical problem of molecule formation on microscopic grain surfaces are analyzed. Exact analytic results are obtained that can be compared with numerical simulations, demonstrating that stochastic gauge techniques can give exact results...
Quantum Discord Dynamics in Two Different Non-Markovian Reservoirs
Institute of Scientific and Technical Information of China (English)
DING Bang-Fu; WANG Xiao-Yun; LIU Jing-Feng; YAN Lin; ZHAO He-Ping
2011-01-01
The quantum discord dynamics of two non-coupled two-level atoms independently interacting with their reservoir is studied under two kinds of non-Markovian conditions,namely,an off-resonant case with atomic transition frequency and a photonic band gap.In the first case,the phenomenon of the quantum discord loss and the oscillatory behavior of the quantum discord can occur by changing the detuning quantity and reducing the spectral coupling width for any initial Bell state.Under the second condition,the trapping phenomenon of the quantum discord can be presented by adjusting the width of gap,that is,the quantum discord of two atoms keep a nonzero constant for a long time.Entanglement,as a kind of quantum correlation without a classical counterpart,plays an important role in quantum information and communication theory,[1,2] quantum teleportation,[3] quantum cryptography[4,5] and universal quantum computing.[6]%We report the first implementation of transparent electrodes in bottom-gate graphene transistors used for photo detection. Compared to conventional nontransparent electrodes, the transparent electrodes allow photons to transmit through to the graphene beneath, providing an enlarged absorption area and thereby giving rise to an enhancement of photocurrent generation. The devices are fabricated with an asymmetric metallization scheme and the experimental results show that the maximum photocurrent density using the transparent electrodes (ITO and Pd/ITO) is over two times higher than that using the nontransparent electrodes (Ti and Pd), indicating a significant enhancement in the performance of graphene photo sensors.
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.
Maxwell boundary conditions impose non-Lindblad master equation
Bamba, Motoaki
2016-01-01
From the Hamiltonian connecting the inside and outside of an Fabry-Perot cavity, which is derived from the Maxwell boundary conditions at a mirror of the cavity, a master equation of a non-Lindblad form is derived when the cavity embeds matters, although we can transform it to the Lindblad form by performing the rotating-wave approximation to that Hamiltonian. We calculate absorption spectra by these Lindblad and non-Lindblad master equations and also by the Maxwell boundary conditions in framework of the classical electrodynamics, which we consider the most reliable approach. We found that, compared to the Lindblad master equation, the absorption spectra by the non-Lindblad one agree better with those by the Maxwell boundary conditions. Although the discrepancy is highlighted only in the ultra-strong light-matter interaction regime with a relatively large broadening, the master equation of the non-Lindblad form is preferable rather than of the Lindblad one for pursuing the consistency with the classical elec...
Chemical master equation closure for computer-aided synthetic biology.
Smadbeck, Patrick; Kaznessis, Yiannis N
2015-01-01
With inexpensive DNA synthesis technologies, we can now construct biological systems by quickly piecing together DNA sequences. Synthetic biology is the promising discipline that focuses on the construction of these new biological systems. Synthetic biology is an engineering discipline, and as such, it can benefit from mathematical modeling. This chapter focuses on mathematical models of biological systems. These models take the form of chemical reaction networks. The importance of stochasticity is discussed and methods to simulate stochastic reaction networks are reviewed. A closure scheme solution is also presented for the master equation of chemical reaction networks. The master equation is a complete model of randomly evolving molecular populations. Because of its ambitious character, the master equation remained unsolved for all but the simplest of molecular interaction networks for over 70 years. With the first complete solution of chemical master equations, a wide range of experimental observations of biomolecular interactions may be mathematically conceptualized. We anticipate that models based on the closure scheme described herein may assist in rationally designing synthetic biological systems.
Master equation approach to reversible and conservative discrete systems.
Urbina, Felipe; Rica, Sergio
2016-12-01
A master equation approach is applied to a reversible and conservative cellular automaton model (Q2R). The Q2R model is a dynamical variation of the Ising model for ferromagnetism that possesses quite a rich and complex dynamics. The configuration space is composed of a huge number of cycles with exponentially long periods. Following Nicolis and Nicolis [G. Nicolis and C. Nicolis, Phys. Rev. A 38, 427 (1988)0556-279110.1103/PhysRevA.38.427], a coarse-graining approach is applied to the time series of the total magnetization, leading to a master equation that governs the macroscopic irreversible dynamics of the Q2R automata. The methodology is replicated for various lattice sizes. In the case of small systems, we show that the master equation leads to a tractable probability transfer matrix of moderate size, which provides a master equation for a coarse-grained probability distribution. The method is validated and some explicit examples are discussed.
Maxwell boundary conditions imply non-Lindblad master equation
Bamba, Motoaki; Imoto, Nobuyuki
2016-09-01
From the Hamiltonian connecting the inside and outside of a Fabry-Pérot cavity, which is derived from the Maxwell boundary conditions at a mirror of the cavity, a master equation of a non-Lindblad form is derived when the cavity embeds matters, although we can transform it to the Lindblad form by performing the rotating-wave approximation to the connecting Hamiltonian. We calculate absorption spectra by these Lindblad and non-Lindblad master equations and also by the Maxwell boundary conditions in the framework of the classical electrodynamics, which we consider the most reliable approach. We found that, compared to the Lindblad master equation, the absorption spectra by the non-Lindblad one agree better with those by the Maxwell boundary conditions. Although the discrepancy is highlighted only in the ultrastrong light-matter interaction regime with a relatively large broadening, the master equation of the non-Lindblad form is preferable rather than of the Lindblad one for pursuing the consistency with the classical electrodynamics.
An algebraic solution of Lindblad-type master equations
Energy Technology Data Exchange (ETDEWEB)
Klimov, A B; Romero, J L [Departamento de Fisica, Universidad de Guadalajara, Revolucion 1500, 44410, Guadalajara, Jal. (Mexico)
2003-06-01
We propose an algebraic solution for a wide class of Lindblad-type master equations. Examples of dissipation in free field evolution, field evolution in the Kerr medium, two-photon field dissipation, atomic dissipation and two-mode field dissipation are given.
Master equation approach to reversible and conservative discrete systems
Urbina, Felipe; Rica, Sergio
2016-12-01
A master equation approach is applied to a reversible and conservative cellular automaton model (Q2R). The Q2R model is a dynamical variation of the Ising model for ferromagnetism that possesses quite a rich and complex dynamics. The configuration space is composed of a huge number of cycles with exponentially long periods. Following Nicolis and Nicolis [G. Nicolis and C. Nicolis, Phys. Rev. A 38, 427 (1988), 10.1103/PhysRevA.38.427], a coarse-graining approach is applied to the time series of the total magnetization, leading to a master equation that governs the macroscopic irreversible dynamics of the Q2R automata. The methodology is replicated for various lattice sizes. In the case of small systems, we show that the master equation leads to a tractable probability transfer matrix of moderate size, which provides a master equation for a coarse-grained probability distribution. The method is validated and some explicit examples are discussed.
Master equations and the theory of stochastic path integrals.
Weber, Markus F; Frey, Erwin
2017-04-01
This review provides a pedagogic and self-contained introduction to master equations and to their representation by path integrals. Since the 1930s, master equations have served as a fundamental tool to understand the role of fluctuations in complex biological, chemical, and physical systems. Despite their simple appearance, analyses of master equations most often rely on low-noise approximations such as the Kramers-Moyal or the system size expansion, or require ad-hoc closure schemes for the derivation of low-order moment equations. We focus on numerical and analytical methods going beyond the low-noise limit and provide a unified framework for the study of master equations. After deriving the forward and backward master equations from the Chapman-Kolmogorov equation, we show how the two master equations can be cast into either of four linear partial differential equations (PDEs). Three of these PDEs are discussed in detail. The first PDE governs the time evolution of a generalized probability generating function whose basis depends on the stochastic process under consideration. Spectral methods, WKB approximations, and a variational approach have been proposed for the analysis of the PDE. The second PDE is novel and is obeyed by a distribution that is marginalized over an initial state. It proves useful for the computation of mean extinction times. The third PDE describes the time evolution of a 'generating functional', which generalizes the so-called Poisson representation. Subsequently, the solutions of the PDEs are expressed in terms of two path integrals: a 'forward' and a 'backward' path integral. Combined with inverse transformations, one obtains two distinct path integral representations of the conditional probability distribution solving the master equations. We exemplify both path integrals in analysing elementary chemical reactions. Moreover, we show how a well-known path integral representation of averaged observables can be recovered from them. Upon
Master equations and the theory of stochastic path integrals
Weber, Markus F.; Frey, Erwin
2017-04-01
This review provides a pedagogic and self-contained introduction to master equations and to their representation by path integrals. Since the 1930s, master equations have served as a fundamental tool to understand the role of fluctuations in complex biological, chemical, and physical systems. Despite their simple appearance, analyses of master equations most often rely on low-noise approximations such as the Kramers-Moyal or the system size expansion, or require ad-hoc closure schemes for the derivation of low-order moment equations. We focus on numerical and analytical methods going beyond the low-noise limit and provide a unified framework for the study of master equations. After deriving the forward and backward master equations from the Chapman-Kolmogorov equation, we show how the two master equations can be cast into either of four linear partial differential equations (PDEs). Three of these PDEs are discussed in detail. The first PDE governs the time evolution of a generalized probability generating function whose basis depends on the stochastic process under consideration. Spectral methods, WKB approximations, and a variational approach have been proposed for the analysis of the PDE. The second PDE is novel and is obeyed by a distribution that is marginalized over an initial state. It proves useful for the computation of mean extinction times. The third PDE describes the time evolution of a ‘generating functional’, which generalizes the so-called Poisson representation. Subsequently, the solutions of the PDEs are expressed in terms of two path integrals: a ‘forward’ and a ‘backward’ path integral. Combined with inverse transformations, one obtains two distinct path integral representations of the conditional probability distribution solving the master equations. We exemplify both path integrals in analysing elementary chemical reactions. Moreover, we show how a well-known path integral representation of averaged observables can be recovered from
A non-Markovian model of rill erosion
Winter, C.; Damron, M.
2009-12-01
Stochastic processes with reinforcement are inherently non-Markovian and therefore may model geophysical processes with memory, for instance patterns of rill erosion, more realistically than Markovian models. Reinforcement provides a bias to a system that is equivalent to infinite memory, making a system more likely to occupy a given state the more often the state is visited. Some well-studied examples in applied mathematics include variations on the urn of P'olya and reinforced random walks. Many natural phenomena exhibit similar behavior: for instance, an overall pattern of rills is relatively stable once it is established, although small details of the pattern may change frequently and catastrophes that permanently alter it may occasionally occur. To model the phenomenology of rill erosion, we propose a simple discrete time, infinite-memory random process defined on the nodes and edges of an oriented diagonal lattice. Lattice models have often been used to investigate the morphology of natural drainage networks, but our focus is as much on the dynamics of network formation as it is on morphology. The lattice in our model starts out smooth in the sense that it has no edges initially, but it sprouts edges everywhere the instant the process starts, much as rain can start soil erosion everywhere on a hillslope at once. Exactly one edge (rill segment) descends from each node, and it points either left or right. Sediment loads travel along networks of edges and are accumulated at nodes. At every node and at every time step, a simple two parameter reinforcing law randomly determines the direction of the node’s output and then is updated. The degree of reinforcement is set by comparing the node's current sediment load to the load history of the entire network above it and is governed by two system parameters representing respectively rainfall intensity and the soil’s resistance to change. The current pattern of connections among nodes represents the present state of
Jiang, Li; Zhang, Guo-Feng
2017-03-01
By using the effective non-Markovian measure (Breuer et al., Phys. Rev. Lett. 103, 210401 2009) we investigate non-Markovian dynamics of a pair of two-level atoms (TLAs) system, each of which interacting with a local reservoir. We show that subsystem dynamics can be controlled by manipulating the coupling between TLAs, temperature and relaxation rate of the atoms. Moreover, the correlation between non-Markovianity of subsystem and entanglement between the subsystem and the structured bath is investigated, the results show that the emergence of non-Markovianity has a negative effect on the entanglement.
Non-Markovianity, coherence, and system-environment correlations in a long-range collision model
Ćakmak, B.; Pezzutto, M.; Paternostro, M.; Müstecaplıoǧlu, Ö. E.
2017-08-01
We consider the dynamics of a collisional model in which both the system and environment are embodied by spin-1 /2 particles. In order to include non-Markovian features in our model, we introduce interactions among the environmental qubits and investigate the effect that different models of such interaction have on the degree of non-Markovianity of the system's dynamics. By extending that interaction beyond the nearest neighbor, we enhance the degree of non-Markovianity in the system's dynamics. A further significant increase can be observed if a collective interaction with the forthcoming environmental qubits is considered. However, the observed degree of non-Markovianity in this case is nonmonotonic with the increasing number of qubits included in the interaction. Moreover, one can establish a connection between the degree of non-Markovianity in the evolution of the system and the fading behavior of quantum coherence in its state as the number of collisions grows. We complement our study with an investigation of system-environment correlations and present an example of their importance on a physical upper bound on the trace distance derivative.
Coherence Properties of Discrete Static Kinks, Master Thesis
Landa, H
2009-01-01
A chain of interacting particles subject also to a nonlinear on-site potential admits stable soliton-like configurations : static kinks. The linear normal-modes around such a kink contain a discrete set of localized, gap-separated modes. Quantization of the Hamiltonian in these modes results in an interacting system of phonons. We investigate numerically the coherence properties of such localized modes at low temperatures using a non-Markovian master equation. We show that low decoherence rates can be achieved in these nonlinear configurations for a surprisingly long time. If realized in the ion trap, kink internal modes may be advantageously used for Quantum Information Processing.
Extended master equation models for molecular communication networks
Chou, Chun Tung
2012-01-01
We consider molecular communication networks consisting of transmitters and receivers distributed in a fluidic medium. In such networks, a transmitter sends one or more signalling molecules, which are diffused over the medium, to the receiver to realise the communication. In order to be able to engineer synthetic molecular communication networks, mathematical models for these networks are required. This paper proposes a new stochastic model for molecular communication networks called reaction-diffusion master equation with exogenous input (RDMEX). The key idea behind RDMEX is to model the transmitters as time sequences specify the emission patterns of signalling molecules, while diffusion in the medium and chemical reactions at the receivers are modelled as Markov processes using master equation. An advantage of RDMEX is that it can readily be used to model molecular communication networks with multiple transmitters and receivers. For the case where the reaction kinetics at the receivers is linear, we show ho...
Correlation Function and Generalized Master Equation of Arbitrary Age
2007-11-02
Correlation function and generalized master equation of arbitrary age Paolo Allegrini,1 Gerardo Aquino,2,* Paolo Grigolini,2,3,4 Luigi Palatella,5...P.O. Box 311427, Denton, Texas 76203-1427, USA 3Dipartimento di Fisica dell’Università di Pisa and INFM, Via Buonarroti 2, 56127 Pisa, Italy 4Istituto...dei Processi Chimico Fisici del CNR Area della Ricerca di Pisa, Via G. Moruzzi 1, 56124 Pisa, Italy 5Dipartimento di Fisica and Istituto dei Sistemi
Properties of quantum Markovian master equations. [Semigroup law, detailed balance
Energy Technology Data Exchange (ETDEWEB)
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.
Excess entropy production in quantum system: Quantum master equation approach
Nakajima, Satoshi; Tokura, Yasuhiro
2016-01-01
For open systems described by the quantum master equation (QME), we investigate the excess entropy production under quasistatic operations between nonequilibrium steady states. The average entropy production is composed of the time integral of the instantaneous steady entropy production rate and the excess entropy production. We define average entropy production rate using the average energy and particle currents, which are calculated by using the full counting statistics with QME. The excess...
Three faces of the second law. I. Master equation formulation.
Esposito, Massimiliano; Van den Broeck, Christian
2010-07-01
We propose a formulation of stochastic thermodynamics for systems subjected to nonequilibrium constraints (i.e. broken detailed balance at steady state) and furthermore driven by external time-dependent forces. A splitting of the second law occurs in this description leading to three second-law-like relations. The general results are illustrated on specific solvable models. The present paper uses a master equation based approach.
Unification of witnessing initial system-environment correlations and witnessing non-Markovianity
Rodríguez-Rosario, César A; Mazzola, Laura; Aspuru-Guzik, Alán
2012-01-01
We show the connection between a witness that detects dynamical maps with initial system-environment correlations and a witness that detects non-Markovian open quantum systems. Our analysis is based on studying the role that state preparation plays in witnessing violations of contractivity of open quantum system dynamics. Contractivity is a property of some quantum processes where the trace distance of density matrices decrease with time. From this, we show how a witness of initial-correlations is an upper bound to a witness of non-Markovianity. We discuss how this relationship shows further connections between initial system-environment correlations and non-Markovianity at an instance of time in open quantum systems.
Equivalence of the measures of non-Markovianity for open two-level systems
Energy Technology Data Exchange (ETDEWEB)
Zeng Haosheng; Tang Ning; Zheng Yanping; Wang Guoyou [Key Laboratory of Low-Dimensional Quantum Structures and Quantum Control of Ministry of Education, and Department of Physics, Hunan Normal University, Changsha 410081 (China)
2011-09-15
Different measures have been presented to depict the deviation of quantum time evolution in open systems from Markovian processes. We demonstrate that the measure proposed by Breuer, Laine, and Piilo [Phys. Rev. Lett. 103, 210401 (2009)] and the two measures proposed by Rivas, Huelga, and Plenio [Phys. Rev. Lett. 105, 050403 (2010)] have exactly the same non-Markovian time-evolution intervals and thus are really equivalent to each other when they are applied to open two-level systems coupled to environments via the Jaynes-Cummings or dephasing models. This equivalence implies that the three measures, in different ways, capture the intrinsic character of the non-Markovianity of quantum evolutional processes. We also show that the maximization in the definition of the first measure can be actually removed for the considered models without influencing the sensibility of the measure to detect non-Markovianity.
Reaction rates for a generalized reaction-diffusion master equation.
Hellander, Stefan; Petzold, Linda
2016-01-01
It has been established that there is an inherent limit to the accuracy of the reaction-diffusion master equation. Specifically, there exists a fundamental lower bound on the mesh size, below which the accuracy deteriorates as the mesh is refined further. In this paper we extend the standard reaction-diffusion master equation to allow molecules occupying neighboring voxels to react, in contrast to the traditional approach, in which molecules react only when occupying the same voxel. We derive reaction rates, in two dimensions as well as three dimensions, to obtain an optimal match to the more fine-grained Smoluchowski model and show in two numerical examples that the extended algorithm is accurate for a wide range of mesh sizes, allowing us to simulate systems that are intractable with the standard reaction-diffusion master equation. In addition, we show that for mesh sizes above the fundamental lower limit of the standard algorithm, the generalized algorithm reduces to the standard algorithm. We derive a lower limit for the generalized algorithm which, in both two dimensions and three dimensions, is of the order of the reaction radius of a reacting pair of molecules.
Reaction rates for a generalized reaction-diffusion master equation
Hellander, Stefan; Petzold, Linda
2016-01-01
It has been established that there is an inherent limit to the accuracy of the reaction-diffusion master equation. Specifically, there exists a fundamental lower bound on the mesh size, below which the accuracy deteriorates as the mesh is refined further. In this paper we extend the standard reaction-diffusion master equation to allow molecules occupying neighboring voxels to react, in contrast to the traditional approach, in which molecules react only when occupying the same voxel. We derive reaction rates, in two dimensions as well as three dimensions, to obtain an optimal match to the more fine-grained Smoluchowski model and show in two numerical examples that the extended algorithm is accurate for a wide range of mesh sizes, allowing us to simulate systems that are intractable with the standard reaction-diffusion master equation. In addition, we show that for mesh sizes above the fundamental lower limit of the standard algorithm, the generalized algorithm reduces to the standard algorithm. We derive a lower limit for the generalized algorithm which, in both two dimensions and three dimensions, is of the order of the reaction radius of a reacting pair of molecules.
Non-Markovian closure models for large eddy simulations using the Mori-Zwanzig formalism
Parish, Eric J.; Duraisamy, Karthik
2017-01-01
This work uses the Mori-Zwanzig (M-Z) formalism, a concept originating from nonequilibrium statistical mechanics, as a basis for the development of coarse-grained models of turbulence. The mechanics of the generalized Langevin equation (GLE) are considered, and insight gained from the orthogonal dynamics equation is used as a starting point for model development. A class of subgrid models is considered which represent nonlocal behavior via a finite memory approximation [Stinis, arXiv:1211.4285 (2012)], the length of which is determined using a heuristic that is related to the spectral radius of the Jacobian of the resolved variables. The resulting models are intimately tied to the underlying numerical resolution and are capable of approximating non-Markovian effects. Numerical experiments on the Burgers equation demonstrate that the M-Z-based models can accurately predict the temporal evolution of the total kinetic energy and the total dissipation rate at varying mesh resolutions. The trajectory of each resolved mode in phase space is accurately predicted for cases where the coarse graining is moderate. Large eddy simulations (LESs) of homogeneous isotropic turbulence and the Taylor-Green Vortex show that the M-Z-based models are able to provide excellent predictions, accurately capturing the subgrid contribution to energy transfer. Last, LESs of fully developed channel flow demonstrate the applicability of M-Z-based models to nondecaying problems. It is notable that the form of the closure is not imposed by the modeler, but is rather derived from the mathematics of the coarse graining, highlighting the potential of M-Z-based techniques to define LES closures.
Temperature characteristics of quantum dot devices: Rate vs. Master Equation Models
DEFF Research Database (Denmark)
Berg, Tommy Winther; Bischoff, Svend; Magnúsdóttir, Ingibjörg;
2001-01-01
The change of transparency current with temperature for quantum dot devices depends strongly on whether a rate or master equation model is used. The master equation model successfully explains experimental observations of negative characteristic temperatures.......The change of transparency current with temperature for quantum dot devices depends strongly on whether a rate or master equation model is used. The master equation model successfully explains experimental observations of negative characteristic temperatures....
Quantum trajectories under frequent measurements in a non-Markovian environment
Xu, Luting; Li, Xin-Qi
2016-09-01
In this work we generalize the quantum trajectory (QT) theory from Markovian to non-Markovian environments. We model the non-Markovian environment by using a Lorentzian spectral density function with bandwidth (Λ ), and find a perfect "scaling" property with the measurement frequency (τ-1) in terms of the scaling variable x =Λ τ . Our result bridges the gap between the existing QT theory and the Zeno effect, by rendering them as two extremes corresponding to x →∞ and x →0 , respectively. This x -dependent criterion improves the idea of using τ alone and quantitatively identifies the validity condition of the conventional QT theory.
Non-Markovian Quantum Evolution: Time-Local Generators and Memory Kernels
Chruściński, Dariusz; Należyty, Paweł
2016-06-01
In this paper we provide a basic introduction to the topic of quantum non-Markovian evolution presenting both time-local and memory kernel approach to the evolution of open quantum systems. We start with the standard notion of a classical Markovian stochastic process and generalize it to classical Markovian stochastic evolution which in turn becomes a starting point of the quantum setting. Our approach is based on the notion of P-divisible, CP-divisible maps and their refinements to k-divisible maps. Basic methods enabling one to detect non-Markovianity of the quantum evolution are also presented. Our analysis is illustrated by several simple examples.
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...
Jesenko, Simon
2013-01-01
We analyze efficiency of excitation energy transfer in photosynthetic complexes in transient and stationary setting. In the transient setting the absorption process is modeled as an individual event resulting in a subsequent relaxation dynamics. In the stationary setting the absorption is a continuous stationary process, leading to the nonequilibrium steady state. We show that, as far as the efficiency is concerned, both settings can be considered to be the same, as they result in almost identical efficiency. We also show that non-Markovianity has no effect on the resulting efficiency, i.e., corresponding Markovian dynamics results in identical efficiency. Even more, if one maps dynamics to appropriate classical rate equations, the same efficiency as in quantum case is obtained.
Li, Chuang; Yang, Sen; Song, Jie; Xia, Yan; Ding, Weiqiang
2017-05-15
In this paper, a scheme for the generation of long-living entanglement between two distant Λ-type three-level atoms separately trapped in two dissipative cavities is proposed. In this scheme, two dissipative cavities are coupled to their own non-Markovian environments and two three-level atoms are driven by the classical fields. The entangled state between the two atoms is produced by performing Bell state measurement (BSM) on photons leaving the dissipative cavities. Using the time-dependent Schördinger equation, we obtain the analytical results for the evolution of the entanglement. It is revealed that, by manipulating the detunings of classical field, the long-living stationary entanglement between two atoms can be generated in the presence of dissipation.
On the Thermal Symmetry of Markovian Master Equation
Tay, B A
2007-01-01
The quantum Markovian master equation of the reduced dynamics of a harmonic oscillator coupled to a thermal reservoir is shown to possess a thermal symmetry. This symmetry is a Bogoliubov transformation that can be represented by a hyperbolic rotation acting in the Liouville space of the reduced dynamics. The Liouville space is obtained as an extension from the Hilbert space by introducing tilde variables as carried out in thermofield dynamics formalism. The angle of rotation depends on the temperature of the reservoir, or the value of Planck's constant. The symmetry connects the thermal states of the system between any temperature, including absolute zero that contains a purely quantum effect. The Caldeira-Leggett equation and the classical Fokker-Planck equation also possess a thermal symmetry. We discuss how the thermal symmetry affects the change in the shape of a Gaussian wave packet. We also construct temperature dependent density states of a harmonic oscillator, which contain thermal ground states as w...
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 ...
Non-Markovian signatures in the current noise of a charge qubit
DEFF Research Database (Denmark)
Braggio, A.; Flindt, Christian; Novotny, T.
2008-01-01
We investigate the current noise of a charge qubit coupled to a phonon bath in different parameter regimes. We find, using the theory of Full Counting Statistics of non-Markovian systems, that the current fluctuations are strongly influenced by memory effects generated from the interplay between ...
Observation of Non-Markovian Dynamics of a Single Quantum Dot in a Micropillar Cavity
DEFF Research Database (Denmark)
Madsen, Kristian Høeg; Ates, Serkan; Lund-Hansen, Toke;
2011-01-01
We measure the detuning-dependent dynamics of a quasiresonantly excited single quantum dot coupled to a micropillar cavity. The system is modeled with the dissipative Jaynes-Cummings model where all experimental parameters are determined by explicit measurements. We observe non-Markovian dynamics...
Non-markovianity and CHSH-Bell inequality violation in multipartite dissipative systems
Thilagam, A
2012-01-01
We examine the non-Markovian dynamics in a multipartite system of two initially correlated atomic qubits, each located in a single-mode leaky cavity and interacting with its own bosonic reservoir. We show the dominance of non-Markovian features, as quantified by the difference in fidelity of the evolved system with its density matrix at an earlier time, in three specific two-qubit partitions associated with the cavity-cavity and atom-reservoir density matrices within the same subsystem, and the cavity-reservoir reduced matrix across the two subsystems. The non-Markovianity in the cavity-cavity subsystem is seen to be optimized in the vicinity of the exceptional point. The CHSH-Bell inequality computed for various two-qubit partitions show that high non-locality present in a specific subsystem appears in conjunction with enhanced non-Markovian dynamics in adjacent subsystems. This is in contrast to the matching existence of non-locality and quantum correlations in regions spanned by time t and the cavity decay...
Mode suppression in the non-Markovian limit by time-gated stimulated photon echo
de Boeij, W.P.; Pshenichnikov, M.S; Wiersma, D. A.
1996-01-01
It is demonstrated that enhanced mode suppression in stimulated photon echo experiments can be obtained by diagonal time gating of the echo. This technique is especially important when the optical dynamics of the system is non-Markovian. A two-mode Brownian oscillator model is used to analyze the ef
Sufficient conditions for a memory-kernel master equation
Chruściński, Dariusz; Kossakowski, Andrzej
2016-08-01
We derive sufficient conditions for the memory-kernel governing nonlocal master equation which guarantee a legitimate (completely positive and trace-preserving) dynamical map. It turns out that these conditions provide natural parametrizations of the dynamical map being a generalization of the Markovian semigroup. This parametrization is defined by the so-called legitimate pair—monotonic quantum operation and completely positive map—and it is shown that such a class of maps covers almost all known examples from the Markovian semigroup, the semi-Markov evolution, up to collision models and their generalization.
Application of Perturbation Theory to a Master Equation
Directory of Open Access Journals (Sweden)
B. M. Villegas-Martínez
2016-01-01
Full Text Available We develop a matrix perturbation method for the Lindblad master equation. The first- and second-order corrections are obtained and the method is generalized for higher orders. The perturbation method developed is applied to the problem of a lossy cavity filled with a Kerr medium; the second-order corrections are estimated and compared with the known exact analytic solution. The comparison is done by calculating the Q-function, the average number of photons, and the distance between density matrices.
Generalized master equation for modular exciton density transfer
Jang, Seogjoo; Fleming, Graham; Whaley, K Birgitta
2013-01-01
A generalized master equation (GME) governing quantum evolution of modular exciton density (MED) is derived for large scale light harvesting systems composed of weakly interacting modules of multiple chromophores. The GME-MED offers a practical framework to incorporate real time coherent quantum dynamics calculations at small length scales into dynamics over large length scales, without assumptions of time scale separation or specific forms of intra-module quantum dynamics. A test of the GME-MED for four sites of the Fenna-Matthews-Olson complex demonstrates how coherent dynamics of excitonic populations over many coupled chromophores can be accurately described by transitions between subgroups (modules) of delocalized excitons.
Coarse graining of master equations with fast and slow states
DEFF Research Database (Denmark)
Pigolotti, Simone; Vulpiani, Angelo
2008-01-01
We propose a general method for simplifying master equations by eliminating from the description rapidly evolving states. The physical recipe we impose is the suppression of these states and a renormalization of the rates of all the surviving states. In some cases, this decimation procedure can...... be analytically carried out and is consistent with other analytical approaches, such as in the problem of the random walk in a double well potential. We discuss the application of our method to nontrivial examples: diffusion in a lattice with defects and a model of an enzymatic reaction outside the steady state...
A Master Equation for Multi-Dimensional Non-Linear Field Theories
Park, Q H
1992-01-01
A master equation ( $n$ dimensional non--Abelian current conservation law with mutually commuting current components ) is introduced for multi-dimensional non-linear field theories. It is shown that the master equation provides a systematic way to understand 2-d integrable non-linear equations as well as 4-d self-dual equations and, more importantly, their generalizations to higher dimensions.
Diffusive Limits of the Master Equation in Inhomogeneous Media
Sattin, F; Salasnich, L
2015-01-01
In inhomogeneous environments several expressions for the flux of a diffusing quantity may apply--from Fick-Fourier's to Fokker-Planck's--depending upon the system studied. The integro-differential Master Equation (ME) provides a fairly generic framework for describing the dynamics of arbitrary systems driven by stochastic rules. Diffusive dynamics does arise as long-wavelength limit of the ME. However, while it is straightforward to obtain a diffusion equation with Fokker-Planck flux, its Fick-Fourier counterpart has never been worked out from the ME. In this work we show under which hypothesis the Fick's flux can actually be recovered from the ME. Analytical considerations are supported by explicit computer models.
Quantum Master Equation for QED in Exact Renormalization Group
Igarashi, Yuji; Sonoda, Hidenori
2007-01-01
Recently, one of us (H.S.) gave an explicit form of the Ward-Takahashi identity for the Wilson action of QED. We first rederive the identity using a functional method. The identity makes it possible to realize the gauge symmetry even in the presence of a momentum cutoff. In the cutoff dependent realization, the abelian nature of the gauge symmetry is lost, breaking the nilpotency of the BRS transformation. Using the Batalin-Vilkovisky formalism, we extend the Wilson action by including the antifield contributions. Then, the Ward-Takahashi identity for the Wilson action is lifted to a quantum master equation, and the modified BRS transformation regains nilpotency. We also obtain a flow equation for the extended Wilson action.
Extended master equation models for molecular communication networks.
Chou, Chun Tung
2013-06-01
We consider molecular communication networks consisting of transmitters and receivers distributed in a fluidic medium. In such networks, a transmitter sends one or more signaling molecules, which are diffused over the medium, to the receiver to realize the communication. In order to be able to engineer synthetic molecular communication networks, mathematical models for these networks are required. This paper proposes a new stochastic model for molecular communication networks called reaction-diffusion master equation with exogenous input (RDMEX). The key idea behind RDMEX is to model the transmitters as time series of signaling molecule counts, while diffusion in the medium and chemical reactions at the receivers are modeled as Markov processes using master equation. An advantage of RDMEX is that it can readily be used to model molecular communication networks with multiple transmitters and receivers. For the case where the reaction kinetics at the receivers is linear, we show how RDMEX can be used to determine the mean and covariance of the receiver output signals, and derive closed-form expressions for the mean receiver output signal of the RDMEX model. These closed-form expressions reveal that the output signal of a receiver can be affected by the presence of other receivers. Numerical examples are provided to demonstrate the properties of the model.
Institute of Scientific and Technical Information of China (English)
FAN Hong-Yi; LI Chao
2004-01-01
We extend the approach of solving master equations for density matrices by projecting it onto the thermal entangled state representation (Hong-Yi Fan and Jun-Hua Chen, J. Phys. A35 (2002) 6873) to two-mode case. In this approach the two-photon master equations can be directly and conveniently converted into c-number partial differential equations. As an example, we solve the typical master equation for two-photon process in some limiting cases.
Generalized master equations for non-Poisson dynamics on networks
Hoffmann, Till; Porter, Mason A.; Lambiotte, Renaud
2012-10-01
The traditional way of studying temporal networks is to aggregate the dynamics of the edges to create a static weighted network. This implicitly assumes that the edges are governed by Poisson processes, which is not typically the case in empirical temporal networks. Accordingly, we examine the effects of non-Poisson inter-event statistics on the dynamics of edges, and we apply the concept of a generalized master equation to the study of continuous-time random walks on networks. We show that this equation reduces to the standard rate equations when the underlying process is Poissonian and that its stationary solution is determined by an effective transition matrix whose leading eigenvector is easy to calculate. We conduct numerical simulations and also derive analytical results for the stationary solution under the assumption that all edges have the same waiting-time distribution. We discuss the implications of our work for dynamical processes on temporal networks and for the construction of network diagnostics that take into account their nontrivial stochastic nature.
Delay chemical master equation: direct and closed-form solutions
Leier, Andre; Marquez-Lago, Tatiana T.
2015-01-01
The stochastic simulation algorithm (SSA) describes the time evolution of a discrete nonlinear Markov process. This stochastic process has a probability density function that is the solution of a differential equation, commonly known as the chemical master equation (CME) or forward-Kolmogorov equation. In the same way that the CME gives rise to the SSA, and trajectories of the latter are exact with respect to the former, trajectories obtained from a delay SSA are exact representations of the underlying delay CME (DCME). However, in contrast to the CME, no closed-form solutions have so far been derived for any kind of DCME. In this paper, we describe for the first time direct and closed solutions of the DCME for simple reaction schemes, such as a single-delayed unimolecular reaction as well as chemical reactions for transcription and translation with delayed mRNA maturation. We also discuss the conditions that have to be met such that such solutions can be derived. PMID:26345616
Master Equation Approach to Molecular Motor's Directed Motion
Institute of Scientific and Technical Information of China (English)
FENG Juan; ZHUO Yi-Zhong
2005-01-01
@@ The master equation approach based on the periodic one-dimensional three-state hopping model is developed to study the molecular motor's directed motion. An explicit solution Px ( t ) is obtained for the probability distribution as a function of the time for any initial distribution Px(0) with all the transients included. We introduce dj to represent the sub-step lengths, which can reflect how the external load affects the individual rate via load distribution factors θ+j and θ-j. A wide variety of molecular motor behaviour under external load f can readily be obtained by the unequal-distance transition model with load-dependent transition rates. By comparison with the experiments, namely of the drift velocity v and the randomness parameter r versus adenosine triphosphate concentration and external load f, it is shown that the model presented here can rather satisfactorily explain the available data.
Master equation approach of classical noise in intersubband detectors
Delga, A.; Carras, M.; Trinité, V.; Guériaux, V.; Doyennette, L.; Nedelcu, A.; Schneider, H.; Berger, V.
2012-06-01
Electronic transport in intersubband detectors is investigated theoretically and experimentally. Within the framework of inter-Wannier-Stark levels electron scattering, consistent dark current and low-frequency noise expressions are obtained through the resolution of the two first moments of a master equation for classical particles. In particular, the formulation of noise bridges over the vision of uncorrelated Johnson and shot contributions. Theoretical predictions are compared to measurements for five quantum well detectors, either photovoltaic or photoconductive, whose detection wavelength span from 8μm to 17μm. Quantitative agreement with experiment is found for a broad range of biases and temperatures. Correlation effects are discussed and proven to either reduce or enhance the noise.
Symmetry of bilinear master equations for a quantum oscillator
Tay, B. A.
2017-02-01
We study the most general continuous transformation on the generators of bilinear master equations of a quantum oscillator. We find that transformation operators that preserve the hermiticity of density operators and conserve the probability of reduced dynamics should be adjoint-symmetric, and they are not limited to the pure product of unitary operators in the bra and ket space but could be a mixture of them. We need to include the more general transformation operators to explore the full symmetry of generic reduced dynamics. We discuss how the operators are related to those considered in previous works, and illustrate how they leave the reduced dynamics form invariant, or map one into the other. The positive semidefinite requirement on the density operator can be imposed to give a valid range of transformation parameters.
Master equation approach to DNA breathing in heteropolymer DNA
DEFF Research Database (Denmark)
Ambjörnsson, Tobias; Banik, Suman K; Lomholt, Michael A
2007-01-01
After crossing an initial barrier to break the first base-pair (bp) in double-stranded DNA, the disruption of further bps is characterized by free energies up to a few k(B)T. Thermal motion within the DNA double strand therefore causes the opening of intermittent single-stranded denaturation zones......, the DNA bubbles. The unzipping and zipping dynamics of bps at the two zipper forks of a bubble, where the single strand of the denatured zone joins the still intact double strand, can be monitored by single molecule fluorescence or NMR methods. We here establish a dynamic description of this DNA breathing...... in a heteropolymer DNA with given sequence in terms of a master equation that governs the time evolution of the joint probability distribution for the bubble size and position along the sequence. The transfer coefficients are based on the Poland-Scheraga free energy model. We derive the autocorrelation function...
Master equation approach to DNA breathing in heteropolymer DNA
DEFF Research Database (Denmark)
Ambjörnsson, Tobias; Banik, Suman K; Lomholt, Michael A
2007-01-01
After crossing an initial barrier to break the first base-pair (bp) in double-stranded DNA, the disruption of further bps is characterized by free energies up to a few k(B)T. Thermal motion within the DNA double strand therefore causes the opening of intermittent single-stranded denaturation zones......, the DNA bubbles. The unzipping and zipping dynamics of bps at the two zipper forks of a bubble, where the single strand of the denatured zone joins the still intact double strand, can be monitored by single molecule fluorescence or NMR methods. We here establish a dynamic description of this DNA breathing...... in a heteropolymer DNA with given sequence in terms of a master equation that governs the time evolution of the joint probability distribution for the bubble size and position along the sequence. The transfer coefficients are based on the Poland-Scheraga free energy model. We derive the autocorrelation function...
Bistability in the Chemical Master Equation for Dual Phosphorylation Cycles
Bazzani, A; Giampieri, E; Remondini, D; Cooper, L N
2011-01-01
Dual phospho/dephosphorylation cycles, as well as covalent enzymatic-catalyzed modifications of substrates, are widely diffused within cellular systems and are crucial for the control of complex responses such as learning, memory and cellular fate determination. Despite the large body of deterministic studies and the increasing work aimed to elucidate the effect of noise in such systems, some aspects remain unclear. Here we study the stationary distribution provided by the two-dimensional Chemical Master Equation for a well known model of a two step phospho/dephosphorylation cycle using the quasi steady state approximation of the enzymatic kinetics. Our aim is to analyze the role of fluctuations and the molecules distribution properties in the transition to a bistable regime. When detailed balance conditions are satisfied it is possible to compute equilibrium distributions in a closed and explicit form. When detailed balance is not satisfied, the stationary non-equilibrium state is strongly influenced by the ...
Reaction-diffusion master equation in the microscopic limit
Hellander, Stefan; Hellander, Andreas; Petzold, Linda
2012-04-01
Stochastic modeling of reaction-diffusion kinetics has emerged as a powerful theoretical tool in the study of biochemical reaction networks. Two frequently employed models are the particle-tracking Smoluchowski framework and the on-lattice reaction-diffusion master equation (RDME) framework. As the mesh size goes from coarse to fine, the RDME initially becomes more accurate. However, recent developments have shown that it will become increasingly inaccurate compared to the Smoluchowski model as the lattice spacing becomes very fine. Here we give a general and simple argument for why the RDME breaks down. Our analysis reveals a hard limit on the voxel size for which no local RDME can agree with the Smoluchowski model and lets us quantify this limit in two and three dimensions. In this light we review and discuss recent work in which the RDME has been modified in different ways in order to better agree with the microscale model for very small voxel sizes.
On the Reaction Diffusion Master Equation in the Microscopic Limit
Hellander, Stefan; Petzold, Linda
2011-01-01
Stochastic modeling of reaction-diffusion kinetics has emerged as a powerful theoretical tool in the study of biochemical reaction networks. Two frequently employed models are the particle-tracking Smoluchowski framework and the on-lattice Reaction-Diffusion Master Equation (RDME) framework. As the mesh size goes from coarse to fine, the RDME initially becomes more accurate. However, recent developments have shown that it will become increasingly inaccurate compared to the Smoluchowski model as the lattice spacing becomes very fine. In this paper we give a new, general and simple argument for why the RDME breaks down. Our analysis reveals a hard limit on the voxel size for which no local RDME can agree with the Smoluchowski model.
Solution to the Master Equation of a Free Damped Harmonic Oscillator with Linear Driving
Institute of Scientific and Technical Information of China (English)
杨洁; 逯怀新; 赵博; 赵梅生; 张永德
2003-01-01
We use the Lie algebra representation theory for superoperators to solve the master equation for a harmonic oscillator with a linear driving term in a squeezed thermal reservoir. By using the quantum displacement transformation and squeeze transformation, we show that the master equation has an su(1, 1) Lie algebra structure,with which we obtain the explicit solution to the master equation. A simple but typical example is given to illustrate our method.
Suarez, Ernesto
2014-01-01
A number of modern sampling methods probe long time behavior in complex biomolecules using a set of relatively short trajectory segments. Markov state models (MSMs) can be useful in analyzing such data sets, but in particularly complex landscapes, the available trajectory data may prove insufficient for constructing valid Markov models. Here, we explore the potential utility of history-dependent analyses applied to relatively poor decompositions of configuration space for which MSMs are inadequate. Our approaches build on previous work [Suarez et. al., JCTC 2014] showing that, with sufficient history information, unbiased equilibrium and non-equilibrium observables can be obtained even for arbitrary non-Markovian divisions of phase space. We explore a range of non-Markovian approximations using varying amounts of history information to model the finite length of trajectory segments, applying the analyses to toy models as well as several proteins previously studied by microsec-milisec scale atomistic simulatio...
Implications of non-Markovian quantum dynamics for the Landauer bound
Pezzutto, Marco; Paternostro, Mauro; Omar, Yasser
2016-12-01
We study the dynamics of a spin-1/2 particle interacting with a multi-spin environment, modelling the corresponding open system dynamics through a collision-based model. The environmental particles are prepared in individual thermal states, and we investigate the effects of a distribution of temperatures across the spin environment on the evolution of the system, particularly how thermalisation in the long-time limit is affected. We study the phenomenology of the heat exchange between system and environment and consider the information-to-energy conversion process, induced by the system-environment interaction and embodied by the Landauer principle. Furthermore, by considering an interacting-particles environment, we tune the dynamics of the system from an explicit Markovian evolution up to a strongly non-Markovian one, investigating the connections between non-Markovianity, the establishment of system-environment correlations, and the breakdown of the validity of Landauer principle.
Non-Markovian effect on the geometric phase of a dissipative qubit
Chen, Juan-Juan; Tong, Qing-Jun; Luo, Hong-Gang; Oh, C H
2010-01-01
We study 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 is 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 to 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.
Violation of the scaling relation and non-Markovian nature of earthquake aftershocks
Abe, Sumiyoshi
2008-01-01
The statistical properties of earthquake aftershocks are studied. The scaling relation for the exponents of the Omori law and the power-law calm time distribution (i.e., the interoccurrence time distribution), which is valid if a sequence of aftershocks is a singular Markovian process, is carefully examined. Data analysis shows significant violation of the scaling relation, implying the non-Markovian nature of aftershocks.
De Boeij, W. P.; Pshenichnikov, M. S.; Wiersma, D. A.
1996-01-01
We demonstrate a novel technique for efficient vibrational mode suppression in stimulated photon echo by diagonal time-gating. This is especially important if the system exhibits non-Markovian optical dynamics.
Equivalence of the measures of non-Markovianity for open two-level systems
Zeng, Hao-Sheng; Tang, Ning; Zheng, Yan-Ping; Wang, Guo-You
2011-09-01
Different measures have been presented to depict the deviation of quantum time evolution in open systems from Markovian processes. We demonstrate that the measure proposed by Breuer, Laine, and Piilo [Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.103.210401 103, 210401 (2009)] and the two measures proposed by Rivas, Huelga, and Plenio [Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.105.050403 105, 050403 (2010)] have exactly the same non-Markovian time-evolution intervals and thus are really equivalent to each other when they are applied to open two-level systems coupled to environments via the Jaynes-Cummings or dephasing models. This equivalence implies that the three measures, in different ways, capture the intrinsic character of the non-Markovianity of quantum evolutional processes. We also show that the maximization in the definition of the first measure can be actually removed for the considered models without influencing the sensibility of the measure to detect non-Markovianity.
Master equation solutions in the linear regime of characteristic formulation of general relativity
M., C E Cedeño
2015-01-01
From the field equations in the linear regime of the characteristic formulation of general relativity, Bishop, for a Schwarzschild's background, and M\\"adler, for a Minkowski's background, were able to show that it is possible to derive a fourth order ordinary differential equation, called master equation, for the $J$ metric variable of the Bondi-Sachs metric. Once $\\beta$, another Bondi-Sachs potential, is obtained from the field equations, and $J$ is obtained from the master equation, the other metric variables are solved integrating directly the rest of the field equations. In the past, the master equation was solved for the first multipolar terms, for both the Minkowski's and Schwarzschild's backgrounds. Also, M\\"adler recently reported a generalisation of the exact solutions to the linearised field equations when a Minkowski's background is considered, expressing the master equation family of solutions for the vacuum in terms of Bessel's functions of the first and the second kind. Here, we report new sol...
Data-driven non-Markovian closure models
Kondrashov, Dmitri; Chekroun, Mickaël D.; Ghil, Michael
2015-03-01
This paper has two interrelated foci: (i) obtaining stable and efficient data-driven closure models by using a multivariate time series of partial observations from a large-dimensional system; and (ii) comparing these closure models with the optimal closures predicted by the Mori-Zwanzig (MZ) formalism of statistical physics. Multilayer stochastic models (MSMs) are introduced as both a generalization and a time-continuous limit of existing multilevel, regression-based approaches to closure in a data-driven setting; these approaches include empirical model reduction (EMR), as well as more recent multi-layer modeling. It is shown that the multilayer structure of MSMs can provide a natural Markov approximation to the generalized Langevin equation (GLE) of the MZ 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 derived on the structure of 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 broad class of MSM applications, a class that includes non-polynomial predictors and nonlinearities that do not necessarily preserve quadratic energy invariants. 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. It is shown that the resulting closure model with energy-conserving nonlinearities efficiently 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 Lotka-Volterra model of population dynamics in its chaotic regime. The challenges here include the rarity of strange attractors in the model's parameter
Symmetric and antisymmetric forms of the Pauli master equation
Klimenko, A. Y.
2016-07-01
When applied to matter and antimatter states, the Pauli master equation (PME) may have two forms: time-symmetric, which is conventional, and time-antisymmetric, which is suggested in the present work. The symmetric and antisymmetric forms correspond to symmetric and antisymmetric extensions of thermodynamics from matter to antimatter — this is demonstrated by proving the corresponding H-theorem. The two forms are based on the thermodynamic similarity of matter and antimatter and differ only in the directions of thermodynamic time for matter and antimatter (the same in the time-symmetric case and the opposite in the time-antisymmetric case). We demonstrate that, while the symmetric form of PME predicts an equibalance between matter and antimatter, the antisymmetric form of PME favours full conversion of antimatter into matter. At this stage, it is impossible to make an experimentally justified choice in favour of the symmetric or antisymmetric versions of thermodynamics since we have no experience of thermodynamic properties of macroscopic objects made of antimatter, but experiments of this kind may become possible in the future.
Institute of Scientific and Technical Information of China (English)
侯邦品; 王顺金; 余万伦
2003-01-01
By using the algebraic structure in the operator dual space in the master equation for the driven dissipative harmonic oscillator, we have rewritten the master equation as a Schrodinger-like equation. Then we have used three gauge transformations and obtained an exact solution to the master equation in the particle number representation.
Herschlag, Gregory J; Mitran, Sorin; Lin, Guang
2015-06-21
We develop a hierarchy of approximations to the master equation for systems that exhibit translational invariance and finite-range spatial correlation. Each approximation within the hierarchy is a set of ordinary differential equations that considers spatial correlations of varying lattice distance; the assumption is that the full system will have finite spatial correlations and thus the behavior of the models within the hierarchy will approach that of the full system. We provide evidence of this convergence in the context of one- and two-dimensional numerical examples. Lower levels within the hierarchy that consider shorter spatial correlations are shown to be up to three orders of magnitude faster than traditional kinetic Monte Carlo methods (KMC) for one-dimensional systems, while predicting similar system dynamics and steady states as KMC methods. We then test the hierarchy on a two-dimensional model for the oxidation of CO on RuO2(110), showing that low-order truncations of the hierarchy efficiently capture the essential system dynamics. By considering sequences of models in the hierarchy that account for longer spatial correlations, successive model predictions may be used to establish empirical approximation of error estimates. The hierarchy may be thought of as a class of generalized phenomenological kinetic models since each element of the hierarchy approximates the master equation and the lowest level in the hierarchy is identical to a simple existing phenomenological kinetic models.
Derivation of exact master equation with stochastic description: dissipative harmonic oscillator.
Li, Haifeng; Shao, Jiushu; Wang, Shikuan
2011-11-01
A systematic procedure for deriving the master equation of a dissipative system is reported in the framework of stochastic description. For the Caldeira-Leggett model of the harmonic-oscillator bath, a detailed and elementary derivation of the bath-induced stochastic field is presented. The dynamics of the system is thereby fully described by a stochastic differential equation, and the desired master equation would be acquired with statistical averaging. It is shown that the existence of a closed-form master equation depends on the specificity of the system as well as the feature of the dissipation characterized by the spectral density function. For a dissipative harmonic oscillator it is observed that the correlation between the stochastic field due to the bath and the system can be decoupled, and the master equation naturally results. Such an equation possesses the Lindblad form in which time-dependent coefficients are determined by a set of integral equations. It is proved that the obtained master equation is equivalent to the well-known Hu-Paz-Zhang equation based on the path-integral technique. The procedure is also used to obtain the master equation of a dissipative harmonic oscillator in time-dependent fields.
Brett, Tobias; Galla, Tobias
2013-06-21
We develop a systematic approach to the linear-noise approximation for stochastic reaction systems with distributed delays. Unlike most existing work our formalism does not rely on a master equation; instead it is based upon a dynamical generating functional describing the probability measure over all possible paths of the dynamics. We derive general expressions for the chemical Langevin equation for a broad class of non-Markovian systems with distributed delay. Exemplars of a model of gene regulation with delayed autoinhibition and a model of epidemic spread with delayed recovery provide evidence of the applicability of our results.
Elephants can always remember: Exact long-range memory effects in a non-Markovian random walk
Schütz, Gunter M.; Trimper, Steffen
2004-10-01
We consider a discrete-time random walk where the random increment at time step t depends on the full history of the process. We calculate exactly the mean and variance of the position and discuss its dependence on the initial condition and on the memory parameter p . At a critical value pc(1)=1/2 where memory effects vanish there is a transition from a weakly localized regime [where the walker (elephant) returns to its starting point] to an escape regime. Inside the escape regime there is a second critical value where the random walk becomes superdiffusive. The probability distribution is shown to be governed by a non-Markovian Fokker-Planck equation with hopping rates that depend both on time and on the starting position of the walk. On large scales the memory organizes itself into an effective harmonic oscillator potential for the random walker with a time-dependent spring constant k=(2p-1)/t . The solution of this problem is a Gaussian distribution with time-dependent mean and variance which both depend on the initiation of the process.
Liu, Da-Jiang; Chen, Hung-Ting; Lin, Victor S-Y; Evans, J W
2010-04-21
We analyze a model for polymerization at catalytic sites distributed within parallel linear pores of a mesoporous material. Polymerization occurs primarily by reaction of monomers diffusing into the pores with the ends of polymers near the pore openings. Monomers and polymers undergo single-file diffusion within the pores. Model behavior, including the polymer length distribution, is determined by kinetic Monte Carlo simulation of a suitable atomistic-level lattice model. While the polymers remain within the pore, their length distribution during growth can be described qualitatively by a Markovian rate equation treatment. However, once they become partially extruded, the distribution is shown to exhibit non-Markovian scaling behavior. This feature is attributed to the long-tail in the "return-time distribution" for the protruding end of the partially extruded polymer to return to the pore, such return being necessary for further reaction and growth. The detailed form of the scaled length distribution is elucidated by application of continuous-time random walk theory.
Horowitz, Jordan M.
2015-01-01
The stochastic thermodynamics of a dilute, well-stirred mixture of chemically-reacting species is built on the stochastic trajectories of reaction events obtained from the Chemical Master Equation. However, when the molecular populations are large, the discrete Chemical Master Equation can be approximated with a continuous diffusion process, like the Chemical Langevin Equation or Low Noise Approximation. In this paper, we investigate to what extent these diffusion approximations inherit the s...
Energy Technology Data Exchange (ETDEWEB)
Horowitz, Jordan M., E-mail: jordan.horowitz@umb.edu [Department of Physics, University of Massachusetts at Boston, Boston, Massachusetts 02125 (United States)
2015-07-28
The stochastic thermodynamics of a dilute, well-stirred mixture of chemically reacting species is built on the stochastic trajectories of reaction events obtained from the chemical master equation. However, when the molecular populations are large, the discrete chemical master equation can be approximated with a continuous diffusion process, like the chemical Langevin equation or low noise approximation. In this paper, we investigate to what extent these diffusion approximations inherit the stochastic thermodynamics of the chemical master equation. We find that a stochastic-thermodynamic description is only valid at a detailed-balanced, equilibrium steady state. Away from equilibrium, where there is no consistent stochastic thermodynamics, we show that one can still use the diffusive solutions to approximate the underlying thermodynamics of the chemical master equation.
Horowitz, Jordan M
2015-07-28
The stochastic thermodynamics of a dilute, well-stirred mixture of chemically reacting species is built on the stochastic trajectories of reaction events obtained from the chemical master equation. However, when the molecular populations are large, the discrete chemical master equation can be approximated with a continuous diffusion process, like the chemical Langevin equation or low noise approximation. In this paper, we investigate to what extent these diffusion approximations inherit the stochastic thermodynamics of the chemical master equation. We find that a stochastic-thermodynamic description is only valid at a detailed-balanced, equilibrium steady state. Away from equilibrium, where there is no consistent stochastic thermodynamics, we show that one can still use the diffusive solutions to approximate the underlying thermodynamics of the chemical master equation.
Closed description of arbitrariness in resolving quantum master equation
Directory of Open Access Journals (Sweden)
Igor A. Batalin
2016-07-01
Full Text Available In the most general case of the Delta exact operator valued generators constructed of an arbitrary Fermion operator, we present a closed solution for the transformed master action in terms of the original master action in the closed form of the corresponding path integral. We show in detail how that path integral reduces to the known result in the case of being the Delta exact generators constructed of an arbitrary Fermion function.
Closed description of arbitrariness in resolving quantum master equation
Batalin, Igor A
2016-01-01
In the most general case of the Delta exact operator valued generators constructed of an arbitrary Fermion operator, we present a closed solution for the transformed master action in terms of the original master action in the closed form of the corresponding path integral. We show in detail how that path integral reduces to the known result in the case of being the Delta exact generators constructed of an arbitrary Fermion function.
Closed description of arbitrariness in resolving quantum master equation
Batalin, Igor A.; Lavrov, Peter M.
2016-07-01
In the most general case of the Delta exact operator valued generators constructed of an arbitrary Fermion operator, we present a closed solution for the transformed master action in terms of the original master action in the closed form of the corresponding path integral. We show in detail how that path integral reduces to the known result in the case of being the Delta exact generators constructed of an arbitrary Fermion function.
Closed description of arbitrariness in resolving quantum master equation
Energy Technology Data Exchange (ETDEWEB)
Batalin, Igor A., E-mail: batalin@lpi.ru [P.N. Lebedev Physical Institute, Leninsky Prospect 53, 119 991 Moscow (Russian Federation); Tomsk State Pedagogical University, Kievskaya St. 60, 634061 Tomsk (Russian Federation); Lavrov, Peter M., E-mail: lavrov@tspu.edu.ru [Tomsk State Pedagogical University, Kievskaya St. 60, 634061 Tomsk (Russian Federation); National Research Tomsk State University, Lenin Av. 36, 634050 Tomsk (Russian Federation)
2016-07-10
In the most general case of the Delta exact operator valued generators constructed of an arbitrary Fermion operator, we present a closed solution for the transformed master action in terms of the original master action in the closed form of the corresponding path integral. We show in detail how that path integral reduces to the known result in the case of being the Delta exact generators constructed of an arbitrary Fermion function.
Non-Markovian spiking statistics of a neuron with delayed feedback in presence of refractoriness.
Kravchuk, Kseniia; Vidybida, Alexander
2014-02-01
Spiking statistics of a self-inhibitory neuron is considered. The neuron receives excitatory input from a Poisson stream and inhibitory impulses through a feedback line with a delay. After triggering, the neuron is in the refractory state for a positive period of time. Recently, [35,6], it was proven for a neuron with delayed feedback and without the refractory state, that the output stream of interspike intervals (ISI) cannot be represented as a Markov process. The refractory state presence, in a sense limits the memory range in the spiking process, which might restore Markov property to the ISI stream. Here we check such a possibility. For this purpose, we calculate the conditional probability density P (tn+1 l tn,...,t1,t0), and prove exactly that it does not reduce to P (tn+1 l tn,...,t1) for any n ⋝0. That means, that activity of the system with refractory state as well cannot be represented as a Markov process of any order. We conclude that it is namely the delayed feedback presence which results in non-Markovian statistics of neuronal firing. As delayed feedback lines are common for any realistic neural network, the non-Markovian statistics of the network activity should be taken into account in processing of experimental data.
Non-Markovian Quantum Fluctuations and Superradiance Near a Photonic Band Edge
Vats, N; Vats, Nipun; John, Sajeev
1998-01-01
We discuss a point model for the collective emission of light from N two-level atoms in a photonic bandgap material, each with an atomic resonant frequency near the edge of the gap. In the limit of a low initial occupation of the excited atomic state, our system is shown to possess novel atomic spectra and population statistics. For a high initial excited state population, mean field theory suggests a fractionalized inversion and a macroscopic polarization for the atoms in the steady state, both of which can be controlled by an external d.c. field. This atomic steady state is accompanied by a non--zero expectation value of the electric field operators for field modes located in the vicinity of the atoms. The nature of homogeneous broadening near the band edge is shown to differ markedly from that in free space due to non-Markovian memory effects in the radiation dynamics. Non-Markovian vacuum fluctuations are shown to yield a partially coherent steady state polarization with a random phase. In contrast with t...
Tripartite entanglement dynamics in the presence of Markovian or non-Markovian environment
Park, DaeKil
2016-08-01
We study on the tripartite entanglement dynamics when each party is initially entangled with other parties, but they locally interact with their own Markovian or non-Markovian environment. First we consider three GHZ-type initial states, all of which have GHZ-symmetry provided that the parameters are chosen appropriately. However, this symmetry is broken due to the effect of environment. The corresponding π -tangles, one of the tripartite entanglement measures, are analytically computed at arbitrary time. For Markovian case while the tripartite entanglement for type I exhibits an entanglement sudden death, the dynamics for the remaining cases decays normally in time with the half-life rule. For non-Markovian case the revival phenomenon of entanglement occurs after complete disappearance of entanglement. We also consider two W-type initial states. For both cases the π -tangles are analytically derived. The revival phenomenon also occurs in this case. On the analytical ground the robustness or fragility issue against the effect of environment is examined for both GHZ-type and W-type initial states.
Non-Markovian dynamics of quantum coherence of two-level system driven by classical field
Huang, Zhiming; Situ, Haozhen
2017-09-01
In this paper, we study the quantum coherence dynamics of two-level atom system embedded in non-Markovian reservoir in the presence of classical driving field. We analyze the influence of memory effects, classical driving, and detuning on the quantum coherence. It is found that the quantum coherence has different behaviors in resonant case and non-resonant case. In the resonant case, in stark contrast with previous results, the strength of classical driving plays a negative effect on quantum coherence, while detuning parameter has the opposite effect. However, in non-resonant case through a long time, classical driving and detuning parameter have a different influence on quantum coherence compared with resonant case. Due to the memory effect of environment, in comparison with Markovian regime, quantum coherence presents vibrational variations in non-Markovian regime. In the resonant case, all quantum coherence converges to a fixed maximum value; in the non-resonant case, quantum coherence evolves to different stable values. For zero-coherence initial states, quantum coherence can be generated with evolution time. Our discussions and results should be helpful in manipulating and preserving the quantum coherence in dissipative environment with classical driving field.
Quantum Monte-Carlo method applied to Non-Markovian barrier transmission
Hupin, G
2010-01-01
In nuclear fusion and fission, fluctuation and dissipation arise due to the coupling of collective degrees of freedom with internal excitations. Close to the barrier, both quantum, statistical and non-Markovian effects are expected to be important. In this work, a new approach based on quantum Monte-Carlo addressing this problem is presented. The exact dynamics of a system coupled to an environment is replaced by a set of stochastic evolutions of the system density. The quantum Monte-Carlo method is applied to systems with quadratic potentials. In all range of temperature and coupling, the stochastic method matches the exact evolution showing that non-Markovian effects can be simulated accurately. A comparison with other theories like Nakajima-Zwanzig or Time-ConvolutionLess ones shows that only the latter can be competitive if the expansion in terms of coupling constant is made at least to fourth order. A systematic study of the inverted parabola case is made at different temperatures and coupling constants....
Quantum Monte Carlo method applied to non-Markovian barrier transmission
Hupin, Guillaume; Lacroix, Denis
2010-01-01
In nuclear fusion and fission, fluctuation and dissipation arise because of the coupling of collective degrees of freedom with internal excitations. Close to the barrier, quantum, statistical, and non-Markovian effects are expected to be important. In this work, a new approach based on quantum Monte Carlo addressing this problem is presented. The exact dynamics of a system coupled to an environment is replaced by a set of stochastic evolutions of the system density. The quantum Monte Carlo method is applied to systems with quadratic potentials. In all ranges of temperature and coupling, the stochastic method matches the exact evolution, showing that non-Markovian effects can be simulated accurately. A comparison with other theories, such as Nakajima-Zwanzig or time-convolutionless, shows that only the latter can be competitive if the expansion in terms of coupling constant is made at least to fourth order. A systematic study of the inverted parabola case is made at different temperatures and coupling constants. The asymptotic passing probability is estimated by different approaches including the Markovian limit. Large differences with an exact result are seen in the latter case or when only second order in the coupling strength is considered, as is generally assumed in nuclear transport models. In contrast, if fourth order in the coupling or quantum Monte Carlo method is used, a perfect agreement is obtained.
Ebadi, H.; Saeedian, M.; Ausloos, M.; Jafari, G. R.
2016-11-01
The Boolean network is one successful model to investigate discrete complex systems such as the gene interacting phenomenon. The dynamics of a Boolean network, controlled with Boolean functions, is usually considered to be a Markovian (memory-less) process. However, both self-organizing features of biological phenomena and their intelligent nature should raise some doubt about ignoring the history of their time evolution. Here, we extend the Boolean network Markovian approach: we involve the effect of memory on the dynamics. This can be explored by modifying Boolean functions into non-Markovian functions, for example, by investigating the usual non-Markovian threshold function —one of the most applied Boolean functions. By applying the non-Markovian threshold function on the dynamical process of the yeast cell cycle network, we discover a power-law-like memory with a more robust dynamics than the Markovian dynamics.
Exact Solution of the Curved Dirac Equation in Polar Coordinates: Master Function Approach
Directory of Open Access Journals (Sweden)
H. Panahi
2015-01-01
Full Text Available We show that the (2+1 curved Dirac equation in polar coordinates can be transformed into Schrodinger-like differential equation for upper spinor component. We compare this equation with the Schrodinger equation derived from shape invariance property of second order differential equations of mathematical physics. This formalism enables us to determine the electrostatic potential and relativistic energy in terms of master function and corresponding weight function. We also obtain the spinor wave function in terms of orthogonal polynomials.
Fourth-order master equation for a charged harmonic oscillator coupled to an electromagnetic field
Kurt, Arzu; Eryigit, Resul
Using Krylov averaging method, we have derived a fourth-order master equation for a charged harmonic oscillator weakly coupled to an electromagnetic field. Interaction is assumed to be of velocity coupling type which also takes into account the diagmagnetic term. Exact analytical expressions have been obtained for the second, the third and the fourth-order corrections to the diffusion and the drift terms of the master equation. We examined the validity range of the second order master equation in terms of the coupling constant and the bath cutoff frequency and found that for the most values of those parameters, the contribution from the third and the fourth order terms have opposite signs and cancel each other. Inclusion of the third and the fourth-order terms is found to not change the structure of the master equation. Bolu, Turkey.
Modelling with the master equation solution methods and applications in social and natural sciences
Haag, Günter
2017-01-01
This book presents the theory and practical applications of the Master equation approach, which provides a powerful general framework for model building in a variety of disciplines. The aim of the book is to not only highlight different mathematical solution methods, but also reveal their potential by means of practical examples. Part I of the book, which can be used as a toolbox, introduces selected statistical fundamentals and solution methods for the Master equation. In Part II and Part III, the Master equation approach is applied to important applications in the natural and social sciences. The case studies presented mainly hail from the social sciences, including urban and regional dynamics, population dynamics, dynamic decision theory, opinion formation and traffic dynamics; however, some applications from physics and chemistry are treated as well, underlining the interdisciplinary modelling potential of the Master equation approach. Drawing upon the author’s extensive teaching and research experience...
Numerical integration of the master equation in some models of stochastic epidemiology.
Directory of Open Access Journals (Sweden)
Garrett Jenkinson
Full Text Available The processes by which disease spreads in a population of individuals are inherently stochastic. The master equation has proven to be a useful tool for modeling such processes. Unfortunately, solving the master equation analytically is possible only in limited cases (e.g., when the model is linear, and thus numerical procedures or approximation methods must be employed. Available approximation methods, such as the system size expansion method of van Kampen, may fail to provide reliable solutions, whereas current numerical approaches can induce appreciable computational cost. In this paper, we propose a new numerical technique for solving the master equation. Our method is based on a more informative stochastic process than the population process commonly used in the literature. By exploiting the structure of the master equation governing this process, we develop a novel technique for calculating the exact solution of the master equation--up to a desired precision--in certain models of stochastic epidemiology. We demonstrate the potential of our method by solving the master equation associated with the stochastic SIR epidemic model. MATLAB software that implements the methods discussed in this paper is freely available as Supporting Information S1.
Derivation of exact master equation with stochastic description: Dissipative harmonic oscillator
Li, Haifeng; Wang, Shikuan
2011-01-01
A systematic procedure for deriving the master equation of a dissipative system is reported in the framework of stochastic description. For the Caldeira-Leggett model of the harmonic-oscillator bath, a detailed and elementary derivation of the bath-induced stochastic field is presented. The dynamics of the system is thereby fully described by a stochastic differential equation and the desired master equation would be acquired with statistical averaging. It is shown that the existence of a closed-form master equation depends on the specificity of the system as well as the feature of the dissipation characterized by the spectral density function. For a dissipative harmonic oscillator it is observed that the correlation between the stochastic field due to the bath and the system can be decoupled and the master equation naturally comes out. Such an equation possesses the Lindblad form in which time dependent coefficients are determined by a set of integral equations. It is proved that the obtained master equation...
Cerrillo, Javier; Buser, Maximilian; Brandes, Tobias
2016-12-01
Nonequilibrium transport properties of quantum systems have recently become experimentally accessible in a number of platforms in so-called full-counting experiments that measure transient and steady-state nonequilibrium transport dynamics. We show that the effect of the measurement back-action can be exploited to establish general relationships between transport coefficients in the transient regime which take the form of fluctuation-dissipation theorems in the steady state. This result becomes most conspicuous in the transient dynamics of open quantum systems under strong-coupling to non-Markovian environments in nonequilibrium settings. In order to explore this regime, a new simulation method based in a hierarchy of equations of motion has been developed. We instantiate our proposal with the study of energetic conductance between two baths connected via a few level system.
Wen, Kai; Sakata, Fumihiko; Li, Zhu-Xia; Wu, Xi-Zhen; Zhang, Ying-Xun; Zhou, Shan-Gui
2013-07-05
Macroscopic parameters as well as precise information on the random force characterizing the Langevin-type description of the nuclear fusion process around the Coulomb barrier are extracted from the microscopic dynamics of individual nucleons by exploiting the numerical simulation of the improved quantum molecular dynamics. It turns out that the dissipation dynamics of the relative motion between two fusing nuclei is caused by a non-Gaussian distribution of the random force. We find that the friction coefficient as well as the time correlation function of the random force takes particularly large values in a region a little bit inside of the Coulomb barrier. A clear non-Markovian effect is observed in the time correlation function of the random force. It is further shown that an emergent dynamics of the fusion process can be described by the generalized Langevin equation with memory effects by appropriately incorporating the microscopic information of individual nucleons through the random force and its time correlation function.
Non-Markovian Quantum Error Deterrence by Dynamical Decoupling in a General Environment
Shiokawa, K
2005-01-01
A dynamical decoupling scheme for the deterrence of errors in the non-Markovian (usually corresponding to low temperature, short time, and strong coupling) regimes suitable for qubits constructed out of a multilevel structure is studied. We use the effective spin-boson model (ESBM) introduced recently [K. Shiokawa and B. L. Hu, Phys. Rev. A70, 062106 (2004)] as a low temperature limit of the quantum Brownian oscillator model, where one can obtain exact solutions for a general environment with colored noises. In our decoupling scheme a train of pairs of strong pulses are used to evolve the interaction Hamiltonian instantaneously. Using this scheme we show that the dynamical decoupling method can suppress $1/f$ noise with slower and hence more accessible pulses than previously studied, but it still fails to decouple super-Ohmic types of environments.
Suppressing non-Markovian noises by coupling the qubit to a chaotic device
Zhang, Jing; Zhang, Wei-Min; Wu, Re-Bing; Tarn, Tzyh-Jong
2011-01-01
To suppress decoherence of solid-state qubits which are coupled to the non-Markovian noises, we propose a strategy to couple the qubit with a chaotic device, of which the broad power distribution in the high-frequency domain can be used to freeze the noises just like the dynamical decoupling control (DDC) method. Compared with the DDC, high-frequency components can be generated by the chaotic device even driven by a low-frequency field and we do not need to optimize the control fields to generate complex control pulses. As an application to superconducting circuits, we find that various noises in a wide frequency domain, including low-frequency $1/f$, high-frequency Ohmic, sub-Ohmic, and super-Ohmic noises, can be efficiently suppressed by coupling the qubit to a Duffing oscillator, and the decoherence rate of the qubit is efficiently decreased for about $100$ times in magnitude.
Work distribution for a particle moving in an optical trap and non-Markovian bath
Indian Academy of Sciences (India)
Alok Samanta; K Srinivasu; Swapan K Ghosh
2009-09-01
We propose a simple approach to derive an exact analytical expression of work distribution for a system consisting of a colloidal particle trapped in an optical harmonic potential well, which is being pulled at a constant velocity through a solution represented by a non-Markovian bath. The thermal environment is represented by a bath composed of an infinite set of harmonic oscillators, and a model Hamiltonian for the trapped colloidal particle is constructed by representing the interaction with the bathvia linear dissipative mechanism. We have studied the effects of pulling time, pulling speed, and the adiabatic limit. It is also observed that only at long time the total work is completely converted into dissipative work.
Devi, A R Usha; Sudha,
2010-01-01
Dynamical A and B maps have been employed extensively by Sudarshan and co-workers to investigate open system evolution of quantum systems. A canonical structure of the A-map is introduced here. It is shown that this canonical A-map enables us to investigate if the dynamics is completely positive (CP) or non-completely positive (NCP) in an elegant way and hence, it subsumes the basic results on open system dynamics. Identifying memory effects in open system evolution is gaining increasing importance recently and here, a criterion of non-Markovianity, based on the relative entropy of the dynamical state is proposed. The relative entropy difference of the dynamical system serves as a complementary characterization - though not related directly - to the fidelity difference criterion proposed recently. Three typical examples of open system evolution of a qubit, prepared initially in a correlated state with another qubit (environment), and evolving jointly under a specific unitary dynamics - which corresponds to a ...
Analysis of non-Markovian coupling of a lattice-trapped atom to free space
Stewart, Michael; Krinner, Ludwig; Pazmiño, Arturo; Schneble, Dominik
2017-01-01
Behavior analogous to that of spontaneous emission in photonic band-gap materials has been predicted for an atom-optical system consisting of an atom confined in a well of a state-dependent optical lattice that is coupled to free space through an internal-state transition [de Vega et al., Phys. Rev. Lett. 101, 260404 (2008), 10.1103/PhysRevLett.101.260404]. Using the Weisskopf-Wigner approach and considering a one-dimensional geometry, we analyze the properties of this system in detail, including the evolution of the lattice-trapped population, the momentum distribution of emitted matter waves, and the detailed structure of an evanescent matter-wave state below the continuum boundary. We compare and contrast our findings for the transition from Markovian to non-Markovian behaviors to those previously obtained for three dimensions.
Nourmandipour, A.; Tavassoly, M. K.; Rafiee, M.
2016-02-01
We provide an analytical investigation of the pairwise entanglement dynamics for a system, consisting of an arbitrary number of qubits dissipating into a common and non-Markovian environment for both weak- and strong-coupling regimes. In the latter case, a revival of pairwise entanglement due to the memory depth of the environment is observed. The leakage of photons into a continuum state is assumed to be the source of dissipation. We show that for an initially Werner state, the environment washes out the pairwise entanglement, but a series of nonselective measurements can protect the relevant entanglement. On the other hand, by limiting the number of qubits initially in the superposition of single excitation, a stationary entanglement can be created between qubits initially in the excited and ground states. Finally, we determine the stationary distribution of the entanglement versus the total number of qubits in the system.
Experimental on-demand recovery of entanglement by local operations within non-Markovian dynamics.
Orieux, Adeline; D'Arrigo, Antonio; Ferranti, Giacomo; Lo Franco, Rosario; Benenti, Giuliano; Paladino, Elisabetta; Falci, Giuseppe; Sciarrino, Fabio; Mataloni, Paolo
2015-02-25
In many applications entanglement must be distributed through noisy communication channels that unavoidably degrade it. Entanglement cannot be generated by local operations and classical communication (LOCC), implying that once it has been distributed it is not possible to recreate it by LOCC. Recovery of entanglement by purely local control is however not forbidden in the presence of non-Markovian dynamics, and here we demonstrate in two all-optical experiments that such entanglement restoration can even be achieved on-demand. First, we implement an open-loop control scheme based on a purely local operation, without acquiring any information on the environment; then, we use a closed-loop scheme in which the environment is measured, the outcome controling the local operations on the system. The restored entanglement is a manifestation of "hidden" quantum correlations resumed by the local control. Relying on local control, both schemes improve the efficiency of entanglement sharing in distributed quantum networks.
Dark matter halo assembly bias: environmental dependence in the non-Markovian excursion set theory
Zhang, Jun; Riotto, Antonio
2013-01-01
In the standard excursion set model for the growth of structure, the statistical properties of haloes are governed by the halo mass and are independent of the larger scale environment in which the haloes reside. Numerical simulations, however, have found the spatial distributions of haloes to depend not only on their mass but also on the details of their assembly history and environment. Here we present a theoretical framework for incorporating this "assembly bias" into the excursion set model. Our derivations are based on modifications of the path integral approach of Maggiore & Riotto (2010) that models halo formation as a non-Markovian random walk process. The perturbed density field is assumed to evolve stochastically with the smoothing scale and exhibits correlated walks in the presence of a density barrier. We write down conditional probabilities for multiple barrier crossings, and derive from them analytic expressions for descendant and progenitor halo mass functions and halo merger rates as a func...
Experimental measurement of non-Markovian dynamics and self-diffusion in a strongly coupled plasma
Strickler, T S; McQuillen, P; Daligault, J; Killian, T C
2015-01-01
We present a study of the collisional relaxation of ion velocities in a strongly coupled, ultracold neutral plasma on short timescales compared to the inverse collision rate. Non-exponential decay towards equilibrium for the average velocity of a tagged population of ions heralds non-Markovian dynamics and a breakdown of assumptions underlying standard kinetic theory. We prove the equivalence of the average-velocity curve to the velocity autocorrelation function, a fundamental statistical quantity that provides access to equilibrium transport coefficients and aspects of individual particle trajectories in a regime where experimental measurements have been lacking. From our data, we calculate the ion self-diffusion constant. This demonstrates the utility of ultracold neutral plasmas for isolating the effects of strong coupling on collisional processes, which is of interest for dense laboratory and astrophysical plasmas.
Dynamics of open quantum spin systems : An assessment of the quantum master equation approach
Zhao, P.; De Raedt, H.; Miyashita, S.; Jin, F.; Michielsen, K.
2016-01-01
Data of the numerical solution of the time-dependent Schrodinger equation of a system containing one spin-1/2 particle interacting with a bath of up to 32 spin-1/2 particles is used to construct a Markovian quantum master equation describing the dynamics of the system spin. The procedure of obtainin
Master equation for a chemical wave front with perturbation of local equilibrium
Dziekan, P.; Lemarchand, A.; Nowakowski, B.
2011-08-01
In order to develop a stochastic description of gaseous reaction-diffusion systems, which includes a reaction-induced departure from local equilibrium, we derive a modified expression of the master equation from analytical calculations based on the Boltzmann equation. We apply the method to a chemical wave front of Fisher-Kolmogorov-Petrovsky-Piskunov type, whose propagation speed is known to be sensitive to small perturbations. The results of the modified master equation are compared successfully with microscopic simulations of the particle dynamics using the direct simulation Monte Carlo method. The modified master equation constitutes an efficient tool at the mesoscopic scale, which incorporates the nonequilibrium effect without need of determining the particle velocity distribution function.
Chou, C H; Yu, T; Chou, Chung-Hsien; Yu, Ting
2007-01-01
In this paper we derive an exact master equation for two coupled quantum harmonic oscillators interacting via bilinear coupling with a common environment made up of many harmonic oscillators at arbitrary temperature for a general spectral density function. We first show a simple derivation based on the observation that the two harmonic oscillator model can be effectively mapped into that of a single harmonic oscillator in a general environment plus a free harmonic oscillator. Since the exact one harmonic oscillator master equation is known [Hu, Paz and Zhang, Phys. Rev. D \\textbf{45}, 2843 (1992)], the exact master equation with all its coefficients for this two harmonic oscillator model can be easily deduced from the known results of the single harmonic oscillator case. In the second part we give an influence functional treatment of this model and provide explicit expressions for the evolution operator of the reduced density matrix which are useful for the study of decoherence and disentanglement issues. We ...
An extended master-equation approach applied to aggregation in freeway traffic
Institute of Scientific and Technical Information of China (English)
Li Jun-Wei; Lin Bo-Liang; Huang Yong-Chang
2008-01-01
We restudy the master-equation approach applied to aggregation in a one-dimensional freeway,where the decay transition probabilities for the jump processes are reconstructed based on a car-following model. According to the reconstructed transition probabilities,the clustering behaviours and the stochastic properties of the master equation in a one-lane freeway traffic model are investigated in detail.The numerical results show that the size of the clusters initially below the critical size of the unstable cluster and initially above that of the unstable cluster all enter the same stable state,which also accords with the nucleation theory and is known from the result in earlier work.Moreover,we have obtained more reasonable parameters of the master equation based on some results of cellular automata models.
Fokker-Planck quantum master equation for mixed quantum-semiclassical dynamics.
Ding, Jin-Jin; Wang, Yao; Zhang, Hou-Dao; Xu, Rui-Xue; Zheng, Xiao; Yan, YiJing
2017-01-14
We revisit Caldeira-Leggett's quantum master equation representing mixed quantum-classical theory, but with limited applications. Proposed is a Fokker-Planck quantum master equation theory, with a generic bi-exponential correlation function description on semiclassical Brownian oscillators' environments. The new theory has caustic terms that bridge between the quantum description on primary systems and the semiclassical or quasi-classical description on environments. Various parametrization schemes, both analytical and numerical, for the generic bi-exponential environment bath correlation functions are proposed and scrutinized. The Fokker-Planck quantum master equation theory is of the same numerical cost as the original Caldeira-Leggett's approach but acquires a significantly broadened validity and accuracy range, as illustrated against the exact dynamics on model systems in quantum Brownian oscillators' environments, at moderately low temperatures.
Modified Bloch-Redfield Master Equation for Incoherent Excitation of Multilevel Quantum Systems
Tscherbul, Timur V
2014-01-01
We present an efficient theoretical method for calculating the time evolution of the density matrix of a multilevel quantum system weakly interacting with incoherent light. The method combines the Bloch-Redfield theory with a partial secular approximation for one-photon coherences, resulting in a master equation that explicitly exposes the reliance on transition rates and the angles between transition dipole moments in the energy basis. The modified Bloch-Redfield master equation allows an unambiguous distinction between the regimes of quantum coherent vs. incoherent energy transfer under incoherent light illumination. The fully incoherent regime is characterized by orthogonal transition dipole moments in the energy basis, leading to a dynamical evolution governed by a coherence-free Pauli-type master equation. The coherent regime requires non-orthogonal transition dipole moments in the energy basis, and leads to the generation of noise-induced quantum coherences and population-to-coherence couplings. As a fi...
Master Equation Approach to Current-Voltage Characteristics of Solar Cells
Oh, Sangchul; Zhang, Yiteng; Alharbi, Fahhad; Kais, Sabre
2015-03-01
The current-voltage characteristics of solar cells is obtained using quantum master equations for electrons, holes, and excitons, in which generation, recombination, and transport processes are taken into account. As a first example, we simulate a photocell with a molecular aggregate donor to investigate whether a delocalized quantum state could enhance the efficiency. As a second example, we calculate the current-voltage characteristics of conventional p-n junction solar cells and perovskite solar cells using the master equation. The connection between the drift-diffusion model and the master equation method is established. The short-circuit current and the open-circuit voltage are calculated numerically as a function of the intensity of the sunlight and material properties such as energy gaps, diffusion constants, etc.
Panja, D.
2010-01-01
Any first course on polymer physics teaches that the dynamics of a tagged monomer of a polymer is anomalously subdiffusive, i.e., the mean-square displacement of a tagged monomer increases as tα for some α < 1 until the terminal relaxation time τ of the polymer. Beyond time τ the motion of the tagge
Number-conserving master equation theory for a dilute Bose-Einstein condensate
Schelle, Alexej; Delande, Dominique; Buchleitner, Andreas
2010-01-01
We describe the transition of $N$ weakly interacting atoms into a Bose-Einstein condensate within a number-conserving quantum master equation theory. Based on the separation of time scales for condensate formation and non-condensate thermalization, we derive a master equation for the condensate subsystem in the presence of the non-condensate environment under the inclusion of all two body interaction processes. We numerically monitor the condensate particle number distribution during condensate formation, and derive a condition under which the unique equilibrium steady state of a dilute, weakly interacting Bose-Einstein condensate is given by a Gibbs-Boltzmann thermal state of $N$ non-interacting atoms.
Zhou, Yanjun; Yin, Cangtao
2016-12-01
The Fokker-Planck equation (FPE) of the unimolecular reaction with Tsallis distribution is established by means of approximation to the master equation. The memory effect, taken into transition probability, is relevant and important for lots of anomalous phenomena. The Taylor expansion for large volume is applied to derive the power-law FPE. The steady-state solution of FPE and microscopic dynamics Ito-Langevin equation of concentration variables are therefore obtained and discussed. Two unimolecular reactions are taken as examples and the concentration distributions with different power-law parameters are analyzed, which may imply strong memory effect of hopping process.
Qubit Decoherence and Non-Markovian Dynamics at Low Temperatures via an Effective Spin-Boson Model
Shiokawa, K
2004-01-01
Quantum Brownian oscillator model (QBM), in the Fock-space representation, can be viewed as a multi-level spin-boson model. At sufficiently low temperature, the oscillator degrees of freedom are dynamically reduced to the lowest two levels and the system behaves effectively as a two-level (E2L) spin-boson model (SBM) in this limit. We discuss the physical mechanism of level reduction and analyze the behavior of E2L-SBM from the QBM solutions. The availability of close solutions for the QBM enables us to study the non-Markovian features of decoherence and leakage in a SBM in the non-perturbative regime (e.g. without invoking the Born approximation) in better details than before. Our result captures very well the characteristic non-Markovian short time low temperature behavior common in many models.
Salimi, S.; Haseli, S.; Khorashad, A. S.; Adabi, F.
2016-09-01
The interaction between system and environment is a fundamental concept in the theory of open quantum systems. As a result of the interaction, an amount of correlation (both classical and quantum) emerges between the system and the environment. In this work, we recall the quantity that will be very useful to describe the emergence of the correlation between the system and the environment, namely, the total entropy production. Appearance of total entropy production is due to the entanglement production between the system and the environment. In this work, we discuss about the role of the total entropy production for detecting the non-Markovianity. By utilizing the relation between the total entropy production and total correlation between subsystems, one can see a temporary decrease of total entropy production is a signature of non-Markovianity. We apply our criterion for the special case, where the composite system has initial correlation with environment.
Quantum Master Equation and Filter for Systems Driven by Fields in a Single Photon State
Gough, J E; Nurdin, H I
2011-01-01
The aim of this paper is to determine quantum master and filter equations for systems coupled to continuous-mode single photon fields. The system and field are described using a quantum stochastic unitary model, where the continuous-mode single photon state for the field is determined by a wavepacket pulse shape. The master equation is derived from this model and is given in terms of a system of coupled equations. The output field carries information about the system from the scattered photon, and is continuously monitored. The quantum filter is determined with the aid of an embedding of the system into a larger system, and is given by a system of coupled stochastic differential equations. An example is provided to illustrate the main results.
Firing statistics of inhibitory neuron with delayed feedback. II: Non-Markovian behavior.
Kravchuk, K G; Vidybida, A K
2013-06-01
The instantaneous state of a neural network consists of both the degree of excitation of each neuron the network is composed of and positions of impulses in communication lines between the neurons. In neurophysiological experiments, the neuronal firing moments are registered, but not the state of communication lines. But future spiking moments depend essentially on the past positions of impulses in the lines. This suggests, that the sequence of intervals between firing moments (inter-spike intervals, ISIs) in the network could be non-Markovian. In this paper, we address this question for a simplest possible neural "net", namely, a single inhibitory neuron with delayed feedback. The neuron receives excitatory input from the driving Poisson stream and inhibitory impulses from its own output through the feedback line. We obtain analytic expressions for conditional probability density P(tn+1|tn, …, t1, t0), which gives the probability to get an output ISI of duration tn+1 provided the previous (n+1) output ISIs had durations tn, …, t1, t0. It is proven exactly, that P(tn+1|tn, …, t1, t0) does not reduce to P(tn+1|tn, …, t1) for any n≥0. This means that the output ISIs stream cannot be represented as a Markov chain of any finite order.
Extracting work from a single reservoir in the non-Markovian underdamped regime.
Paredes-Altuve, Oscar; Medina, Ernesto; Colmenares, Pedro J
2016-12-01
We derive optimal-work finite time protocols for a colloidal particle in a harmonic well in the general non-Markovian underdamped regime in contact with a single reservoir. Optimal-work protocols with and without measurements of position and velocity are shown to be linear in time. In order to treat the underdamped regime one must address forcing the particle at the start and at the end of a protocol, conditions which dominate the short time behavior of the colloidal particle. We find that for protocols without measurement the least work by an external agent decreases linearly for forced start-stop conditions while those only forced at starting conditions are quadratic (slower) at short times, while both decrease asymptotically to zero for quasistatic processes. When measurements are performed, protocols with start-end forcing are still more efficient at short times but can be overtaken by start-only protocols at a threshold time. Measurement protocols derive work from the reservoir but always below that predicted by Sagawa's generalization of the second law. Velocity measurement protocols are more efficient in deriving work than position measurements.
Non-Markovian property of afterpulsing effect in single-photon avalanche detector
Wang, Fang-Xiang; Li, Ya-Ping; He, De-Yong; Wang, Chao; Han, Yun-Guang; Wang, Shuang; Yin, Zhen-Qiang; Han, Zheng-Fu
2016-01-01
The single-photon avalanche photodiode(SPAD) has been widely used in research on quantum optics. The afterpulsing effect, which is an intrinsic character of SPAD, affects the system performance in most experiments and needs to be carefully handled. For a long time, afterpulsing has been presumed to be determined by the pre-ignition avalanche. We studied the afterpulsing effect of a commercial InGaAs/InP SPAD (The avalanche photodiode model is: Princeton Lightwave PGA-300) and demonstrated that its afterpulsing is non-Markovian, with a memory effect in the avalanching history. Theoretical analysis and experimental results clearly indicate that the embodiment of this memory effect is the afterpulsing probability, which increases as the number of ignition-avalanche pulses increase. This conclusion makes the principle of the afterpulsing effect clearer and is instructive to the manufacturing processes and afterpulsing evaluation of high-count-rate SPADs. It can also be regarded as a fundamental premise to handle ...
Fuchsia and master integrals for splitting functions from differential equations in QCD
Gituliar, O
2016-01-01
We report on the recent progress in reducing differential equations for Feynman master integrals to canonical form with the help of a method proposed by Roman Lee. For the first time, we present Fuchsia --- our open-source implementation of the Lee algorithm written in Python using mathematical routines of a free computer algebra system SageMath. We demonstrate Fuchsia by reducing differential equations for NLO contributions to splitting functions in QCD, which contain both loops and legs integrals.
Quantum transport in 1d systems via a master equation approach: numerics and an exact solution
Znidaric, Marko
2010-01-01
We discuss recent findings about properties of quantum nonequilibrium steady states. In particular we focus on transport properties. It is shown that the time dependent density matrix renormalization method can be used successfully to find a stationary solution of Lindblad master equation. Furthermore, for a specific model an exact solution is presented.
Critical Dynamics : The Expansion of the Master Equation Including a Critical Point
Dekker, H.
1980-01-01
In this thesis it is shown how to solve the master equation for a Markov process including a critical point by means of successive approximations in terms of a small parameter. A critical point occurs if, by adjusting an externally controlled quantity, the system shows a transition from normal monos
Non-Markovian coarse-grained modeling of polymeric fluids based on the Mori-Zwanzig formalism
Li, Zhen; Bian, Xin; Li, Xiantao; Karniadakis, George
The Mori-Zwanzig formalism for coarse-graining a complex dynamical system typically introduces memory effects. The Markovian assumption of delta-correlated fluctuating forces is often employed to simplify the formulation of coarse-grained (CG) models and numerical implementations. However, when the time scales of a system are not clearly separated, the memory effects become strong and the Markovian assumption becomes inaccurate. To this end, we incorporate memory effects into CG modeling by preserving non-Markovian interactions between CG variables based on the Mori-Zwanzig formalism. For a specific example, molecular dynamics (MD) simulations of star polymer melts are performed while the corresponding CG system is defined by grouping many bonded atoms into single clusters. Then, the effective interactions between CG clusters as well as the memory kernel are obtained from the MD simulations. The constructed CG force field with a memory kernel leads to a non-Markovian dissipative particle dynamics (NM-DPD). Quantitative comparisons on both static and dynamic properties between the CG models with Markovian and non-Markovian approximations will be presented. Supported by the DOE Center on Mathematics for Mesoscopic Modeling of Materials (CM4) and an INCITE grant.
Chou, Chung-Hsien; Yu, Ting; Hu, B L
2008-01-01
In this paper we derive an exact master equation for two coupled quantum harmonic oscillators interacting via bilinear coupling with a common environment at arbitrary temperature made up of many harmonic oscillators with a general spectral density function. We first show a simple derivation based on the observation that the two harmonic oscillator model can be effectively mapped into that of a single harmonic oscillator in a general environment plus a free harmonic oscillator. Since the exact one harmonic oscillator master equation is available [B. L. Hu, J. P. Paz, and Y. Zhang, Phys. Rev. D 45, 2843 (1992)], the exact master equation with all its coefficients for this two harmonic oscillator model can be easily deduced from the known results of the single harmonic oscillator case. In the second part we give an influence functional treatment of this model and provide explicit expressions for the evolutionary operator of the reduced density matrix which are useful for the study of decoherence and disentanglement issues. We show three applications of this master equation: on the decoherence and disentanglement of two harmonic oscillators due to their interaction with a common environment under Markovian approximation, and a derivation of the uncertainty principle at finite temperature for a composite object, modeled by two interacting harmonic oscillators. The exact master equation for two, and its generalization to N, harmonic oscillators interacting with a general environment are expected to be useful for the analysis of quantum coherence, entanglement, fluctuations, and dissipation of mesoscopic objects toward the construction of a theoretical framework for macroscopic quantum phenomena.
Energy Technology Data Exchange (ETDEWEB)
Roura, Albert [Los Alamos National Laboratory; Fleming, C H [UNIV OF MARYLAND; Hu, B L [UNIV OF MARYLAND
2008-01-01
We revisit the model of a system made up of a Brownian quantum oscillator linearly coupled to an environment made up of many quantum oscillators at finite temperature. We show that the HPZ master equation for the reduced density matrix derived earlier [B.L. Hu, J.P. Paz, Y. Zhang, Phys. Rev. D 45, 2843 (1992)] has incorrectly specified coefficients for the case of nonlocal dissipation. We rederive the QBM master equation, correctly specifying all coefficients, and determine the position uncertainty to be free of excessive cutoff sensitivity. Our coefficients and solutions are reduced entirely to contour integration for analytic spectra at arbitrary temperature, coupling strength, and cut-off. As an illustration we calculate the master equation coefficients and solve the master equation for ohmic coupling (with finite cutoff) and example supra-ohmic and sub-ohmic spectral densities. We determine the effect of an external force on the quantum oscillator and also show that our representation of the master equation and solutions naturally extends to a system of multiple oscillators bilinearly coupled to themselves and the bath in arbitrary fashion. This produces a formula for investigating the standard quantum limit which is central to addressing many theoretical issues in macroscopic quantum phenomena and experimental concerns related to low temperature precision measurements. We find that in a dissipative environment, all initial states settle down to a Gaussian density matrix whose covariance is determined by the thermal reservoir and whose mean is determined by the external force. We specify the thermal covariance for the spectral densities we explore.
On the non-linearity of the master equation describing spin-selective radical-ion-pair reactions
Kominis, I. K.
2010-01-01
We elaborate on the physical meaning of the non-linear master equation that was recently derived to account for spin-selective radical-ion-pair reactions. Based on quite general arguments, we show that such a non-linear master equation is indeed to be expected.
Institute of Scientific and Technical Information of China (English)
游波; 岑理相
2015-01-01
Understanding the non-Markovian dynamics of dissipative processes induced by memory effects of the environment is a fundamental subject of open quantum systems. Because of the complexity of open quantum systems, e.g., the multiple energy scales involving that of the system, the environment, and their mutual coupling, it is generally a challenging task to characterize the relationship among the parameters of the system dynamics and the reservoir spectra. For the two-level spontaneous emission model within structured environments, it was shown in a recent literature (Opt. Lett. 38, 3650) that a functional relation could be established between the asymptotically non-decaying population and the spectral density of the reservoir as the system undergoes a long-time evolution. It hence renders a distinct perspective to look into the character of long-lived quantum coherence in the corresponding non-Markovian process. This article is devoted to further investigate the phenomena of limit cycle oscillations possibly occurring in such non-Markovian dissipative systems in a long-time evolution. For a two-level system subjected to an environment with Ohmic class spectra, due to the presence of a unique bound-state mode of the system, the evolution trajectory of the given initial states will converge to a limit cycle in the Bloch space. The dependence of the radius and the location of the limit cycle on the spectral density function of the reservoir are manifested by virtue of the described functional relation. For the model subjected to a photonic crystal environment with multiple bands, our studies reveal that, owing to the presence of two or more bound states, the evolution trajectory of the system will converge to a toric curve of a paraboloid in the Bloch space and the phenomena of periodic or quasi-periodic oscillations could exhibit. While the equation of the parabolic curve is fully determined by the initial values of the state vector in the Bloch space, our results
Operator Approach to the Master Equation for the One-Step Process
Hnatič, M.; Eferina, E. G.; Korolkova, A. V.; Kulyabov, D. S.; Sevastyanov, L. A.
2016-02-01
Background. Presentation of the probability as an intrinsic property of the nature leads researchers to switch from deterministic to stochastic description of the phenomena. The kinetics of the interaction has recently attracted attention because it often occurs in the physical, chemical, technical, biological, environmental, economic, and sociological systems. However, there are no general methods for the direct study of this equation. The expansion of the equation in a formal Taylor series (the so called Kramers-Moyal's expansion) is used in the procedure of stochastization of one-step processes. Purpose. However, this does not eliminate the need for the study of the master equation. Method. It is proposed to use quantum field perturbation theory for the statistical systems (the so-called Doi method). Results: This work is a methodological material that describes the principles of master equation solution based on quantum field perturbation theory methods. The characteristic property of the work is that it is intelligible for non-specialists in quantum field theory. Conclusions: We show the full equivalence of the operator and combinatorial methods of obtaining and study of the one-step process master equation.
On the master equation approach to diffusive grain-surface chemistry: the H, O, CO system
Stantcheva, T; Herbst, E
2002-01-01
We have used the master equation approach to study a moderately complex network of diffusive reactions occurring on the surfaces of interstellar dust particles. This network is meant to apply to dense clouds in which a large portion of the gas-phase carbon has already been converted to carbon monoxide. Hydrogen atoms, oxygen atoms, and CO molecules are allowed to accrete onto dust particles and their chemistry is followed. The stable molecules produced are oxygen, hydrogen, water, carbon dioxide (CO2), formaldehyde (H2CO), and methanol (CH3OH). The surface abundances calculated via the master equation approach are in good agreement with those obtained via a Monte Carlo method but can differ considerably from those obtained with standard rate equations.
Approximate-master-equation approach for the Kinouchi-Copelli neural model on networks
Wang, Chong-Yang; Wu, Zhi-Xi; Chen, Michael Z. Q.
2017-01-01
In this work, we use the approximate-master-equation approach to study the dynamics of the Kinouchi-Copelli neural model on various networks. By categorizing each neuron in terms of its state and also the states of its neighbors, we are able to uncover how the coupled system evolves with respective to time by directly solving a set of ordinary differential equations. In particular, we can easily calculate the statistical properties of the time evolution of the network instantaneous response, the network response curve, the dynamic range, and the critical point in the framework of the approximate-master-equation approach. The possible usage of the proposed theoretical approach to other spreading phenomena is briefly discussed.
Non-Markovian reduced dynamics based upon a hierarchical effective-mode representation
Energy Technology Data Exchange (ETDEWEB)
Burghardt, Irene [Institute of Physical and Theoretical Chemistry, Goethe University Frankfurt, Max-von-Laue-Str. 7, 60438 Frankfurt (Germany); Martinazzo, Rocco [Dipartimento di Chimica, Universita degli Studi di Milano, v. Golgi 19, 20133 Milano (Italy); Hughes, Keith H. [School of Chemistry, Bangor University, Bangor, Gwynedd LL57 2UW (United Kingdom)
2012-10-14
A reduced dynamics representation is introduced which is tailored to a hierarchical, Mori-chain type representation of a bath of harmonic oscillators which are linearly coupled to a subsystem. We consider a spin-boson system where a single effective mode is constructed so as to absorb all system-environment interactions, while the residual bath modes are coupled bilinearly to the primary mode and among each other. Using a cumulant expansion of the memory kernel, correlation functions for the primary mode are obtained, which can be suitably approximated by truncated chains representing the primary-residual mode interactions. A series of reduced-dimensional bath correlation functions is thus obtained, which can be expressed as Fourier-Laplace transforms of spectral densities that are given in truncated continued-fraction form. For a master equation which is second order in the system-bath coupling, the memory kernel is re-expressed in terms of local-in-time equations involving auxiliary densities and auxiliary operators.
A Master Equation for Gravitational Decoherence: Probing the Textures of Spacetime
Anastopoulos, C
2013-01-01
We give a first principles derivation of a master equation for the evolution of a quantum matter field in a linearly perturbed Minkowski spacetime, based solely on quantum field theory and general relativity. We make no additional assumptions nor introduce extra ingredients, as is often done in alternative quantum theories. When the quantum matter field is projected to a one-particle state, the master equation for a non-relativistic quantum particle in a weak gravitational field predicts decoherence in the momentum basis, in contrast to most existing theories of gravitational decoherence. We point out the gauge nature of time and space reparameterizations in matter-gravity couplings, and warn that `intrinsic' decoherence or alternative quantum theories invoking stochastic dynamics arising from temporal or spatial fluctuations violate this fundamental symmetry of classical general relativity. Interestingly we find that the decoherence rate depends on extra parameters other than the Planck scale, an important f...
Energy Technology Data Exchange (ETDEWEB)
Gelß, Patrick, E-mail: p.gelss@fu-berlin.de; Matera, Sebastian, E-mail: matera@math.fu-berlin.de; Schütte, Christof, E-mail: schuette@mi.fu-berlin.de
2016-06-01
In multiscale modeling of heterogeneous catalytic processes, one crucial point is the solution of a Markovian master equation describing the stochastic reaction kinetics. Usually, this is too high-dimensional to be solved with standard numerical techniques and one has to rely on sampling approaches based on the kinetic Monte Carlo method. In this study we break the curse of dimensionality for the direct solution of the Markovian master equation by exploiting the Tensor Train Format for this purpose. The performance of the approach is demonstrated on a first principles based, reduced model for the CO oxidation on the RuO{sub 2}(110) surface. We investigate the complexity for increasing system size and for various reaction conditions. The advantage over the stochastic simulation approach is illustrated by a problem with increased stiffness.
Effects of system-bath coupling on Photosynthetic heat engine: A polaron master equation approach
Qin, M; Zhao, X L; Yi, X X
2016-01-01
In this paper, we apply the polaron master equation, which offers the possibilities to interpolate between weak and strong system-bath coupling, to study how system-bath couplings affect charge transfer processes in Photosystem II reaction center (PSII RC) inspired quantum heat engine (QHE) model in a wide parameter range. The effects of bath correlation and temperature, together with the combined effects of these factors are also discussed in details. The results show a variety of dynamical behaviours. We interpret these results in terms of noise-assisted transport effect and dynamical localization which correspond to two mechanisms underpinning the transfer process in photosynthetic complexes: One is resonance energy transfer and the other is dynamical localization effect captured by the polaron master equation. The effects of system-bath coupling and bath correlation are incorporated in the effective system-bath coupling strength determining whether noise-assisted transport effect or dynamical localization...
Energy Technology Data Exchange (ETDEWEB)
Kurt, Arzu; Eryigit, Resul, E-mail: resul@ibu.edu.tr
2015-12-18
The master equation for a charged harmonic oscillator coupled to an electromagnetic reservoir is investigated up to fourth order in the interaction strength by using Krylov averaging method. The interaction is in the velocity-coupling form and includes a diamagnetic term. Exact analytical expressions for the second-, the third-, and the fourth-order contributions to mass renormalization, decay constant, normal and anomalous diffusion coefficients are obtained for the blackbody type environment. It is found that, generally, the third- and the fourth-order contributions have opposite signs when their magnitudes are comparable to that of the second-order one. - Highlights: • Exact analytical expressions for up to the fourth-order master equation are obtained. • High and low temperature limits of anomalous diffusion coefficients are elucidated. • Convergence range of the oscillator and the bath parameters discussed.
Energy Technology Data Exchange (ETDEWEB)
Jin, Jinshuang, E-mail: jsjin@hznu.edu.cn [Department of Physics, Hangzhou Normal University, Hangzhou 310036 (China); Li, Jun [Department of Physics, Hangzhou Normal University, Hangzhou 310036 (China); College of Physics and Electronic Engineering, Dezhou University, Dezhou 253023 (China); Liu, Yu [State Key Laboratory for Superlattices and Microstructures, Institute of Semiconductors, Chinese Academy of Sciences, Beijing 100083 (China); Li, Xin-Qi, E-mail: lixinqi@bnu.edu.cn [State Key Laboratory for Superlattices and Microstructures, Institute of Semiconductors, Chinese Academy of Sciences, Beijing 100083 (China); Department of Physics, Beijing Normal University, Beijing 100875 (China); Department of Chemistry, Hong Kong University of Science and Technology, Kowloon (Hong Kong); Yan, YiJing, E-mail: yyan@ust.hk [Department of Chemistry, Hong Kong University of Science and Technology, Kowloon (Hong Kong); Hefei National Laboratory for Physical Sciences at the Microscale, University of Science and Technology of China, Hefei, Anhui 230026 (China)
2014-06-28
Beyond the second-order Born approximation, we propose an improved master equation approach to quantum transport under self-consistent Born approximation. The basic idea is to replace the free Green's function in the tunneling self-energy diagram by an effective reduced propagator under the Born approximation. This simple modification has remarkable consequences. It not only recovers the exact results for quantum transport through noninteracting systems under arbitrary voltages, but also predicts the challenging nonequilibrium Kondo effect. Compared to the nonequilibrium Green's function technique that formulates the calculation of specific correlation functions, the master equation approach contains richer dynamical information to allow more efficient studies for such as the shot noise and full counting statistics.
Jin, Jinshuang; Li, Jun; Liu, Yu; Li, Xin-Qi; Yan, YiJing
2014-06-28
Beyond the second-order Born approximation, we propose an improved master equation approach to quantum transport under self-consistent Born approximation. The basic idea is to replace the free Green's function in the tunneling self-energy diagram by an effective reduced propagator under the Born approximation. This simple modification has remarkable consequences. It not only recovers the exact results for quantum transport through noninteracting systems under arbitrary voltages, but also predicts the challenging nonequilibrium Kondo effect. Compared to the nonequilibrium Green's function technique that formulates the calculation of specific correlation functions, the master equation approach contains richer dynamical information to allow more efficient studies for such as the shot noise and full counting statistics.
A Master Equation Approach to Modeling Short-term Behaviors of the Stock Market
Zhao, Conan; Yang, Xiaoxiang; Mazilu, Irina
2015-03-01
Short term fluctuations in stock prices are highly random, due to the multitude of external factors acting on the price determination process. While long-term economic factors such as inflation and revenue growth rate affect short-term price fluctuation, it is difficult to obtain the complete set of information and uncertainties associated with a given period of time. Instead, we propose a simpler short-term model based on only prior price averages and extrema. In this paper, we take a master equation under the random walk hypothesis and fit parameters based on AAPL stock price data over the past ten years. We report results for small system sizes and for the short term average price. These results may lead to a general closed-form solution to this particular master equation.
Schinabeck, C.; Erpenbeck, A.; Härtle, R.; Thoss, M.
2016-11-01
Within the hierarchical quantum master equation (HQME) framework, an approach is presented, which allows a numerically exact description of nonequilibrium charge transport in nanosystems with strong electronic-vibrational coupling. The method is applied to a generic model of vibrationally coupled transport considering a broad spectrum of parameters ranging from the nonadiabatic to the adiabatic regime and including both resonant and off-resonant transport. We show that nonequilibrium effects are important in all these regimes. In particular, in the off-resonant transport regime, the inelastic cotunneling signal is analyzed for a vibrational mode in full nonequilibrium, revealing a complex interplay of different transport processes and deviations from the commonly used G0/2 rule of thumb. In addition, the HQME approach is used to benchmark approximate master equation and nonequilibrium Green's function methods.
Lane, Thomas J.; Pande, Vijay S.
2012-12-01
Motivated by the observed time scales in protein systems said to fold "downhill," we have studied the finite, linear master equation, with uniform rates forward and backward as a model of the downhill process. By solving for the system eigenvalues, we prove the claim that in situations where there is no free energy barrier a transition between single- and multi-exponential kinetics occurs at sufficient bias (towards the native state). Consequences for protein folding, especially the downhill folding scenario, are briefly discussed.
Tscherbul, Timur V; Brumer, Paul
2015-03-14
We present an efficient theoretical method for calculating the time evolution of the density matrix of a multilevel quantum system weakly interacting with incoherent light. The method combines the Bloch-Redfield theory with a partial secular approximation for one-photon coherences, resulting in a master equation that explicitly exposes the reliance on transition rates and the angles between transition dipole moments in the energy basis. The partial secular Bloch-Redfield master equation allows an unambiguous distinction between the regimes of quantum coherent vs. incoherent energy transfer under incoherent light illumination. The fully incoherent regime is characterized by orthogonal transition dipole moments in the energy basis, leading to a dynamical evolution governed by a coherence-free Pauli-type master equation. The coherent regime requires non-orthogonal transition dipole moments in the energy basis and leads to the generation of noise-induced quantum coherences and population-to-coherence couplings. As a first application, we consider the dynamics of excited state coherences arising under incoherent light excitation from a single ground state and observe population-to-coherence transfer and the formation of non-equilibrium quasisteady states in the regime of small excited state splitting. Analytical expressions derived earlier for the V-type system [T. V. Tscherbul and P. Brumer, Phys. Rev. Lett. 113, 113601 (2014)] are found to provide a nearly quantitative description of multilevel excited-state populations and coherences in both the small- and large-molecule limits.
Ikeda, Tatsushi; Tanimura, Yoshitaka
2015-01-01
We explore and describe the roles of inter-molecular vibrations in terms of a Brownian oscillator (BO) model with linear-linear (LL) and square-linear (SL) system-bath interactions, which we use to analyze two-dimensional (2D) THz-Raman spectra obtained by means of molecular dynamics (MD) simulations. In addition to linear absorption (1D IR), we calculate 2D Raman-THz-THz, THz-Raman-THz, and THz-THz-Raman signals for liquid formamide, water, and methanol using an equilibrium non-equilibrium hybrid MD simulation. The calculated 1D IR and 2D THz-Raman signals are then accounted by the LL+SL BO model with the use of the hierarchal Fokker-Planck equations for a non-perturbative and non-Markovian noise. All of the characteristic 2D profiles of the simulated signals are reproduced using the LL+SL BO model, indicating that the present model captures the essential features of the inter-molecular motion. We analyze the fitted the 2D profiles in terms of anharmonicity, nonlinear polarizability, and dephasing time. The ...
Energy Technology Data Exchange (ETDEWEB)
Rossi, Matteo A. C., E-mail: matteo.rossi@unimi.it [Quantum Technology Lab, Dipartimento di Fisica, Università degli Studi di Milano, 20133 Milano (Italy); Paris, Matteo G. A., E-mail: matteo.paris@fisica.unimi.it [Quantum Technology Lab, Dipartimento di Fisica, Università degli Studi di Milano, 20133 Milano (Italy); CNISM, Unità Milano Statale, I-20133 Milano (Italy)
2016-01-14
We address the interaction of single- and two-qubit systems with an external transverse fluctuating field and analyze in detail the dynamical decoherence induced by Gaussian noise and random telegraph noise (RTN). Upon exploiting the exact RTN solution of the time-dependent von Neumann equation, we analyze in detail the behavior of quantum correlations and prove the non-Markovianity of the dynamical map in the full parameter range, i.e., for either fast or slow noise. The dynamics induced by Gaussian noise is studied numerically and compared to the RTN solution, showing the existence of (state dependent) regions of the parameter space where the two noises lead to very similar dynamics. We show that the effects of RTN noise and of Gaussian noise are different, i.e., the spectrum alone is not enough to summarize the noise effects, but the dynamics under the effect of one kind of noise may be simulated with high fidelity by the other one.
Non-Markovian Persistence at the PC point of a 1d non-equilibrium kinetic Ising model
Menyhard, N; Menyhard, Nora; Odor, Geza
1997-01-01
One-dimensional non-equilibrium kinetic Ising models evolving under the competing effect of spin flips at zero temperature and nearest neighbour spin exchanges exhibiting a parity-conserving (PC) phase transition on the level of kinks are investigated here numerically from the point of view of the underlying spin system. The dynamical persistency exponent $\\Theta$ and the exponent $lambda$ characterising the two-time autocorrelation function of the total magnetization under non-equilibrium conditions are reported. It is found that the PC transition has strong effect: the process becomes non-Markovian and the above exponents exhibit drastic changes as compared to the Glauber-Ising case.
Martínez-Morales, José L.
The master equations in the Euclidean Schwarzschild-Tangherlini space-time of a small static perturbation are studied. For each harmonic mode on the sphere there are two solutions that behave differently at infinity. One solution goes like the power 2-l-n of the radial variable, the other solution goes like the power l. These solutions occur in power series. The second main statement of the paper is that any eigentensor of the Lichnerowicz operator in a Euclidean Schwarzschild space-time with an eigenvalue different from zero is essentially singular at infinity. Possible applications of the stability of instantons are discussed. We present the analysis of a small static perturbation of the Euclidean Schwarzschild-Tangherlini metric tensor. The higher order perturbations will appear later. We determine independently the static perturbations of the Schwarzschild quantum black hole in dimension 1+n≥4, where the system of equations is reduced to master equations — ordinary differential equations. The solutions are hypergeometric functions which in some cases can be reduced to polynomials. In the same Schwarzschild background, we analyze static perturbations of the scalar mode and show that there does not exist any static perturbation that is regular everywhere outside the event horizon and is well-behaved at the spatial infinity. This confirms the uniqueness of the spherically symmetric static empty quantum black hole, within the perturbation framework. Our strategy for treating the stability problem is also applicable to other symmetric quantum black holes with a nonzero cosmological constant.
Vaccaro, S R
2016-01-01
The Na+ current in nerve and muscle membranes may be described in terms of the activation variable m(t) and the inactivation variable h(t), which are dependent on the transitions of S4 sensors in each of the ion channel domains DI to DIV. The time-dependence of the Na+ current and the rate equations satisfied by m(t) and h(t) may be derived from the solution to a master equation which describes the coupling between two activation sensors regulating the Na+ channel conductance and a two stage inactivation process. The voltage dependence of the rate functions for inactivation and recovery from inactivation are consistent with the empirically determined Hodgkin-Huxley expressions, and exhibit saturation for both depolarized and hyperpolarized clamp potentials.
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.
The Master Equation for Two-Level Accelerated Systems at Finite Temperature
Tomazelli, J. L.; Cunha, R. O.
2016-10-01
In this work, we study the behaviour of two weakly coupled quantum systems, described by a separable density operator; one of them is a single oscillator, representing a microscopic system, while the other is a set of oscillators which perform the role of a reservoir in thermal equilibrium. From the Liouville-Von Neumann equation for the reduced density operator, we devise the master equation that governs the evolution of the microscopic system, incorporating the effects of temperature via Thermofield Dynamics formalism by suitably redefining the vacuum of the macroscopic system. As applications, we initially investigate the behaviour of a Fermi oscillator in the presence of a heat bath consisting of a set of Fermi oscillators and that of an atomic two-level system interacting with a scalar radiation field, considered as a reservoir, by constructing the corresponding master equation which governs the time evolution of both sub-systems at finite temperature. Finally, we calculate the energy variation rates for the atom and the field, as well as the atomic population levels, both in the inertial case and at constant proper acceleration, considering the two-level system as a prototype of an Unruh detector, for admissible couplings of the radiation field.
Proton-pumping mechanism of cytochrome c oxidase: A kinetic master-equation approach
Kim, Young C.; Hummer, Gerhard
2011-01-01
Cytochrome c oxidase (CcO) is an efficient energy transducer that reduces oxygen to water and converts the released chemical energy into an electrochemical membrane potential. As a true proton pump, CcO translocates protons across the membrane against this potential. Based on a wealth of experiments and calculations, an increasingly detailed picture of the reaction intermediates in the redox cycle has emerged. However, the fundamental mechanism of proton pumping coupled to redox chemistry remains largely unresolved. Here we examine and extend a kinetic master-equation approach to gain insight into redox-coupled proton pumping in CcO. Basic principles of the CcO proton pump emerge from an analysis of the simplest kinetic models that retain essential elements of the experimentally determined structure, energetics, and kinetics, and that satisfy fundamental physical principles. The master-equation models allow us to address the question of how pumping can be achieved in a system in which all reaction steps are reversible. Whereas proton pumping does not require the direct modulation of microscopic reaction barriers, such kinetic gating greatly increases the pumping efficiency. Further efficiency gains can be achieved by partially decoupling the proton uptake pathway from the ative-site region. Such a mechanism is consistent with the proposed Glu valve, in which the side chain of a key glutamic acid shuttles between the D channel and the active-site region. We also show that the models predict only small proton leaks even in the absence of turnover. The design principles identified here for CcO provide a blueprint for novel biology-inspired fuel cells, and the master-equation formulation should prove useful also for other molecular machines. PMID:21946020
Proton-pumping mechanism of cytochrome c oxidase: a kinetic master-equation approach.
Kim, Young C; Hummer, Gerhard
2012-04-01
Cytochrome c oxidase is an efficient energy transducer that reduces oxygen to water and converts the released chemical energy into an electrochemical membrane potential. As a true proton pump, cytochrome c oxidase translocates protons across the membrane against this potential. Based on a wealth of experiments and calculations, an increasingly detailed picture of the reaction intermediates in the redox cycle has emerged. However, the fundamental mechanism of proton pumping coupled to redox chemistry remains largely unresolved. Here we examine and extend a kinetic master-equation approach to gain insight into redox-coupled proton pumping in cytochrome c oxidase. Basic principles of the cytochrome c oxidase proton pump emerge from an analysis of the simplest kinetic models that retain essential elements of the experimentally determined structure, energetics, and kinetics, and that satisfy fundamental physical principles. The master-equation models allow us to address the question of how pumping can be achieved in a system in which all reaction steps are reversible. Whereas proton pumping does not require the direct modulation of microscopic reaction barriers, such kinetic gating greatly increases the pumping efficiency. Further efficiency gains can be achieved by partially decoupling the proton uptake pathway from the active-site region. Such a mechanism is consistent with the proposed Glu valve, in which the side chain of a key glutamic acid shuttles between the D channel and the active-site region. We also show that the models predict only small proton leaks even in the absence of turnover. The design principles identified here for cytochrome c oxidase provide a blueprint for novel biology-inspired fuel cells, and the master-equation formulation should prove useful also for other molecular machines. .
Computational study of p53 regulation via the chemical master equation
Vo, Huy D.; Sidje, Roger B.
2016-06-01
A stochastic model of cellular p53 regulation was established in Leenders, and Tuszynski (2013 Front. Oncol. 3 1-16) to study the interactions of p53 with MDM2 proteins, where the stochastic analysis was done using a Monte Carlo approach. We revisit that model here using an alternative scheme, which is to directly solve the chemical master equation (CME) by an adaptive Krylov-based finite state projection method that combines the stochastic simulation algorithm with other computational strategies, namely Krylov approximation techniques to the matrix exponential, divide and conquer, and aggregation. We report numerical results that demonstrate the extend of tackling the CME with this combination of tools.
Kurt, Arzu; Eryigit, Resul
2015-12-01
The master equation for a charged harmonic oscillator coupled to an electromagnetic reservoir is investigated up to fourth order in the interaction strength by using Krylov averaging method. The interaction is in the velocity-coupling form and includes a diamagnetic term. Exact analytical expressions for the second-, the third-, and the fourth-order contributions to mass renormalization, decay constant, normal and anomalous diffusion coefficients are obtained for the blackbody type environment. It is found that, generally, the third- and the fourth-order contributions have opposite signs when their magnitudes are comparable to that of the second-order one.
Lane, Thomas
2012-01-01
Motivated by claims about the nature of the observed timescales in protein systems said to fold downhill, we have studied the finite, linear master equation which is a model of the downhill process. By solving for the system eigenvalues, we prove the often stated claim that in situations where there is no free energy barrier, a transition between single and multi-exponential kinetics occurs at sufficient bias (towards the native state). Consequences for protein folding, especially the downhill folding scenario, are briefly discussed.
Iemini, Fernando; da Silva Souza, Leonardo; Debarba, Tiago; Cesário, André T.; Maciel, Thiago O.; Vianna, Reinaldo O.
2017-05-01
We obtain the analytical expression for the Kraus decomposition of the quantum map of an environment modeled by an arbitrary quadratic fermionic Hamiltonian acting on one or two qubits, and derive simple functions to check the non-positivity of the intermediate map. These functions correspond to two different sufficient criteria for non-Markovianity. In the particular case of an environment represented by the Ising Hamiltonian, we discuss the two sources of non-Markovianity in the model, one due to the finite size of the lattice, and another due to the kind of interactions.
Directory of Open Access Journals (Sweden)
Gianni Pagnini
2012-01-01
inhomogeneity and nonstationarity properties of the medium. For instance, when this superposition is applied to the time-fractional diffusion process, the resulting Master Equation emerges to be the governing equation of the Erdélyi-Kober fractional diffusion, that describes the evolution of the marginal distribution of the so-called generalized grey Brownian motion. This motion is a parametric class of stochastic processes that provides models for both fast and slow anomalous diffusion: it is made up of self-similar processes with stationary increments and depends on two real parameters. The class includes the fractional Brownian motion, the time-fractional diffusion stochastic processes, and the standard Brownian motion. In this framework, the M-Wright function (known also as Mainardi function emerges as a natural generalization of the Gaussian distribution, recovering the same key role of the Gaussian density for the standard and the fractional Brownian motion.
Master equation with quantized atomic motion including dipole-dipole interactions
Damanet, François; Braun, Daniel; Martin, John
2016-05-01
We derive a markovian master equation for the internal dynamics of an ensemble of two-level atoms including all effects related to the quantization of their motion. Our equation provides a unifying picture of the consequences of recoil and indistinguishability of atoms beyond the Lamb-Dicke regime on both their dissipative and conservative dynamics, and is relevant for experiments with ultracold trapped atoms. We give general expressions for the decay rates and the dipole-dipole shifts for any motional states, and we find analytical formulas for a number of relevant states (Gaussian states, Fock states and thermal states). In particular, we show that the dipole-dipole interactions and cooperative photon emission can be modulated through the external state of motion. The effects predicted should be experimentally observable with Rydberg atoms. FD would like to thank the F.R.S.-FNRS for financial support. FD is a FRIA Grant holder of the Fonds de la Recherche Scientifique-FNRS.
Alfonso, Lester; Zamora, Jose; Cruz, Pedro
2015-04-01
The stochastic approach to coagulation considers the coalescence process going in a system of a finite number of particles enclosed in a finite volume. Within this approach, the full description of the system can be obtained from the solution of the multivariate master equation, which models the evolution of the probability distribution of the state vector for the number of particles of a given mass. Unfortunately, due to its complexity, only limited results were obtained for certain type of kernels and monodisperse initial conditions. In this work, a novel numerical algorithm for the solution of the multivariate master equation for stochastic coalescence that works for any type of kernels and initial conditions is introduced. The performance of the method was checked by comparing the numerically calculated particle mass spectrum with analytical solutions obtained for the constant and sum kernels, with an excellent correspondence between the analytical and numerical solutions. In order to increase the speedup of the algorithm, software parallelization techniques with OpenMP standard were used, along with an implementation in order to take advantage of new accelerator technologies. Simulations results show an important speedup of the parallelized algorithms. This study was funded by a grant from Consejo Nacional de Ciencia y Tecnologia de Mexico SEP-CONACYT CB-131879. The authors also thanks LUFAC® Computacion SA de CV for CPU time and all the support provided.
Directory of Open Access Journals (Sweden)
V. Ilyin
2013-03-01
Full Text Available The unified description of diffusion processes that cross over from a ballistic behavior at short times to normal or anomalous diffusion (sub- or superdiffusion at longer times is constructed on the basis of a non-Markovian generalization of the Fokker-Planck equation. The necessary non- Markovian kinetic coefficients are determined by the observable quantities (mean- and mean square displacements. Solutions of the non-Markovian equation describing diffusive processes in the physical space are obtained. For long times these solutions agree with the predictions of continuous random walk theory; they are however much superior at shorter times when the effect of the ballistic behavior is crucial.
Lü, Zhiguo
2011-01-01
We investigate the dynamical information exchange between a two-state system and its environment which is measured by von Neumann entropy. It is found that in the underdamping regime, the entropy dynamics exhibits an extremely non-Markovian oscillation-hump feature, in which oscillations manifest quantum coherence and a hump of envelop demonstrates temporal memory of bath. It indicates that the process of entropy exchange is bidirectional. When the coupling strength increases a certain threshold, the hump along with ripple disappears, which is indicative of the coherent-incoherent dynamical crossover. The long-time limit of entropy evolution reaches the ground state value which agrees with that of numerical renormalization group.
da Silva, Roberto; Lamb, Luis; Prado, Sandra
2012-01-01
We propose a novel algorithm that outputs the final standings of a soccer league, based on a simple dynamics that mimics a soccer tournament. In our model, a team is created with a defined potential(ability) which is updated during the tournament according to the results of previous games. The updated potential modifies a teams' future winning/losing probabilities. We show that this evolutionary game is able to reproduce the statistical properties of final standings of actual editions of the Brazilian tournament (Brasileir\\~{a}o). However, other leagues such as the Italian and the Spanish tournaments have notoriously non-Gaussian traces and cannot be straightforwardly reproduced by this evolutionary non-Markovian model. A complete understanding of these phenomena deserves much more attention, but we suggest a simple explanation based on data collected in Brazil: Here several teams were crowned champion in previous editions corroborating that the champion typically emerges from random fluctuations that partly ...
DEFF Research Database (Denmark)
Nielsen, Per Kær; Nielsen, Torben Roland; Lodahl, Peter;
2010-01-01
We investigate the influence of electron-phonon interactions on the dynamical properties of a quantum-dot-cavity QED system. We show that non-Markovian effects in the phonon reservoir lead to strong changes in the dynamics, arising from photon-assisted dephasing processes, not present in Markovian...
Vaccaro, S. R.
2016-11-01
The Na+ current in nerve and muscle membranes may be described in terms of the activation variable m (t ) and the inactivation variable h (t ) , which are dependent on the transitions of S4 sensors of each of the Na+ channel domains DI to DIV. The time-dependence of the Na+ current and the rate equations satisfied by m (t ) and h (t ) may be derived from the solution to a master equation that describes the coupling between two or three activation sensors regulating the Na+ channel conductance and a two-stage inactivation process. If the inactivation rate from the closed or open states increases as the S4 sensors activate, a more general form of the Hodgkin-Huxley expression for the open-state probability may be derived where m (t ) is dependent on both activation and inactivation processes. The voltage dependence of the rate functions for inactivation and recovery from inactivation are consistent with the empirically determined expressions and exhibit saturation for both depolarized and hyperpolarized clamp potentials.
Vaccaro, S R
2016-11-01
The Na^{+} current in nerve and muscle membranes may be described in terms of the activation variable m(t) and the inactivation variable h(t), which are dependent on the transitions of S4 sensors of each of the Na^{+} channel domains DI to DIV. The time-dependence of the Na^{+} current and the rate equations satisfied by m(t) and h(t) may be derived from the solution to a master equation that describes the coupling between two or three activation sensors regulating the Na^{+} channel conductance and a two-stage inactivation process. If the inactivation rate from the closed or open states increases as the S4 sensors activate, a more general form of the Hodgkin-Huxley expression for the open-state probability may be derived where m(t) is dependent on both activation and inactivation processes. The voltage dependence of the rate functions for inactivation and recovery from inactivation are consistent with the empirically determined expressions and exhibit saturation for both depolarized and hyperpolarized clamp potentials.
Kuwata, Keith T.; Valin, Lukas C.
2008-01-01
Methacrolein is a major product of isoprene ozonolysis, and methacrolein oxide is an important ozonolysis intermediate. We use CBS-QB3 and RRKM/master equation calculations to characterize all methacrolein formation pathways and all the unimolecular reactions of methacrolein oxide. Our predicted methacrolein yield agrees with experiment if we assume that all of the dioxirane formed from methacrolein oxide decomposes to methacrolein. The vinyl group of methacrolein oxide allows the species to cyclize to a dioxole with a reaction barrier lower than the barriers to either hydroperoxide or dioxirane formation. Two dioxole derivatives, 1,2-epoxy-2-methyl-3-propanal and 2-methyl-3-oxopropanal, should be measurable products of isoprene ozonolysis.
Generalized Quantum Master Equations In and Out of Equilibrium: When Can One Win?
Kelly, Aaron; Wang, Lu; Markland, Thomas E
2016-01-01
Generalized quantum master equations (GQMEs) are an important tool in modeling chemical and physical processes. The central quantity in these approaches is the memory kernel, which encodes the effect of the projected dynamical degrees of freedom on the observable of interest. For a large number of problems it has been shown that exact and approximate methods can be made dramatically more efficient, and in the latter case more accurate, by proceeding via the GQME formalism. However, there are many situations where utilizing the GQME approach seems to offer no advantage over a direct evaluation of the property of interest. The development of a more detailed understanding of the conditions under which these methods will offer benefits would thus greatly enhance their utility. Here, we derive exact expressions for the memory kernel obtained from projection operators for systems both in and out of equilibrium, and show the conditions under which these expressions will be guaranteed to return an identical result to...
Critical assessment of two-qubit post-Markovian master equations
Campbell, S; Mazzola, L; Gullo, N Lo; Vacchini, B; Busch, Th; Paternostro, M
2012-01-01
A post-Markovian master equation has been recently proposed as a tool to describe the evolution of a system coupled to a memory-keeping environment [A. Shabani and D. A. Lidar, Phys. Rev. A 71, 020101 (R) (2005)]. For a single qubit affected by appropriately chosen environmental conditions, the corresponding dynamics is always legitimate and physical. Here we extend such situation to the case of two qubits, only one of which experiences the environmental effects. We show how, despite the innocence of such an extension, the introduction of the second qubit should be done cum grano salis to avoid consequences such as the breaking of the positivity of the associated dynamical map. This hints at the necessity of using care when adopting phenomenologically derived models for evolutions occurring outside the Markovian framework.
Quantum dot as a spin-current diode: A master-equation approach
DEFF Research Database (Denmark)
Souza, F.M.; Egues, J.C.; Jauho, Antti-Pekka
2007-01-01
We report a study of spin-dependent transport in a system composed of a quantum dot coupled to a normal metal lead and a ferromagnetic lead NM-QD-FM. We use the master equation approach to calculate the spin-resolved currents in the presence of an external bias and an intradot Coulomb interaction....... We find that for a range of positive external biases current flow from the normal metal to the ferromagnet the current polarization =I↑−I↓ / I↑+I↓ is suppressed to zero, while for the corresponding negative biases current flow from the ferromagnet to the normal metal attains a relative maximum value....... The system thus operates as a rectifier for spin-current polarization. This effect follows from an interplay between Coulomb interaction and nonequilibrium spin accumulation in the dot. In the parameter range considered, we also show that the above results can be obtained via nonequilibrium Green functions...
Reformulation and solution of the master equation for multiple-well chemical reactions.
Georgievskii, Yuri; Miller, James A; Burke, Michael P; Klippenstein, Stephen J
2013-11-21
We consider an alternative formulation of the master equation for complex-forming chemical reactions with multiple wells and bimolecular products. Within this formulation the dynamical phase space consists of only the microscopic populations of the various isomers making up the reactive complex, while the bimolecular reactants and products are treated equally as sources and sinks. This reformulation yields compact expressions for the phenomenological rate coefficients describing all chemical processes, i.e., internal isomerization reactions, bimolecular-to-bimolecular reactions, isomer-to-bimolecular reactions, and bimolecular-to-isomer reactions. The applicability of the detailed balance condition is discussed and confirmed. We also consider the situation where some of the chemical eigenvalues approach the energy relaxation time scale and show how to modify the phenomenological rate coefficients so that they retain their validity.
Pfalzgraff, William C; Kelly, Aaron; Markland, Thomas E
2015-12-03
The development of methods that can efficiently and accurately treat nonadiabatic dynamics in quantum systems coupled to arbitrary atomistic environments remains a significant challenge in problems ranging from exciton transport in photovoltaic materials to electron and proton transfer in catalysis. Here we show that our recently introduced MF-GQME approach, which combines Ehrenfest mean field theory with the generalized quantum master equation framework, is able to yield quantitative accuracy over a wide range of charge-transfer regimes in fully atomistic environments. This is accompanied by computational speed-ups of up to 3 orders of magnitude over a direct application of Ehrenfest theory. This development offers the opportunity to efficiently investigate the atomistic details of nonadiabatic quantum relaxation processes in regimes where obtaining accurate results has previously been elusive.
Zalys-Geller, E.; Hatridge, M.; Silveri, M.; Narla, A.; Sliwa, K. M.; Shankar, S.; Girvin, S. M.; Devoret, M. H.
2015-03-01
Remote entanglement of two superconducting qubits may be accomplished by first entangling them with flying coherent microwave pulses, and then erasing the which-path information of these pulses by using a non-degenerate parametric amplifier such as the Josephson Parametric Converter (JPC). Crucially, this process requires no direct interaction between the two qubits. The JPC, however, will fail to completely erase the which-path information if the flying microwave pulses encode any difference in dynamics of the two qubit-cavity systems. This which-path information can easily arise from mismatches in the cavity linewidths and the cavity dispersive shifts from their respective qubits. Through analysis of the Stochastic Master Equation for this system, we have found a strategy for shaping the measurement pulses to eliminate the effect of these mismatches on the entangling measurement. We have then confirmed the effectiveness of this strategy by numerical simulation. Work supported by: IARPA, ARO, and NSF.
Entropy and Entanglement in Master Equation of Effective Hamiltonian for Jaynes-Cummings Model
Institute of Scientific and Technical Information of China (English)
H.A. Hessian; F.A. Mohammed; A.-B.A. Mohamed
2009-01-01
In this paper, we analytically solve the master equation for Jaynes-Cummings model in the dispersive regime including phase damping and the field is assumed to be initially in a superposition of coherent states.Using an established entanglement measure based on the negativity of the eigenvalues of the partially transposed density matrix we find a very strong sensitivity of the maximally generated entanglement to the amount of phase damping.Qualitatively this behavior is also reflected in alternative entanglement measures, but the quantitative agreement between different measures depends on the chosen noise model.The phase decoherenee for this model results in monotonic increase in the total entropy while the atomic sub-entropy keeps its periodic behaviour without any effect.
A master equation for gravitational decoherence: probing the textures of spacetime
Anastopoulos, C.; Hu, B. L.
2013-08-01
We give a first principles derivation of a master equation for the evolution of a quantum matter field in a linearly perturbed Minkowski spacetime, based solely on quantum field theory and general relativity. We make no additional assumptions nor introduce extra ingredients, as is often done in alternative quantum theories. When the quantum matter field is projected to a one-particle state, the master equation for a non-relativistic quantum particle in a weak gravitational field predicts decoherence in the energy basis, in contrast to most existing theories of gravitational decoherence. We point out the gauge nature of time and space reparameterizations in matter-gravity couplings, and warn that ‘intrinsic’ decoherence or alternative quantum theories invoking stochastic dynamics arising from temporal or spatial fluctuations violate this fundamental symmetry of classical general relativity. Interestingly we find that the decoherence rate depends on extra parameters other than the Planck scale, an important feature of gravitational decoherence. This is similar to the dependence of the decoherence rate of a quantum Brownian particle to the temperature and spectral density of the environment it interacts with. The corresponding features when gravity acts as an environment in decohering quantum objects are what we call the ‘textures’ of spacetime. We point out the marked difference between the case when gravity is represented as a background spacetime versus the case when gravity acts like a thermodynamic bath to quantum particles. This points to the possibility of using gravitational decoherence measurements to discern whether gravity is intrinsically elemental or emergent.
MESMER: an open-source master equation solver for multi-energy well reactions.
Glowacki, David R; Liang, Chi-Hsiu; Morley, Christopher; Pilling, Michael J; Robertson, Struan H
2012-09-27
The most commonly used theoretical models for describing chemical kinetics are accurate in two limits. When relaxation is fast with respect to reaction time scales, thermal transition state theory (TST) is the theoretical tool of choice. In the limit of slow relaxation, an energy resolved description like RRKM theory is more appropriate. For intermediate relaxation regimes, where much of the chemistry in nature occurs, theoretical approaches are somewhat less well established. However, in recent years master equation approaches have been successfully used to analyze and predict nonequilibrium chemical kinetics across a range of intermediate relaxation regimes spanning atmospheric, combustion, and (very recently) solution phase organic chemistry. In this article, we describe a Master Equation Solver for Multi-Energy Well Reactions (MESMER), a user-friendly, object-oriented, open-source code designed to facilitate kinetic simulations over multi-well molecular energy topologies where energy transfer with an external bath impacts phenomenological kinetics. MESMER offers users a range of user options specified via keywords and also includes some unique statistical mechanics approaches like contracted basis set methods and nonadiabatic RRKM theory for modeling spin-hopping. It is our hope that the design principles implemented in MESMER will facilitate its development and usage by workers across a range of fields concerned with chemical kinetics. As accurate thermodynamics data become more widely available, electronic structure theory is increasingly reliable, and as our fundamental understanding of energy transfer improves, we envision that tools like MESMER will eventually enable routine and reliable prediction of nonequilibrium kinetics in arbitrary systems.
Ghaderi, Nima
2016-03-28
Expressions for a K-adiabatic master equation for a bimolecular recombination rate constant krec are derived for a bimolecular reaction forming a complex with a single well or complexes with multiple well, where K is the component of the total angular momentum along the axis of least moment of inertia of the recombination product. The K-active master equation is also considered. The exact analytic solutions, i.e., the K-adiabatic and K-active steady-state population distribution function of reactive complexes, g(EJK) and g(EJ), respectively, are derived for the K-adiabatic and K-active master equation cases using properties of inhomogeneous integral equations (Fredholm type). The solutions accommodate arbitrary intermolecular energy transfer models, e.g., the single exponential, double exponential, Gaussian, step-ladder, and near-singularity models. At the high pressure limit, the krec for both the K-adiabatic and K-active master equations reduce, respectively, to the K-adiabatic and K-active bimolecular Rice-Ramsperger-Kassel-Marcus theory (high pressure limit expressions). Ozone and its formation from O + O2 are known to exhibit an adiabatic K. The ratio of the K-adiabatic to the K-active recombination rate constants for ozone formation at the high pressure limit is calculated to be ∼0.9 at 300 K. Results on the temperature and pressure dependence of the recombination rate constants and populations of O3 will be presented elsewhere.
Ghaderi, Nima
2016-03-01
Expressions for a K-adiabatic master equation for a bimolecular recombination rate constant krec are derived for a bimolecular reaction forming a complex with a single well or complexes with multiple well, where K is the component of the total angular momentum along the axis of least moment of inertia of the recombination product. The K-active master equation is also considered. The exact analytic solutions, i.e., the K-adiabatic and K-active steady-state population distribution function of reactive complexes, g(EJK) and g(EJ), respectively, are derived for the K-adiabatic and K-active master equation cases using properties of inhomogeneous integral equations (Fredholm type). The solutions accommodate arbitrary intermolecular energy transfer models, e.g., the single exponential, double exponential, Gaussian, step-ladder, and near-singularity models. At the high pressure limit, the krec for both the K-adiabatic and K-active master equations reduce, respectively, to the K-adiabatic and K-active bimolecular Rice-Ramsperger-Kassel-Marcus theory (high pressure limit expressions). Ozone and its formation from O + O2 are known to exhibit an adiabatic K. The ratio of the K-adiabatic to the K-active recombination rate constants for ozone formation at the high pressure limit is calculated to be ˜0.9 at 300 K. Results on the temperature and pressure dependence of the recombination rate constants and populations of O3 will be presented elsewhere.
Master equation-based analysis of a motor-clutch model for cell traction force.
Bangasser, Benjamin L; Odde, David J
2013-12-01
Microenvironmental mechanics play an important role in determining the morphology, traction, migration, proliferation, and differentiation of cells. A stochastic motor-clutch model has been proposed to describe this stiffness sensitivity. In this work, we present a master equation-based ordinary differential equation (ODE) description of the motor-clutch model, from which we derive an analytical expression to for a cell's optimum stiffness (i.e. the stiffness at which the traction force is maximal). This analytical expression provides insight into the requirements for stiffness sensing by establishing fundamental relationships between the key controlling cell-specific parameters. We find that the fundamental controlling parameters are the numbers of motors and clutches (constrained to be nearly equal), and the time scale of the on-off kinetics of the clutches (constrained to favor clutch binding over clutch unbinding). Both the ODE solution and the analytical expression show good agreement with Monte Carlo motor-clutch output, and reduce computation time by several orders of magnitude, which potentially enables long time scale behaviors (hours-days) to be studied computationally in an efficient manner. The ODE solution and the analytical expression may be incorporated into larger scale models of cellular behavior to bridge the gap from molecular time scales to cellular and tissue time scales.
Dang, Mia; Ramsaran, Kalinda D; Street, Melissa E; Syed, S Noreen; Barclay-Goddard, Ruth; Stratford, Paul W; Miller, Patricia A
2011-01-01
To estimate the predictive accuracy and clinical usefulness of the Chedoke-McMaster Stroke Assessment (CMSA) predictive equations. A longitudinal prognostic study using historical data obtained from 104 patients admitted post cerebrovascular accident was undertaken. Data were abstracted for all patients undergoing rehabilitation post stroke who also had documented admission and discharge CMSA scores. Published predictive equations were used to determine predicted outcomes. To determine the accuracy and clinical usefulness of the predictive model, shrinkage coefficients and predictions with 95% confidence bands were calculated. Complete data were available for 74 patients with a mean age of 65.3±12.4 years. The shrinkage values for the six Impairment Inventory (II) dimensions varied from -0.05 to 0.09; the shrinkage value for the Activity Inventory (AI) was 0.21. The error associated with predictive values was greater than ±1.5 stages for the II dimensions and greater than ±24 points for the AI. This study shows that the large error associated with the predictions (as defined by the confidence band) for the CMSA II and AI limits their clinical usefulness as a predictive measure. Further research to establish predictive models using alternative statistical procedures is warranted.
Indian Academy of Sciences (India)
Marko Žnidarič
2011-11-01
We discuss recent ﬁndings about properties of quantum nonequilibrium steady states. In particular we focus on transport properties. It is shown that the time-dependent density matrix renormalization method can be used successfully to ﬁnd a stationary solution of Lindblad master equation. Furthermore, for a speciﬁc model an exact solution is presented.
Quantum transport under ac drive from the leads: A Redfield quantum master equation approach
Purkayastha, Archak; Dubi, Yonatan
2017-08-01
Evaluating the time-dependent dynamics of driven open quantum systems is relevant for a theoretical description of many systems, including molecular junctions, quantum dots, cavity-QED experiments, cold atoms experiments, and more. Here, we formulate a rigorous microscopic theory of an out-of-equilibrium open quantum system of noninteracting particles on a lattice weakly coupled bilinearly to multiple baths and driven by periodically varying thermodynamic parameters like temperature and chemical potential of the bath. The particles can be either bosonic or fermionic and the lattice can be of any dimension and geometry. Based on the Redfield quantum master equation under Born-Markov approximation, we derive a linear differential equation for an equal time two point correlation matrix, sometimes also called a single-particle density matrix, from which various physical observables, for example, current, can be calculated. Various interesting physical effects, such as resonance, can be directly read off from the equations. Thus, our theory is quite general and gives quite transparent and easy-to-calculate results. We validate our theory by comparing with exact numerical simulations. We apply our method to a generic open quantum system, namely, a double quantum dot coupled to leads with modulating chemical potentials. The two most important experimentally relevant insights from this are as follows: (i) Time-dependent measurements of current for symmetric oscillating voltages (with zero instantaneous voltage bias) can point to the degree of asymmetry in the system-bath coupling and (ii) under certain conditions time-dependent currents can exceed time-averaged currents by several orders of magnitude, and can therefore be detected even when the average current is below the measurement threshold.
Direct solution of the Chemical Master Equation using quantized tensor trains.
Kazeev, Vladimir; Khammash, Mustafa; Nip, Michael; Schwab, Christoph
2014-03-01
The Chemical Master Equation (CME) is a cornerstone of stochastic analysis and simulation of models of biochemical reaction networks. Yet direct solutions of the CME have remained elusive. Although several approaches overcome the infinite dimensional nature of the CME through projections or other means, a common feature of proposed approaches is their susceptibility to the curse of dimensionality, i.e. the exponential growth in memory and computational requirements in the number of problem dimensions. We present a novel approach that has the potential to "lift" this curse of dimensionality. The approach is based on the use of the recently proposed Quantized Tensor Train (QTT) formatted numerical linear algebra for the low parametric, numerical representation of tensors. The QTT decomposition admits both, algorithms for basic tensor arithmetics with complexity scaling linearly in the dimension (number of species) and sub-linearly in the mode size (maximum copy number), and a numerical tensor rounding procedure which is stable and quasi-optimal. We show how the CME can be represented in QTT format, then use the exponentially-converging hp-discontinuous Galerkin discretization in time to reduce the CME evolution problem to a set of QTT-structured linear equations to be solved at each time step using an algorithm based on Density Matrix Renormalization Group (DMRG) methods from quantum chemistry. Our method automatically adapts the "basis" of the solution at every time step guaranteeing that it is large enough to capture the dynamics of interest but no larger than necessary, as this would increase the computational complexity. Our approach is demonstrated by applying it to three different examples from systems biology: independent birth-death process, an example of enzymatic futile cycle, and a stochastic switch model. The numerical results on these examples demonstrate that the proposed QTT method achieves dramatic speedups and several orders of magnitude storage
Busch, Anna; González-García, Núria; Lendvay, György; Olzmann, Matthias
2015-07-16
The thermal decomposition of cyanonitrene, NCN, was studied behind reflected shock waves in the temperature range 1790-2960 K at pressures near 1 and 4 bar. Highly diluted mixtures of NCN3 in argon were shock-heated to produce NCN, and concentration-time profiles of C atoms as reaction product were monitored with atomic resonance absorption spectroscopy at 156.1 nm. Calibration was performed with methane pyrolysis experiments. Rate coefficients for the reaction (3)NCN + M → (3)C + N2 + M (R1) were determined from the initial slopes of the C atom concentration-time profiles. Reaction R1 was found to be in the low-pressure regime at the conditions of the experiments. The temperature dependence of the bimolecular rate coefficient can be expressed with the following Arrhenius equation: k1(bim) = (4.2 ± 2.1) × 10(14) exp[-242.3 kJ mol(-1)/(RT)] cm(3) mol(-1) s(-1). The rate coefficients were analyzed by using a master equation with specific rate coefficients from RRKM theory. The necessary molecular data and energies were calculated with quantum chemical methods up to the CCSD(T)/CBS//CCSD/cc-pVTZ level of theory. From the topography of the potential energy surface, it follows that reaction R1 proceeds via isomerization of NCN to CNN and subsequent C-N bond fission along a collinear reaction coordinate without a tight transition state. The calculations reproduce the magnitude and temperature dependence of the rate coefficient and confirm that reaction R1 is in the low-pressure regime under our experimental conditions.
Direct solution of the Chemical Master Equation using quantized tensor trains.
Directory of Open Access Journals (Sweden)
Vladimir Kazeev
2014-03-01
Full Text Available The Chemical Master Equation (CME is a cornerstone of stochastic analysis and simulation of models of biochemical reaction networks. Yet direct solutions of the CME have remained elusive. Although several approaches overcome the infinite dimensional nature of the CME through projections or other means, a common feature of proposed approaches is their susceptibility to the curse of dimensionality, i.e. the exponential growth in memory and computational requirements in the number of problem dimensions. We present a novel approach that has the potential to "lift" this curse of dimensionality. The approach is based on the use of the recently proposed Quantized Tensor Train (QTT formatted numerical linear algebra for the low parametric, numerical representation of tensors. The QTT decomposition admits both, algorithms for basic tensor arithmetics with complexity scaling linearly in the dimension (number of species and sub-linearly in the mode size (maximum copy number, and a numerical tensor rounding procedure which is stable and quasi-optimal. We show how the CME can be represented in QTT format, then use the exponentially-converging hp-discontinuous Galerkin discretization in time to reduce the CME evolution problem to a set of QTT-structured linear equations to be solved at each time step using an algorithm based on Density Matrix Renormalization Group (DMRG methods from quantum chemistry. Our method automatically adapts the "basis" of the solution at every time step guaranteeing that it is large enough to capture the dynamics of interest but no larger than necessary, as this would increase the computational complexity. Our approach is demonstrated by applying it to three different examples from systems biology: independent birth-death process, an example of enzymatic futile cycle, and a stochastic switch model. The numerical results on these examples demonstrate that the proposed QTT method achieves dramatic speedups and several orders of
Liang, Jie; Qian, Hong
2010-01-01
Modern molecular biology has always been a great source of inspiration for computational science. Half a century ago, the challenge from understanding macromolecular dynamics has led the way for computations to be part of the tool set to study molecular biology. Twenty-five years ago, the demand from genome science has inspired an entire generation of computer scientists with an interest in discrete mathematics to join the field that is now called bioinformatics. In this paper, we shall lay out a new mathematical theory for dynamics of biochemical reaction systems in a small volume (i.e., mesoscopic) in terms of a stochastic, discrete-state continuous-time formulation, called the chemical master equation (CME). Similar to the wavefunction in quantum mechanics, the dynamically changing probability landscape associated with the state space provides a fundamental characterization of the biochemical reaction system. The stochastic trajectories of the dynamics are best known through the simulations using the Gillespie algorithm. In contrast to the Metropolis algorithm, this Monte Carlo sampling technique does not follow a process with detailed balance. We shall show several examples how CMEs are used to model cellular biochemical systems. We shall also illustrate the computational challenges involved: multiscale phenomena, the interplay between stochasticity and nonlinearity, and how macroscopic determinism arises from mesoscopic dynamics. We point out recent advances in computing solutions to the CME, including exact solution of the steady state landscape and stochastic differential equations that offer alternatives to the Gilespie algorithm. We argue that the CME is an ideal system from which one can learn to understand "complex behavior" and complexity theory, and from which important biological insight can be gained.
Quantum filtering of a thermal master equation with a purified reservoir
Genoni, Marco G.; Mancini, Stefano; Wiseman, Howard M.; Serafini, Alessio
2014-12-01
We consider a system subject to a quantum optical master equation at finite temperature and study a class of conditional dynamics obtained by monitoring its totally or partially purified environment. More specifically, drawing from the notion that the thermal state of the environment may be regarded as the local state of a lossy and noisy two-mode squeezed state, we consider conditional dynamics ("unravellings") resulting from the homodyne detection of the two modes of such a state. Thus, we identify a class of unravellings parametrized by the loss rate suffered by the environmental two-mode state, which interpolate between direct detection of the environmental mode alone (occurring for total loss, whereby no correlation between the two environmental modes is left) and full access to the purification of the bath (occurring when no loss is acting and the two-mode state of the environment is pure). We hence show that, while direct detection of the bath is not able to reach the maximal steady-state squeezing allowed by general-dyne unravellings, such optimal values can be obtained when a fully purified bath is accessible. More generally we show that, within our framework, any degree of access to the bath purification improves the performance of filtering protocols in terms of achievable squeezing and entanglement.
Müller, Clemens; Stace, Thomas M.
2017-01-01
Motivated by correlated decay processes producing gain, loss, and lasing in driven semiconductor quantum dots [Phys. Rev. Lett. 113, 036801 (2014), 10.1103/PhysRevLett.113.036801; Science 347, 285 (2015), 10.1126/science.aaa2501; Phys. Rev. Lett. 114, 196802 (2015), 10.1103/PhysRevLett.114.196802], we develop a theoretical technique by using Keldysh diagrammatic perturbation theory to derive a Lindblad master equation that goes beyond the usual second-order perturbation theory. We demonstrate the method on the driven dissipative Rabi model, including terms up to fourth order in the interaction between the qubit and both the resonator and environment. This results in a large class of Lindblad dissipators and associated rates which go beyond the terms that have previously been proposed to describe similar systems. All of the additional terms contribute to the system behavior at the same order of perturbation theory. We then apply these results to analyze the phonon-assisted steady-state gain of a microwave field driving a double quantum dot in a resonator. We show that resonator gain and loss are substantially affected by dephasing-assisted dissipative processes in the quantum-dot system. These additional processes, which go beyond recently proposed polaronic theories, are in good quantitative agreement with experimental observations.
Fox, Zachary; Neuert, Gregor; Munsky, Brian
2016-08-01
Emerging techniques now allow for precise quantification of distributions of biological molecules in single cells. These rapidly advancing experimental methods have created a need for more rigorous and efficient modeling tools. Here, we derive new bounds on the likelihood that observations of single-cell, single-molecule responses come from a discrete stochastic model, posed in the form of the chemical master equation. These strict upper and lower bounds are based on a finite state projection approach, and they converge monotonically to the exact likelihood value. These bounds allow one to discriminate rigorously between models and with a minimum level of computational effort. In practice, these bounds can be incorporated into stochastic model identification and parameter inference routines, which improve the accuracy and efficiency of endeavors to analyze and predict single-cell behavior. We demonstrate the applicability of our approach using simulated data for three example models as well as for experimental measurements of a time-varying stochastic transcriptional response in yeast.
The Spin Density Matrix I: General Theory and Exact Master Equations
Kunikeev, Sharif D
2007-01-01
We consider a scenario where interacting electrons confined in quantum dots (QDs) are either too close to be resolved, or we do not wish to apply measurements that resolve them. Then the physical observable is an electron spin only (one cannot unambiguously ascribe a spin to a QD) and the system state is fully described by the spin-density matrix. Accounting for the spatial degrees of freedom, we examine to what extent a Hamiltonian description of the spin-only degrees of freedom is valid. We show that as long as there is no coupling between singlet and triplet states this is indeed the case, but when there is such a coupling there are open systems effects, i.e., the dynamics is non-unitary even without interaction with a true bath. Our primary focus is an investigation of non-unitary effects, based on exact master equations we derive for the spin-density matrix in the Lindblad and time-convolutionless (TCL) forms, and the implications for quantum computation. In particular, we demonstrate that the Heisenberg...
Hellander, Andreas; Lawson, Michael J.; Drawert, Brian; Petzold, Linda
2014-06-01
The efficiency of exact simulation methods for the reaction-diffusion master equation (RDME) is severely limited by the large number of diffusion events if the mesh is fine or if diffusion constants are large. Furthermore, inherent properties of exact kinetic-Monte Carlo simulation methods limit the efficiency of parallel implementations. Several approximate and hybrid methods have appeared that enable more efficient simulation of the RDME. A common feature to most of them is that they rely on splitting the system into its reaction and diffusion parts and updating them sequentially over a discrete timestep. This use of operator splitting enables more efficient simulation but it comes at the price of a temporal discretization error that depends on the size of the timestep. So far, existing methods have not attempted to estimate or control this error in a systematic manner. This makes the solvers hard to use for practitioners since they must guess an appropriate timestep. It also makes the solvers potentially less efficient than if the timesteps were adapted to control the error. Here, we derive estimates of the local error and propose a strategy to adaptively select the timestep when the RDME is simulated via a first order operator splitting. While the strategy is general and applicable to a wide range of approximate and hybrid methods, we exemplify it here by extending a previously published approximate method, the diffusive finite-state projection (DFSP) method, to incorporate temporal adaptivity.
Hellander, Andreas; Lawson, Michael J; Drawert, Brian; Petzold, Linda
2015-01-01
The efficiency of exact simulation methods for the reaction-diffusion master equation (RDME) is severely limited by the large number of diffusion events if the mesh is fine or if diffusion constants are large. Furthermore, inherent properties of exact kinetic-Monte Carlo simulation methods limit the efficiency of parallel implementations. Several approximate and hybrid methods have appeared that enable more efficient simulation of the RDME. A common feature to most of them is that they rely on splitting the system into its reaction and diffusion parts and updating them sequentially over a discrete timestep. This use of operator splitting enables more efficient simulation but it comes at the price of a temporal discretization error that depends on the size of the timestep. So far, existing methods have not attempted to estimate or control this error in a systematic manner. This makes the solvers hard to use for practitioners since they must guess an appropriate timestep. It also makes the solvers potentially less efficient than if the timesteps are adapted to control the error. Here, we derive estimates of the local error and propose a strategy to adaptively select the timestep when the RDME is simulated via a first order operator splitting. While the strategy is general and applicable to a wide range of approximate and hybrid methods, we exemplify it here by extending a previously published approximate method, the Diffusive Finite-State Projection (DFSP) method, to incorporate temporal adaptivity. PMID:26865735
Positioning in a flat two-dimensional space-time: the delay master equation
Coll, Bartolomé; Morales-Lladosa, Juan Antonio
2010-01-01
The basic theory on relativistic positioning systems in a two-dimensional space-time has been presented in two previous papers [Phys. Rev. D {\\bf 73}, 084017 (2006); {\\bf 74}, 104003 (2006)], where the possibility of making relativistic gravimetry with these systems has been analyzed by considering specific examples. Here we study generic relativistic positioning systems in the Minkowski plane. We analyze the information that can be obtained from the data received by a user of the positioning system. We show that the accelerations of the emitters and of the user along their trajectories are determined by the sole knowledge of the emitter positioning data and of the acceleration of only one of the emitters. Moreover, as a consequence of the so called master delay equation, the knowledge of this acceleration is only required during an echo interval, i.e., the interval between the emission time of a signal by an emitter and its reception time after being reflected by the other emitter. We illustrate these result...
Kidon, Lyran; Wilner, Eli Y; Rabani, Eran
2015-12-21
The generalized quantum master equation provides a powerful tool to describe the dynamics in quantum impurity models driven away from equilibrium. Two complementary approaches, one based on Nakajima-Zwanzig-Mori time-convolution (TC) and the other on the Tokuyama-Mori time-convolutionless (TCL) formulations provide a starting point to describe the time-evolution of the reduced density matrix. A key in both approaches is to obtain the so called "memory kernel" or "generator," going beyond second or fourth order perturbation techniques. While numerically converged techniques are available for the TC memory kernel, the canonical approach to obtain the TCL generator is based on inverting a super-operator in the full Hilbert space, which is difficult to perform and thus, nearly all applications of the TCL approach rely on a perturbative scheme of some sort. Here, the TCL generator is expressed using a reduced system propagator which can be obtained from system observables alone and requires the calculation of super-operators and their inverse in the reduced Hilbert space rather than the full one. This makes the formulation amenable to quantum impurity solvers or to diagrammatic techniques, such as the nonequilibrium Green's function. We implement the TCL approach for the resonant level model driven away from equilibrium and compare the time scales for the decay of the generator with that of the memory kernel in the TC approach. Furthermore, the effects of temperature, source-drain bias, and gate potential on the TCL/TC generators are discussed.
Generalized quantum master equations in and out of equilibrium: When can one win?
Kelly, Aaron; Montoya-Castillo, Andrés; Wang, Lu; Markland, Thomas E.
2016-05-01
Generalized quantum master equations (GQMEs) are an important tool in modeling chemical and physical processes. For a large number of problems, it has been shown that exact and approximate quantum dynamics methods can be made dramatically more efficient, and in the latter case more accurate, by proceeding via the GQME formalism. However, there are many situations where utilizing the GQME approach with an approximate method has been observed to return the same dynamics as using that method directly. Here, for systems both in and out of equilibrium, we provide a more detailed understanding of the conditions under which using an approximate method can yield benefits when combined with the GQME formalism. In particular, we demonstrate the necessary manipulations, which are satisfied by exact quantum dynamics, that are required to recast the memory kernel in a form that can be analytically shown to yield the same result as a direct application of the dynamics regardless of the approximation used. By considering the connections between these forms of the kernel, we derive the conditions that approximate methods must satisfy if they are to offer different results when used in conjunction with the GQME formalism. These analytical results thus provide new insights as to when proceeding via the GQME approach can be used to improve the accuracy of simulations.
Ovchinnikov, Igor V
2012-01-01
Here it is shown that the most general Parisi-Sourlas-Wu stochastic quantization procedure applied to any stochastic differential equation (SDE) leads to a Witten-type topological field theory - a model with a global topological Becchi-Rouet-Stora-Tyutin supersymmetry (Q-symmetry). Q-symmetry can be dynamically broken only by (anti-)instantons - ultimately nonlinear sudden tunneling processes of (creation)annihilation of solitons, e.g., avalanches in self-organized criticality (SOC) or (creation)annihilation of vortices in turbulent water. The phases with unbroken Q-symmetry are essentially markovian and can be understood solely in terms of the conventional Fokker-Plank evolution of the probability density. For these phases, Ito interpretation of SDEs and/or Martin-Siggia-Rose approximation of the stochastic quantization are applicable. SOC, turbulence, glasses, quenches etc. constitute the "generalized turbulence" category of stochastic phases with broken Q-symmetry. In this category, (anti-)instantons conde...
Application of quantum master equation for long-term prognosis of asset-prices
Khrennikova, Polina
2016-05-01
This study combines the disciplines of behavioral finance and an extension of econophysics, namely the concepts and mathematical structure of quantum physics. We apply the formalism of quantum theory to model the dynamics of some correlated financial assets, where the proposed model can be potentially applied for developing a long-term prognosis of asset price formation. At the informational level, the asset price states interact with each other by the means of a "financial bath". The latter is composed of agents' expectations about the future developments of asset prices on the finance market, as well as financially important information from mass-media, society, and politicians. One of the essential behavioral factors leading to the quantum-like dynamics of asset prices is the irrationality of agents' expectations operating on the finance market. These expectations lead to a deeper type of uncertainty concerning the future price dynamics of the assets, than given by a classical probability theory, e.g., in the framework of the classical financial mathematics, which is based on the theory of stochastic processes. The quantum dimension of the uncertainty in price dynamics is expressed in the form of the price-states superposition and entanglement between the prices of the different financial assets. In our model, the resolution of this deep quantum uncertainty is mathematically captured with the aid of the quantum master equation (its quantum Markov approximation). We illustrate our model of preparation of a future asset price prognosis by a numerical simulation, involving two correlated assets. Their returns interact more intensively, than understood by a classical statistical correlation. The model predictions can be extended to more complex models to obtain price configuration for multiple assets and portfolios.
Energy Technology Data Exchange (ETDEWEB)
Kidon, Lyran [School of Chemistry, The Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv 69978 (Israel); The Sackler Center for Computational Molecular and Materials Science, Tel Aviv University, Tel Aviv 69978 (Israel); Wilner, Eli Y. [School of Physics and Astronomy, The Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv 69978 (Israel); Rabani, Eran [The Sackler Center for Computational Molecular and Materials Science, Tel Aviv University, Tel Aviv 69978 (Israel); Department of Chemistry, University of California and Lawrence Berkeley National Laboratory, Berkeley California 94720-1460 (United States)
2015-12-21
The generalized quantum master equation provides a powerful tool to describe the dynamics in quantum impurity models driven away from equilibrium. Two complementary approaches, one based on Nakajima–Zwanzig–Mori time-convolution (TC) and the other on the Tokuyama–Mori time-convolutionless (TCL) formulations provide a starting point to describe the time-evolution of the reduced density matrix. A key in both approaches is to obtain the so called “memory kernel” or “generator,” going beyond second or fourth order perturbation techniques. While numerically converged techniques are available for the TC memory kernel, the canonical approach to obtain the TCL generator is based on inverting a super-operator in the full Hilbert space, which is difficult to perform and thus, nearly all applications of the TCL approach rely on a perturbative scheme of some sort. Here, the TCL generator is expressed using a reduced system propagator which can be obtained from system observables alone and requires the calculation of super-operators and their inverse in the reduced Hilbert space rather than the full one. This makes the formulation amenable to quantum impurity solvers or to diagrammatic techniques, such as the nonequilibrium Green’s function. We implement the TCL approach for the resonant level model driven away from equilibrium and compare the time scales for the decay of the generator with that of the memory kernel in the TC approach. Furthermore, the effects of temperature, source-drain bias, and gate potential on the TCL/TC generators are discussed.
Cao, Youfang; Terebus, Anna; Liang, Jie
2016-04-01
The discrete chemical master equation (dCME) provides a general framework for studying stochasticity in mesoscopic reaction networks. Since its direct solution rapidly becomes intractable due to the increasing size of the state space, truncation of the state space is necessary for solving most dCMEs. It is therefore important to assess the consequences of state space truncations so errors can be quantified and minimized. Here we describe a novel method for state space truncation. By partitioning a reaction network into multiple molecular equivalence groups (MEGs), we truncate the state space by limiting the total molecular copy numbers in each MEG. We further describe a theoretical framework for analysis of the truncation error in the steady-state probability landscape using reflecting boundaries. By aggregating the state space based on the usage of a MEG and constructing an aggregated Markov process, we show that the truncation error of a MEG can be asymptotically bounded by the probability of states on the reflecting boundary of the MEG. Furthermore, truncating states of an arbitrary MEG will not undermine the estimated error of truncating any other MEGs. We then provide an overall error estimate for networks with multiple MEGs. To rapidly determine the appropriate size of an arbitrary MEG, we also introduce an a priori method to estimate the upper bound of its truncation error. This a priori estimate can be rapidly computed from reaction rates of the network, without the need of costly trial solutions of the dCME. As examples, we show results of applying our methods to the four stochastic networks of (1) the birth and death model, (2) the single gene expression model, (3) the genetic toggle switch model, and (4) the phage lambda bistable epigenetic switch model. We demonstrate how truncation errors and steady-state probability landscapes can be computed using different sizes of the MEG(s) and how the results validate our theories. Overall, the novel state space
Jin, Jinshuang; Zheng, Xiao; Yan, YiJing
2008-06-21
A generalized quantum master equation theory that governs the exact, nonperturbative quantum dissipation and quantum transport is formulated in terms of hierarchically coupled equations of motion for an arbitrary electronic system in contact with electrodes under either a stationary or a nonstationary electrochemical potential bias. The theoretical construction starts with the influence functional in path integral, in which the electron creation and annihilation operators are Grassmann variables. Time derivatives on the influence functionals are then performed in a hierarchical manner. Both the multiple-frequency dispersion and the non-Markovian reservoir parametrization schemes are considered for the desired hierarchy construction. The resulting hierarchical equations of motion formalism is in principle exact and applicable to arbitrary electronic systems, including Coulomb interactions, under the influence of arbitrary time-dependent applied bias voltage and external fields. Both the conventional quantum master equation and the real-time diagrammatic formalism of Schon and co-workers can be readily obtained at well defined limits of the present theory. We also show that for a noninteracting electron system, the present hierarchical equations of motion formalism terminates at the second tier exactly, and the Landuer-Buttiker transport current expression is recovered. The present theory renders an exact and numerically tractable tool to evaluate various transient and stationary quantum transport properties of many-electron systems, together with the involving nonperturbative dissipative dynamics.
da Silva, Roberto; Vainstein, Mendeli H.; Lamb, Luis C.; Prado, Sandra D.
2013-03-01
We propose a novel probabilistic model that outputs the final standings of a soccer league, based on a simple dynamics that mimics a soccer tournament. In our model, a team is created with a defined potential (ability) which is updated during the tournament according to the results of previous games. The updated potential modifies a team future winning/losing probabilities. We show that this evolutionary game is able to reproduce the statistical properties of final standings of actual editions of the Brazilian tournament (Brasileirão) if the starting potential is the same for all teams. Other leagues such as the Italian (Calcio) and the Spanish (La Liga) tournaments have notoriously non-Gaussian traces and cannot be straightforwardly reproduced by this evolutionary non-Markovian model with simple initial conditions. However, we show that by setting the initial abilities based on data from previous tournaments, our model is able to capture the stylized statistical features of double round robin system (DRRS) tournaments in general. A complete understanding of these phenomena deserves much more attention, but we suggest a simple explanation based on data collected in Brazil: here several teams have been crowned champion in previous editions corroborating that the champion typically emerges from random fluctuations that partly preserve the Gaussian traces during the tournament. On the other hand, in the Italian and Spanish cases, only a few teams in recent history have won their league tournaments. These leagues are based on more robust and hierarchical structures established even before the beginning of the tournament. For the sake of completeness, we also elaborate a totally Gaussian model (which equalizes the winning, drawing, and losing probabilities) and we show that the scores of the Brazilian tournament “Brasileirão” cannot be reproduced. This shows that the evolutionary aspects are not superfluous and play an important role which must be considered in
Bifurcation dynamics of the tempered fractional Langevin equation
Zeng, Caibin; Yang, Qigui; Chen, YangQuan
2016-08-01
Tempered fractional processes offer a useful extension for turbulence to include low frequencies. In this paper, we investigate the stochastic phenomenological bifurcation, or stochastic P-bifurcation, of the Langevin equation perturbed by tempered fractional Brownian motion. However, most standard tools from the well-studied framework of random dynamical systems cannot be applied to systems driven by non-Markovian noise, so it is desirable to construct possible approaches in a non-Markovian framework. We first derive the spectral density function of the considered system based on the generalized Parseval's formula and the Wiener-Khinchin theorem. Then we show that it enjoys interesting and diverse bifurcation phenomena exchanging between or among explosive-like, unimodal, and bimodal kurtosis. Therefore, our procedures in this paper are not merely comparable in scope to the existing theory of Markovian systems but also provide a possible approach to discern P-bifurcation dynamics in the non-Markovian settings.
Bifurcation dynamics of the tempered fractional Langevin equation.
Zeng, Caibin; Yang, Qigui; Chen, YangQuan
2016-08-01
Tempered fractional processes offer a useful extension for turbulence to include low frequencies. In this paper, we investigate the stochastic phenomenological bifurcation, or stochastic P-bifurcation, of the Langevin equation perturbed by tempered fractional Brownian motion. However, most standard tools from the well-studied framework of random dynamical systems cannot be applied to systems driven by non-Markovian noise, so it is desirable to construct possible approaches in a non-Markovian framework. We first derive the spectral density function of the considered system based on the generalized Parseval's formula and the Wiener-Khinchin theorem. Then we show that it enjoys interesting and diverse bifurcation phenomena exchanging between or among explosive-like, unimodal, and bimodal kurtosis. Therefore, our procedures in this paper are not merely comparable in scope to the existing theory of Markovian systems but also provide a possible approach to discern P-bifurcation dynamics in the non-Markovian settings.
Bifurcation dynamics of the tempered fractional Langevin equation
Energy Technology Data Exchange (ETDEWEB)
Zeng, Caibin, E-mail: macbzeng@scut.edu.cn; Yang, Qigui, E-mail: qgyang@scut.edu.cn [School of Mathematics, South China University of Technology, Guangzhou 510640 (China); Chen, YangQuan, E-mail: ychen53@ucmerced.edu [MESA LAB, School of Engineering, University of California, Merced, 5200 N. Lake Road, Merced, California 95343 (United States)
2016-08-15
Tempered fractional processes offer a useful extension for turbulence to include low frequencies. In this paper, we investigate the stochastic phenomenological bifurcation, or stochastic P-bifurcation, of the Langevin equation perturbed by tempered fractional Brownian motion. However, most standard tools from the well-studied framework of random dynamical systems cannot be applied to systems driven by non-Markovian noise, so it is desirable to construct possible approaches in a non-Markovian framework. We first derive the spectral density function of the considered system based on the generalized Parseval's formula and the Wiener-Khinchin theorem. Then we show that it enjoys interesting and diverse bifurcation phenomena exchanging between or among explosive-like, unimodal, and bimodal kurtosis. Therefore, our procedures in this paper are not merely comparable in scope to the existing theory of Markovian systems but also provide a possible approach to discern P-bifurcation dynamics in the non-Markovian settings.
Nakayama, Hiroshi; Furuichi, Akihisa; Kita, Takashi; Nishino, Taneo
1997-04-01
Structural phase transition of epitaxial growing layer is quite important to understand the atomic scale mechanism of molecular beam epitaxy (MBE). GaAs and related alloy semiconductors are typical systems which show variety of such structural transitions during MBE. Structural evolution of surface reconstruction phases and an order-disorder transition in III-V alloy semiconductors are typical cases where such phase transitions appear during epitaxial processes. In this work, a stochastic theory and the Monte-Carlo simulation have been presented to describe the structural evolution of epitaxial growth in binary system. This method, known here as the 'Monte-Carlo master equation (MCME) method', couples a master equation for epitaxial growth kinetics with an Ising Hamiltonian of growing surface. The Monte-Carlo (MC) simulation of binary growing surface with atom-correlation effects has successfully revealed the evolution of atomic structure and the formation of short-range ordering (SRO) during epitaxy. This demonstrates the usefulness of the MCME method in describing the atomic-structural dynamics as compared with a conventional theory of epitaxy based on a diffusion equation and standard nucleation theory.
Luo, JunYan; Yan, Yiying; Huang, Yixiao; Yu, Li; He, Xiao-Ling; Jiao, HuJun
2017-01-01
We investigate the noise correlations of spin and charge currents through an electron spin resonance (ESR)-pumped quantum dot, which is tunnel coupled to three electrodes maintained at an equivalent chemical potential. A recursive scheme is employed with inclusion of the spin degrees of freedom to account for the spin-resolved counting statistics in the presence of non-Markovian effects due to coupling with a dissipative heat bath. For symmetric spin-up and spin-down tunneling rates, an ESR-induced spin flip mechanism generates a pure spin current without an accompanying net charge current. The stochastic tunneling of spin carriers, however, produces universal shot noises of both charge and spin currents, revealing the effective charge and spin units of quasiparticles in transport. In the case of very asymmetric tunneling rates for opposite spins, an anomalous relationship between noise autocorrelations and cross correlations is revealed, where super-Poissonian autocorrelation is observed in spite of a negative cross correlation. Remarkably, with strong dissipation strength, non-Markovian memory effects give rise to a positive cross correlation of the charge current in the absence of a super-Poissonian autocorrelation. These unique noise features may offer essential methods for exploiting internal spin dynamics and various quasiparticle tunneling processes in mesoscopic transport.
Directory of Open Access Journals (Sweden)
Charles E. Smith
2016-05-01
Full Text Available There is increasing interest concerning the details about how quantum systems interact with their surroundings. A number of methodologies have been used to describe these interactions, including Master Equations (ME based on a system-plus-reservoir (S + R approach, and more recently, Steepest Entropy Ascent Quantum Thermodynamics (SEAQT which asserts that entropy is a fundamental physical property and that isolated quantum systems that are not at stable equilibrium may spontaneously relax without environmental influences. In this paper, the ME, SEAQT approaches, and a simple linear difference equation (DE model are compared with each other and experimental data in order to study the behavior of a single trapped ion as it interacts with one or more external heat reservoirs. The comparisons of the models present opportunities for additional study to verify the validity and limitations of these approaches.
Mastering algebra retrains the visual system to perceive hierarchical structure in equations.
Marghetis, Tyler; Landy, David; Goldstone, Robert L
2016-01-01
Formal mathematics is a paragon of abstractness. It thus seems natural to assume that the mathematical expert should rely more on symbolic or conceptual processes, and less on perception and action. We argue instead that mathematical proficiency relies on perceptual systems that have been retrained to implement mathematical skills. Specifically, we investigated whether the visual system-in particular, object-based attention-is retrained so that parsing algebraic expressions and evaluating algebraic validity are accomplished by visual processing. Object-based attention occurs when the visual system organizes the world into discrete objects, which then guide the deployment of attention. One classic signature of object-based attention is better perceptual discrimination within, rather than between, visual objects. The current study reports that object-based attention occurs not only for simple shapes but also for symbolic mathematical elements within algebraic expressions-but only among individuals who have mastered the hierarchical syntax of algebra. Moreover, among these individuals, increased object-based attention within algebraic expressions is associated with a better ability to evaluate algebraic validity. These results suggest that, in mastering the rules of algebra, people retrain their visual system to represent and evaluate abstract mathematical structure. We thus argue that algebraic expertise involves the regimentation and reuse of evolutionarily ancient perceptual processes. Our findings implicate the visual system as central to learning and reasoning in mathematics, leading us to favor educational approaches to mathematics and related STEM fields that encourage students to adapt, not abandon, their use of perception.
Purkayastha, Archak; Dhar, Abhishek; Kulkarni, Manas
2016-06-01
We present the Born-Markov approximated Redfield quantum master equation (RQME) description for an open system of noninteracting particles (bosons or fermions) on an arbitrary lattice of N sites in any dimension and weakly connected to multiple reservoirs at different temperatures and chemical potentials. The RQME can be reduced to the Lindblad equation, of various forms, by making further approximations. By studying the N =2 case, we show that RQME gives results which agree with exact analytical results for steady-state properties and with exact numerics for time-dependent properties over a wide range of parameters. In comparison, the Lindblad equations have a limited domain of validity in nonequilibrium. We conclude that it is indeed justified to use microscopically derived full RQME to go beyond the limitations of Lindblad equations in out-of-equilibrium systems. We also derive closed-form analytical results for out-of-equilibrium time dynamics of two-point correlation functions. These results explicitly show the approach to steady state and thermalization. These results are experimentally relevant for cold atoms, cavity QED, and far-from-equilibrium quantum dot experiments.
Brasil, Carlos Alexandre
2011-01-01
The most general form for the generator of quantum dynamical semigroups is the one proposed by Lindblad, which can be used in several approaches involving quantum mechanics for open systems, from analysis of noise and dissipation to fundamental aspects of the quantum theory of measurement. When dealing with a system interacting with its environment, the trace of the environmental degrees of freedom using the traditional approach of exponentiation of the Hamiltonian terms, originates prohibitive and difficult calculations. This paper presents an alternative analytic method to derive, through superoperator algebra and Nakajima-Zwanzig thermodynamic projectors, a compact and fairly simple master equation describing the reduced system dynamics. As a simple example of the present approach, we analyze a two-level system in contact with an environment, which allows us to observe the decoherence intensification by the interaction.
Nogawa, Tomoaki
2012-10-18
We examine the effectiveness of assuming an equal probability for states far from equilibrium. For this aim, we propose a method to construct a master equation for extensive variables describing nonstationary nonequilibrium dynamics. The key point of the method is the assumption that transient states are equivalent to the equilibrium state that has the same extensive variables, i.e., an equal probability holds for microscopic states in nonequilibrium. We demonstrate an application of this method to the critical relaxation of the two-dimensional Potts model by Monte Carlo simulations. While the one-variable description, which is adequate for equilibrium, yields relaxation dynamics that are very fast, the redundant two-variable description well reproduces the true dynamics quantitatively. These results suggest that some class of the nonequilibrium state can be described with a small extension of degrees of freedom, which may lead to an alternative way to understand nonequilibrium phenomena. © 2012 American Physical Society.
Silveri, M.; Zalys-Geller, E.; Hatridge, M.; Leghtas, Z.; Devoret, M. H.; Girvin, S. M.
2015-03-01
In the remote entanglement process, two distant stationary qubits are entangled with separate flying qubits and the which-path information is erased from the flying qubits by interference effects. As a result, an observer cannot tell from which of the two sources a signal came and the probabilistic measurement process generates perfect heralded entanglement between the two signal sources. Notably, the two stationary qubits are spatially separated and there is no direct interaction between them. We study two transmon qubits in superconducting cavities connected to a Josephson Parametric Converter (JPC). The qubit information is encoded in the traveling wave leaking out from each cavity. Remarkably, the quantum-limited phase-preserving amplification of two traveling waves provided by the JPC can work as a which-path information eraser. By using a stochastic master approach we demonstrate the probabilistic production of heralded entangled states and that unequal qubit-cavity pairs can be made indistinguishable by simple engineering of driving fields. Additionally, we will derive measurement rates, measurement optimization strategies and discuss the effects of finite amplification gain, cavity losses, and qubit relaxations and dephasing. Work supported by IARPA, ARO and NSF.
Nonequilibrium dynamical mean-field theory: an auxiliary quantum master equation approach.
Arrigoni, Enrico; Knap, Michael; von der Linden, Wolfgang
2013-02-22
We introduce a versatile method to compute electronic steady-state properties of strongly correlated extended quantum systems out of equilibrium. The approach is based on dynamical mean-field theory (DMFT), in which the original system is mapped onto an auxiliary nonequilibrium impurity problem imbedded in a Markovian environment. The steady-state Green's function of the auxiliary system is solved by full diagonalization of the corresponding Lindblad equation. The approach can be regarded as the nontrivial extension of the exact-diagonalization-based DMFT to the nonequilibrium case. As a first application, we consider an interacting Hubbard layer attached to two metallic leads and present results for the steady-state current and the nonequilibrium density of states.
Effects of system-bath coupling on a photosynthetic heat engine: A polaron master-equation approach
Qin, M.; Shen, H. Z.; Zhao, X. L.; Yi, X. X.
2017-07-01
Stimulated by suggestions of quantum effects in energy transport in photosynthesis, the fundamental principles responsible for the near-unit efficiency of the conversion of solar to chemical energy became active again in recent years. Under natural conditions, the formation of stable charge-separation states in bacteria and plant reaction centers is strongly affected by the coupling of electronic degrees of freedom to a wide range of vibrational motions. These inspire and motivate us to explore the effects of the environment on the operation of such complexes. In this paper, we apply the polaron master equation, which offers the possibilities to interpolate between weak and strong system-bath coupling, to study how system-bath couplings affect the exciton-transfer processes in the Photosystem II reaction center described by a quantum heat engine (QHE) model over a wide parameter range. The effects of bath correlation and temperature, together with the combined effects of these factors are also discussed in detail. We interpret these results in terms of noise-assisted transport effect and dynamical localization, which correspond to two mechanisms underpinning the transfer process in photosynthetic complexes: One is resonance energy transfer and the other is the dynamical localization effect captured by the polaron master equation. The effects of system-bath coupling and bath correlation are incorporated in the effective system-bath coupling strength determining whether noise-assisted transport effect or dynamical localization dominates the dynamics and temperature modulates the balance of the two mechanisms. Furthermore, these two mechanisms can be attributed to one physical origin: bath-induced fluctuations. The two mechanisms are manifestations of the dual role played by bath-induced fluctuations depending on the range of parameters. The origin and role of coherence are also discussed. It is the constructive interplay between noise and coherent dynamics, rather
Luo, JunYan; Jin, Jinshuang; Wang, Shi-Kuan; Hu, Jing; Huang, Yixiao; He, Xiao-Ling
2016-03-01
We present a generic unraveling scheme for a detailed-balance-preserved quantum master equation applicable for stochastic point processes in mesoscopic transport. It enables us to investigate continuous measurement of a qubit on the level of single quantum trajectories, where essential correlations between the inherent dynamics of the qubit and detector current fluctuations are revealed. Based on this unraveling scheme, feedback control of the charge qubit is implemented to achieve a desired pure state in the presence of the detailed-balance condition. With sufficient feedback strength, coherent oscillations of the measured qubit can be maintained for arbitrary qubit-detector coupling. Competition between the loss and restoration of coherence entailed, respectively, by measurement back action and feedback control is reflected in the noise power spectrum of the detector's output. It is demonstrated unambiguously that the signal-to-noise ratio is significantly enhanced with increasing feedback strength and could even exceed the well-known Korotkov-Averin bound in quantum measurement. The proposed unraveling and feedback scheme offers a transparent and straightforward approach to effectively sustaining ideal coherent oscillations of a charge qubit in the field of quantum computation.
Giirsoy, Gamze; Terebus, Anna; Cao, Youfang; Liang, Jie; Gursoy, Gamze; Terebus, Anna; Youfang Cao; Jie Liang; Gursoy, Gamze; Cao, Youfang; Terebus, Anna; Liang, Jie
2016-08-01
Stochasticity plays important roles in regulation of biochemical reaction networks when the copy numbers of molecular species are small. Studies based on Stochastic Simulation Algorithm (SSA) has shown that a basic reaction system can display stochastic focusing (SF) by increasing the sensitivity of the network as a result of the signal noise. Although SSA has been widely used to study stochastic networks, it is ineffective in examining rare events and this becomes a significant issue when the tails of probability distributions are relevant as is the case of SF. Here we use the ACME method to solve the exact solution of the discrete Chemical Master Equations and to study a network where SF was reported. We showed that the level of SF depends on the degree of the fluctuations of signal molecule. We discovered that signaling noise under certain conditions in the same reaction network can lead to a decrease in the system sensitivities, thus the network can experience stochastic defocusing. These results highlight the fundamental role of stochasticity in biological reaction networks and the need for exact computation of probability landscape of the molecules in the system.
Master equation for the Unruh-DeWitt detector and the universal relaxation time in de Sitter space
Fukuma, Masafumi; Sugishita, Sotaro
2013-01-01
de Sitter space is known to have a thermal character. This can be best seen by an Unruh-DeWitt detector which stays in the Poincare patch and interacts with a scalar field in the Bunch-Davies vacuum. However, since the Bunch-Davies vacuum is the ground state only at the infinite past, if the scalar field starts in the ground state at a finite past, an Unruh-DeWitt detector then will feel as if it is in a medium that is not in thermodynamic equilibrium and that undergoes a relaxation to the equilibrium corresponding to the Bunch-Davies vacuum. In this paper, we first develop a general framework to treat such circumstances and write down the master equation which completely describes the finite time evolution of the density matrix of an Unruh-DeWitt detector in arbitrary background geometry. We then apply this framework to an ideal detector in de Sitter space which can get adjusted to its environment instantaneously, and show that the density distribution of the detector certainly exhibits a relaxation to the G...
Approach to Quantum Kramers' Equation and Barrier Crossing Dynamics
Banerjee, Dhruba; Banik, S K; Ray, D S; Banerjee, Dhruba; Bag, Bidhan Chandra; Banik, Suman Kumar; Ray, Deb Shankar
2002-01-01
We have presented a simple approach to quantum theory of Brownian motion and barrier crossing dynamics. Based on an initial coherent state representation of bath oscillators and an equilibrium canonical distribution of quantum mechanical mean values of their co-ordinates and momenta we have derived a $c$-number generalized quantum Langevin equation. The approach allows us to implement the method of classical non-Markovian Brownian motion to realize an exact generalized non-Markovian quantum Kramers' equation. The equation is valid for arbitrary temperature and friction. We have solved this equation in the spatial diffusion-limited regime to derive quantum Kramers' rate of barrier crossing and analyze its variation as a function of temperature and friction. While almost all the earlier theories rest on quasi-probability distribution functions (like Wigner function) and path integral methods, the present work is based on {\\it true probability distribution functions} and is independent of path integral technique...
Energy Technology Data Exchange (ETDEWEB)
Oliveira, Luciana Renata de; Bazzani, Armando; Giampieri, Enrico; Castellani, Gastone C., E-mail: Gastone.Castellani@unibo.it [Physics and Astronomy Department, Bologna University and INFN Sezione di Bologna (Italy)
2014-08-14
We propose a non-equilibrium thermodynamical description in terms of the Chemical Master Equation (CME) to characterize the dynamics of a chemical cycle chain reaction among m different species. These systems can be closed or open for energy and molecules exchange with the environment, which determines how they relax to the stationary state. Closed systems reach an equilibrium state (characterized by the detailed balance condition (D.B.)), while open systems will reach a non-equilibrium steady state (NESS). The principal difference between D.B. and NESS is due to the presence of chemical fluxes. In the D.B. condition the fluxes are absent while for the NESS case, the chemical fluxes are necessary for the state maintaining. All the biological systems are characterized by their “far from equilibrium behavior,” hence the NESS is a good candidate for a realistic description of the dynamical and thermodynamical properties of living organisms. In this work we consider a CME written in terms of a discrete Kolmogorov forward equation, which lead us to write explicitly the non-equilibrium chemical fluxes. For systems in NESS, we show that there is a non-conservative “external vector field” whose is linearly proportional to the chemical fluxes. We also demonstrate that the modulation of these external fields does not change their stationary distributions, which ensure us to study the same system and outline the differences in the system's behavior when it switches from the D.B. regime to NESS. We were interested to see how the non-equilibrium fluxes influence the relaxation process during the reaching of the stationary distribution. By performing analytical and numerical analysis, our central result is that the presence of the non-equilibrium chemical fluxes reduces the characteristic relaxation time with respect to the D.B. condition. Within a biochemical and biological perspective, this result can be related to the “plasticity property” of biological
Energy Technology Data Exchange (ETDEWEB)
Tojo, C.; Bujan Nunez, M.C. [Departamento de Quimica Fisica, Facultad de Ciencias, Universidad de Vigo, Vigo (Spain)
1996-11-01
The stochastic master equation dP{sub i}/dt=-Sigma{sub j}G{sub i}jp{sub i}(t) is used to calculate the spectral dimension in finite lattices. it can be observed that the entropy function S(t)=-Sigma{sub i}p{sub i}(t)ln(p{sub i}(t)) grows linearly with In(t). (Author) 38 refs.
Grima, Ramon
2015-10-01
It is well known that the linear-noise approximation (LNA) agrees with the chemical master equation, up to second-order moments, for chemical systems composed of zero and first-order reactions. Here we show that this is also a property of the LNA for a subset of chemical systems with second-order reactions. This agreement is independent of the number of interacting molecules.
Directory of Open Access Journals (Sweden)
Chushnyakova Maria
2013-12-01
Full Text Available We performed quantitative theoretical analysis of the high precision data on the fusion excitation function in the reaction 16O + 144Sm involving spherical nuclei. For this purpose the model is developed in which the collision process is described by the stochastic dynamical equations with the retarding friction and colored noise. The friction force is supposed to be proportional to the squared derivative of nucleus-nucleus interaction potential. The latter is calculated within the framework of the double folding approach with the density-dependent M3Y NN-forces. Varying the radial dissipation strength KR and the matter diffuseness of 144Sm we reach χ2 per point equal to 5.4. However the values of KR and the friction retardation time τC appear to be strongly correlated. More high precision data are needed to make more definite conclusions about the values of KR and τC.
Chushnyakova, Maria; Gontchar, Igor
2013-12-01
We performed quantitative theoretical analysis of the high precision data on the fusion excitation function in the reaction 16O + 144Sm involving spherical nuclei. For this purpose the model is developed in which the collision process is described by the stochastic dynamical equations with the retarding friction and colored noise. The friction force is supposed to be proportional to the squared derivative of nucleus-nucleus interaction potential. The latter is calculated within the framework of the double folding approach with the density-dependent M3Y NN-forces. Varying the radial dissipation strength KR and the matter diffuseness of 144Sm we reach χ2 per point equal to 5.4. However the values of KR and the friction retardation time τC appear to be strongly correlated. More high precision data are needed to make more definite conclusions about the values of KR and τC.
Solar Wind Heating as a Non-Markovian Process: Lévy Flight, Fractional Calculus, and κ -functions
Sheldon, R. B.; Adrian, M. L.; Chang, S.; Collier, M.
2001-05-01
Many space and laboratory plasmas are found to possess non-Maxwellian distribution functions. An empirical function promoted by Stan Olbert, which superposes a Maxwellian core with a power-law tail, has been found to emulate many of the plasma distributions discovered in space. These κ -functions, with their associated power-law tail induced anomalous heat flux, have been used by theorists1\\ as the origin of solar coronal heating of solar wind. However, the principle and prerequisite for the robust production of such a non-equilibrium distribution has rarely been explained. We report on recent statistical work2, which shows that the κ -function is one of a general class of solutions to a time-fractional diffusion equation, known as a Lévy stable probability distribution. These solutions arise from time-variable probability distribution (or equivalently, a spatially variable probability in a flowing medium), which demonstrate that anomalously high flux, or equivalently, non-equilibrium thermodynamics govern the outflowing solar wind plasma. We will characterize the parameters that control the degree of deviation from a Maxwellian and attempt to draw physical meaning from the mathematical formalism. 1Scudder, J. Astrophys. J., 1992.\\2Mainardi, F. and R. Gorenflo, J. Computational and Appl. Mathematics, Vol. 118, No 1-2, 283-299 (2000).
Glowacki, David R; Rodgers, W J; Shannon, Robin; Robertson, Struan H; Harvey, Jeremy N
2017-04-28
The extent to which vibrational energy transfer dynamics can impact reaction outcomes beyond the gas phase remains an active research question. Molecular dynamics (MD) simulations are the method of choice for investigating such questions; however, they can be extremely expensive, and therefore it is worth developing cheaper models that are capable of furnishing reasonable results. This paper has two primary aims. First, we investigate the competition between energy relaxation and reaction at 'hotspots' that form on the surface of diamond during the chemical vapour deposition process. To explore this, we developed an efficient reactive potential energy surface by fitting an empirical valence bond model to higher-level ab initio electronic structure theory. We then ran 160 000 NVE trajectories on a large slab of diamond, and the results are in reasonable agreement with experiment: they suggest that energy dissipation from surface hotspots is complete within a few hundred femtoseconds, but that a small fraction of CH3 does in fact undergo dissociation prior to the onset of thermal equilibrium. Second, we developed and tested a general procedure to formulate and solve the energy-grained master equation (EGME) for surface chemistry problems. The procedure we outline splits the diamond slab into system and bath components, and then evaluates microcanonical transition-state theory rate coefficients in the configuration space of the system atoms. Energy transfer from the system to the bath is estimated using linear response theory from a single long MD trajectory, and used to parametrize an energy transfer function which can be input into the EGME. Despite the number of approximations involved, the surface EGME results are in reasonable agreement with the NVE MD simulations, but considerably cheaper. The results are encouraging, because they offer a computationally tractable strategy for investigating non-equilibrium reaction dynamics at surfaces for a broader range of
Awan, Iftikhar A; Burgess, Donald R; Manion, Jeffrey A
2012-03-22
Kassel Marcus/Master Equation (RRKM/ME) analysis has been performed and used to extrapolate the data to temperatures between 700 and 1900 K and pressures of 10 to 1 × 10(5) kPa.
Winter, Pierre M.; Rheaume, Michael; Cooksy, Andrew L.
2017-08-01
We have calculated the temperature-dependent rate coefficients of the addition reactions of butadien-2-yl (C4H5) and acroylyl (C3H3O) radicals with ethene (C2H4), carbon monoxide (CO), formaldehyde (H2CO), hydrogen cyanide (HCN), and ketene (H2CCO), in order to explore the balance between kinetic and thermodynamic control in these combustion-related reactions. For the C4H5 radical, the 1,3-diene form of the addition products is more stable than the 1,2-diene, but the 1,2-diene form of the radical intermediate is stabilized by an allylic delocalization, which may influence the relative activation energies. For the reactions combining C3H3O with C2H4, CO, and HCN, the opposite is true: the 1,2-enone form of the addition products is more stable than the 1,3-enone, whereas the 1,3-enone is the slightly more stable radical species. Optimized geometries and vibrational modes were computed with the QCISD/aug-cc-pVDZ level and basis, followed by single-point CCSD(T)-F12a/cc-pVDZ-F12 energy calculations. Our findings indicate that the kinetics in all cases favor reaction along the 1,3 pathway for both the C4H5 and C3H3O systems. The Rice-Ramsperger-Kassel-Marcus (RRKM) microcanonical rate coefficients and subsequent solution of the chemical master equation were used to predict the time-evolution of our system under conditions from 500 K to 2000 K and from 10-5 bar to 10 bars. Despite the 1,3 reaction pathway being more favorable for the C4H5 system, our results predict branching ratios of the 1,2 to 1,3 product as high as 0.48 at 1 bar. Similar results hold for the acroylyl system under these combustion conditions, suggesting that under kinetic control the branching of these reactions may be much more significant than the thermodynamics would suggest. This effect may be partly attributed to the low energy difference between 1,2 and 1,3 forms of the radical intermediate. No substantial pressure-dependence is found for the overall forward reaction rates until pressures
Shi, Qiang; Geva, Eitan
2003-12-01
The Nakajima-Zwanzig generalized quantum master equation provides a general, and formally exact, prescription for simulating the reduced dynamics of a quantum system coupled to a quantum bath. In this equation, the memory kernel accounts for the influence of the bath on the system's dynamics. The standard approach is based on using a perturbative treatment of the system-bath coupling for calculating this kernel, and is therefore restricted to systems weakly coupled to the bath. In this paper, we propose a new approach for calculating the memory kernel for an arbitrary system-bath coupling. The memory kernel is obtained by solving a set of two coupled integral equations that relate it to a new type of two-time system-dependent bath correlation functions. The feasibility of the method is demonstrated in the case of an asymetrical two-level system linearly coupled to a harmonic bath.
Santra, Siddhartha; Cruikshank, Benjamin; Balu, Radhakrishnan; Jacobs, Kurt
2017-10-01
Fermi’s golden rule applies to a situation in which a single quantum state \\vert \\psi> is coupled to a near-continuum. This ‘quasi-continuum coupling’ structure results in a rate equation for the population of \\vert \\psi> . Here we show that the coupling of a quantum system to the standard model of a thermal environment, a bath of harmonic oscillators, can be decomposed into a ‘cascade’ made up of the quasi-continuum coupling structures of Fermi’s golden rule. This clarifies the connection between the physics of the golden rule and that of a thermal bath, and provides a non-rigorous but physically intuitive derivation of the Markovian master equation directly from the former. The exact solution to the Hamiltonian of the golden rule, known as the Bixon–Jortner model, generalized for an asymmetric spectrum, provides a window on how the evolution induced by the bath deviates from the master equation as one moves outside the Markovian regime. Our analysis also reveals the relationship between the oscillator bath and the ‘random matrix model’ (RMT) of a thermal bath. We show that the cascade structure is the one essential difference between the two models, and the lack of it prevents the RMT from generating transition rates that are independent of the initial state of the system. We suggest that the cascade structure is one of the generic elements of thermalizing many-body systems.
Banik, S K; Ray, D S; Banik, Suman Kumar; Bag, Bidhan Chandra; Ray, Deb Shankar
2002-01-01
Traditionally, the quantum Brownian motion is described by Fokker-Planck or diffusion equations in terms of quasi-probability distribution functions, e.g., Wigner functions. These often become singular or negative in the full quantum regime. In this paper a simple approach to non-Markovian theory of quantum Brownian motion using {\\it true probability distribution functions} is presented. Based on an initial coherent state representation of the bath oscillators and an equilibrium canonical distribution of the quantum mechanical mean values of their co-ordinates and momenta we derive a generalized quantum Langevin equation in $c$-numbers and show that the latter is amenable to a theoretical analysis in terms of the classical theory of non-Markovian dynamics. The corresponding Fokker-Planck, diffusion and the Smoluchowski equations are the {\\it exact} quantum analogues of their classical counterparts. The present work is {\\it independent} of path integral techniques. The theory as developed here is a natural ext...
Some aspects of fractional diffusion equations of single and distributed order
Mainardi, Francesco; Gorenflo, Rudolf
2007-01-01
The time fractional diffusion equation is obtained from the standard diffusion equation by replacing the first-order time derivative with a fractional derivative of order $\\beta \\in (0,1)$. The fundamental solution for the Cauchy problem is interpreted as a probability density of a self-similar non-Markovian stochastic process related to a phenomenon of sub-diffusion (the variance grows in time sub-linearly). A further generalization is obtained by considering a continuous or discrete distribution of fractional time derivatives of order less than one. Then the fundamental solution is still a probability density of a non-Markovian process that, however, is no longer self-similar but exhibits a corresponding distribution of time-scales.
Kishi, Ryohei; Fujii, Hiroaki; Kishimoto, Shingo; Murata, Yusuke; Ito, Soichi; Okuno, Katsuki; Shigeta, Yasuteru; Nakano, Masayoshi
2012-05-03
We develop novel calculation and analysis methods for the dynamic first hyperpolarizabilities β [the second-order nonlinear optical (NLO) properties at the molecular level] in the second-harmonic generation based on the quantum master equation method combined with the ab initio molecular orbital (MO) configuration interaction method. As examples, we have evaluated off-resonant dynamic β values of donor (NH(2))- and/or acceptor (NO(2))-substituted benzenes using these methods, which are shown to reproduce those by the conventional summation-over-states method well. The spatial contributions of electrons to the dynamic β of these systems are also analyzed using the dynamic β density and its partition into the MO contributions. The present results demonstrate the advantage of these methods in unraveling the mechanism of dynamic NLO properties and in building the structure-dynamic NLO property relationships of real molecules.
Entropy production in non-equilibrium systems described by the generalized Langevin equation
Sevilla, Francisco J.; Piña-Perez, Omar
2014-03-01
The generalized Langevin equation for a charged particle under the influence of time-dependent external fields, is employed to study the effects of non-Markovian dissipative terms in the entropy production of non-equilibrium states exhibiting non-zero mass flux. We present results for the case in which the fluctuation-dissipation relation holds. FJS and OPP acknowledge financial support from PAPIIT-IN113114 and PAEP-UNAM respectively.
Directory of Open Access Journals (Sweden)
Andrei Khrennikov
2016-07-01
Full Text Available We present a new conceptual approach for modeling of fluid flows in random porous media based on explicit exploration of the treelike geometry of complex capillary networks. Such patterns can be represented mathematically as ultrametric spaces and the dynamics of fluids by ultrametric diffusion. The images of p-adic fields, extracted from the real multiscale rock samples and from some reference images, are depicted. In this model the porous background is treated as the environment contributing to the coefficients of evolutionary equations. For the simplest trees, these equations are essentially less complicated than those with fractional differential operators which are commonly applied in geological studies looking for some fractional analogs to conventional Euclidean space but with anomalous scaling and diffusion properties. It is possible to solve the former equation analytically and, in particular, to find stationary solutions. The main aim of this paper is to attract the attention of researchers working on modeling of geological processes to the novel utrametric approach and to show some examples from the petroleum reservoir static and dynamic characterization, able to integrate the p-adic approach with multifractals, thermodynamics and scaling. We also present a non-mathematician friendly review of trees and ultrametric spaces and pseudo-differential operators on such spaces.
Energy Technology Data Exchange (ETDEWEB)
Prosen, Tomaz; Zunkovic, Bojan [Department of Physics, FMF, University of Ljubljana, Jadranska 19, SI-1000 Ljubljana (Slovenia)], E-mail: tomaz.prosen@fmf.uni-lj.si
2010-02-15
We generalize the method of third quantization to a unified exact treatment of Redfield and Lindblad master equations for open quadratic systems of n fermions in terms of diagonalization of a 4nx4n matrix. Non-equilibrium thermal driving in terms of the Redfield equation is analyzed in detail. We explain how one can compute all the physically relevant quantities, such as non-equilibrium expectation values of local observables, various entropies or information measures, or time evolution and properties of relaxation. We also discuss how to exactly treat explicitly time-dependent problems. The general formalism is then applied to study a thermally driven open XY spin 1/2 chain. We find that the recently proposed non-equilibrium quantum phase transition in the open XY chain survives the thermal driving within the Redfield model. In particular, the phase of long-range magnetic correlations can be characterized by hypersensitivity of the non-equilibrium steady state to external (bath or bulk) parameters. Studying the heat transport, we find negative differential thermal conductance for sufficiently strong thermal driving as well as non-monotonic dependence of the heat current on the strength of the bath coupling.
US Agency for International Development — OPS Master is a management tool and database for integrated financial planning and portfolio management in USAID Missions. Using OPS Master, the three principal...
Berim, Gersh O.; Ruckenstein, Eli
2003-11-01
A generalized kinetic Ising model is applied to the description of phase transformations in lattice systems. A procedure, based on the conjecture that the probability distribution function of the states of the system is similar to the equilibrium one, is used for closing the infinite chain of kinetic equations. The method is illustrated by treating as an example the one-dimensional Ising model. The predicted rate of phase transformation (RPT) demonstrates various time behaviors dependent upon the details of the interactions between spins and a heat bath. If the parameters W0 and W the reciprocals of which characterize, respectively, the time scales of growth (decay) and splitting (coagulation) of clusters have the same order of magnitude, then the RPT is constant during almost the entire transformation process. For the case W=0, which corresponds to the absence of splitting and coagulation of clusters, the phase transformation follows an exponential law in the final stage and is linear with respect to time during the initial one. It has a similar behavior for W0≫W≠0; however, the RPT in the final stage is much smaller in the last case than for W=0. In the absence of supersaturation, RPT decreases to zero as T→Tc, where Tc(=0 K) is the phase transition temperature for a one-dimensional model. The time-dependent size distribution of clusters is for all times exponential with respect to the cluster size. The average size of the cluster far from both equilibrium and initial state grows linearly in time. Both the above quantities behave in a manner similar to those obtained by Monte Carlo simulations for systems of higher dimension.
Hasenauer, J; Wolf, V; Kazeroonian, A; Theis, F J
2014-09-01
The time-evolution of continuous-time discrete-state biochemical processes is governed by the Chemical Master Equation (CME), which describes the probability of the molecular counts of each chemical species. As the corresponding number of discrete states is, for most processes, large, a direct numerical simulation of the CME is in general infeasible. In this paper we introduce the method of conditional moments (MCM), a novel approximation method for the solution of the CME. The MCM employs a discrete stochastic description for low-copy number species and a moment-based description for medium/high-copy number species. The moments of the medium/high-copy number species are conditioned on the state of the low abundance species, which allows us to capture complex correlation structures arising, e.g., for multi-attractor and oscillatory systems. We prove that the MCM provides a generalization of previous approximations of the CME based on hybrid modeling and moment-based methods. Furthermore, it improves upon these existing methods, as we illustrate using a model for the dynamics of stochastic single-gene expression. This application example shows that due to the more general structure, the MCM allows for the approximation of multi-modal distributions.
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.
Georgiev, Ivan T.; McKay, Susan R.
2005-12-01
We present a general position-space renormalization-group approach for systems in steady states far from equilibrium and illustrate its application to the three-state driven lattice gas. The method is based upon the possibility of a closed form representation of the parameters controlling transition rates of the system in terms of the steady state probability distribution of small clusters, arising from the application of the master equations to small clusters. This probability distribution on various length scales is obtained through a Monte Carlo algorithm on small lattices, which then yields a mapping between parameters on different length scales. The renormalization-group flows indicate the phase diagram, analogous to equilibrium treatments. For the three-state driven lattice gas, we have implemented this procedure and compared the resulting phase diagrams with those obtained directly from simulations. Results in general show the expected topology with one exception. For high densities, an unexpected additional fixed point emerges, which can be understood qualitatively by comparing it with the fixed point of the fully asymmetric exclusion process.
Directory of Open Access Journals (Sweden)
Xinzhi Liu
1998-01-01
Full Text Available This paper studies a class of high order delay partial differential equations. Employing high order delay differential inequalities, several oscillation criteria are established for such equations subject to two different boundary conditions. Two examples are also given.
Institute of Scientific and Technical Information of China (English)
刘景锋; 李凌燕
2013-01-01
Based on one-sided Fourier transformation, a general method is presented to research the spontaneous decay dynamics of an emitter in homogeneous media, non-leaky cavity, leaky cavity and photonic band gap material. It is found that the spontaneous decay properties of the emitters are strongly dependent on the local density of states. The spontaneous emission properties of the emitters can be manipulated through engineering the local density of stats and the high-performance optoelectronic device and quantum information processing device are obtained. This method can be used in Markovian or non-Markovian bath-reservoir environments.%基于单边傅里叶变换,本文提出一种研究辐射子的自发衰减动力学演化的普适方法.利用该方法研究了辐射子处于均匀介质、理想微腔和泄露微腔中的自发辐射动力学演化问题,最后并把这种方法用于处理光子带隙材料中的辐射动力学演化问题.结果表明:辐射子的自发辐射动力学特性由局域态密度决定,可以通过调控辐射子周围的局域态密度来调控辐射子的自发辐射特性,为实现新型的光电子器件提供了理论基础.该方法不仅适用于马尔科夫热库的情况也适用于非马尔科夫热库的情况.
Parameter estimation in stochastic differential equations
Bishwal, Jaya P N
2008-01-01
Parameter estimation in stochastic differential equations and stochastic partial differential equations is the science, art and technology of modelling complex phenomena and making beautiful decisions. The subject has attracted researchers from several areas of mathematics and other related fields like economics and finance. This volume presents the estimation of the unknown parameters in the corresponding continuous models based on continuous and discrete observations and examines extensively maximum likelihood, minimum contrast and Bayesian methods. Useful because of the current availability of high frequency data is the study of refined asymptotic properties of several estimators when the observation time length is large and the observation time interval is small. Also space time white noise driven models, useful for spatial data, and more sophisticated non-Markovian and non-semimartingale models like fractional diffusions that model the long memory phenomena are examined in this volume.
Li, Daniel
2014-01-01
This easy-to-understand tutorial provides you with several engaging projects that show you how to utilize Grunt with various web technologies, teaching you how to master build automation and testing with Grunt in your applications.If you are a JavaScript developer who is looking to streamline their workflow with build-automation, then this book will give you a kick start in fully understanding the importance of the described web technologies and automate their processes using Grunt.
Retarded versus time-nonlocal quantum kinetic equations
Energy Technology Data Exchange (ETDEWEB)
Morawetz, K. [Grand Accelerateur National d' Ions Lourds (GANIL), 14 - Caen (France); Spicka, V.; Lipavsky, P. [Institute of Physics, Academy of Sciences, Praha (Czech Republic)
2000-07-01
The finite duration of the collisions in Fermionic systems as expressed by the retardation time in the non-Markovian Levinson equation is discussed in the quasiclassical limit. The separate individual contributions included in the memory effect resulting in (i) off-shell tails of the Wigner distribution, (ii) renormalization of scattering rates and (iii) of the single-particle energy, (iv) collision delay and (v) related non-local corrections to the scattering integral. In this way we transform the Levison equation into the Landau-Silin equation extended by the non-local corrections known from the theory of dense gases. The derived kinetic equation unifies the Landau theory of quasiparticle transport with the classical kinetic theory of dense gases. The space-time symmetry is discussed versus particle-hole symmetry and a solution is proposed which transforms these two exclusive pictures into each other. (authors)
Olivares-Rivas, Wilmer; Colmenares, Pedro J.
2016-09-01
The non-static generalized Langevin equation and its corresponding Fokker-Planck equation for the position of a viscous fluid particle were solved in closed form for a time dependent external force. Its solution for a constant external force was obtained analytically. The non-Markovian stochastic differential equation, associated to the dynamics of the position under a colored noise, was then applied to the description of the dynamics and persistence time of particles constrained within absorbing barriers. Comparisons with molecular dynamics were very satisfactory.
Brett, Tobias; Galla, Tobias
2014-03-28
We present a heuristic derivation of Gaussian approximations for stochastic chemical reaction systems with distributed delay. In particular, we derive the corresponding chemical Langevin equation. Due to the non-Markovian character of the underlying dynamics, these equations are integro-differential equations, and the noise in the Gaussian approximation is coloured. Following on from the chemical Langevin equation, a further reduction leads to the linear-noise approximation. We apply the formalism to a delay variant of the celebrated Brusselator model, and show how it can be used to characterise noise-driven quasi-cycles, as well as noise-triggered spiking. We find surprisingly intricate dependence of the typical frequency of quasi-cycles on the delay period.
Department of Veterans Affairs — As of June 28, 2010, the Master Veteran Index (MVI) database based on the enhanced Master Patient Index (MPI) is the authoritative identity service within the VA,...
Energy Technology Data Exchange (ETDEWEB)
Goertz, R.C.
1949-03-07
A device for manipulating a pair of tongs behind a shielding barrier has been built and tested. It is called a Master-Slave Manipulator because the slave tongs move in exact correspondence with a master handle. The "slave hands" follow the master hands in complete synchronism. This is the first completely master-slave manipulator known to exist and has proved that this type of manipulation is very successful when the unit is prooperly engineered and built.
Scattering Theory for Lindblad Master Equations
Falconi, Marco; Faupin, Jérémy; Fröhlich, Jürg; Schubnel, Baptiste
2017-03-01
We study scattering theory for a quantum-mechanical system consisting of a particle scattered off a dynamical target that occupies a compact region in position space. After taking a trace over the degrees of freedom of the target, the dynamics of the particle is generated by a Lindbladian acting on the space of trace-class operators. We study scattering theory for a general class of Lindbladians with bounded interaction terms. First, we consider models where a particle approaching the target is always re-emitted by the target. Then we study models where the particle may be captured by the target. An important ingredient of our analysis is a scattering theory for dissipative operators on Hilbert space.
Mastering mathematics statistics & probability
Various
2014-01-01
Mastering Mathematics provides flexible online and print teaching and learning resources. The service focuses on strands within the curriculum to improve progression throughout Secondary Mathematics. Mastering Mathematics Student Books and eBooks are organised into progression strands in line with Mastering Mathematics Teaching and Learning Resources:. - Enable students to identify appropriate remediation or extension steps they need in order to progress, through easy to follow progression charts. - Clear explanations of the tools needed for the chapter followed by questions that develop fluen
Various
2014-01-01
Mastering Mathematics provides flexible online and print teaching and learning resources. The service focuses on strands within the curriculum to improve progression throughout Secondary Mathematics. Mastering Mathematics Student Books and Whiteboard eTextbooks are organised into progression strands in line with Mastering Mathematics Teaching and Learning Resources:. - Enable students to identify appropriate remediation or extension steps they need in order to progress, through easy to follow progression charts. - Clear explanations of the tools needed for the chapter followed by questions tha
Mastering mathematics geometry & measures
Various
2014-01-01
Deliver outstanding lessons that build fluency, problem-solving and mathematical reasoning skills to enable sustained progress at Key Stage 3, in preparation for GCSE. Mastering Mathematics provides flexible online and print teaching and learning resources. The service focuses on strands within the curriculum to improve progression throughout Secondary Mathematics . Mastering Mathematics Student Books and Whiteboard eTextbooks are organised into progression strands in line with Mastering Mathematics Teaching and Learning Resources:. - Enable students to identify appropriate remediation or exte
MASTER TELEVISION ANTENNA SYSTEM.
Rhode Island State Dept. of Education, Providence.
SPECIFICATIONS FOR THE FURNISHING AND INSTALLATION OF TELEVISION MASTER ANTENNA SYSTEMS FOR SECONDARY AND ELEMENTARY SCHOOLS ARE GIVEN. CONTRACTOR REQUIREMENTS, EQUIPMENT, PERFORMANCE STANDARDS, AND FUNCTIONS ARE DESCRIBED. (MS)
Interior design. Mastering the master plan.
Mesbah, C E
1995-10-01
Reflecting on the results of the survey, this proposed interior design master planning process addresses the concerns and issues of both CEOs and facility managers in ways that focus on problem-solving strategies and methods. Use of the interior design master plan process further promotes the goals and outcomes expressed in the survey by both groups. These include enhanced facility image, the efficient selection of finishes and furnishings, continuity despite staff changes, and overall savings in both costs and time. The interior design master plan allows administrators and facility managers to anticipate changes resulting from the restructuring of health care delivery. The administrators and facility managers are then able to respond in ways that manage those changes in the flexible and cost-effective manner they are striving for. This framework permits staff members to concentrate their time and energy on the care of their patients--which is, after all, what it's all about.
Dynamics of Quantum Entanglement in Reservoir with Memory Effects
Institute of Scientific and Technical Information of China (English)
郝翔; 沙金巧; 孙坚; 朱士群
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.
Entanglement dynamics of two interacting qubits under the influence of local dissipation
Indian Academy of Sciences (India)
LONE MUZAFFAR QADIR
2016-07-01
We investigate the dynamics of entanglement given by the concurrence of a two-qubit system in the non-Markovian setting. A quantum master equation is derived, which is solved in the eigenbasis of the system Hamiltonian for X-type initial states. A closed formula for time evolution of concurrence is presented for a pure state. It is shown that under the influence of dissipation non-zero entanglement is created in unentangled twoqubit states which decay in the same way as pure entangled states. We also show that under real circumstances,the decay rate of concurrence is strongly modified by the non-Markovianity of the evolution.
Gress, O.; Balanutsa, P.; Lipunov, V.; Gorbovskoy, E.; Otero, S.; Rebolo, R.; Serra-Ricart, M.; Buckley, D.; Tiurina, N. V.; Kuznetsov, A. S.; Kornilov, V. G.; Vladimirov, V. V.; Kuvshinov, D. A.; Chazov, V. V.; Shumkov, V.; Pogrosheva, T.
2017-02-01
MASTER-IAC auto-detection system ( Lipunov et al., "MASTER Global Robotic Net", Advances in Astronomy, 2010, 30L ) discovered OT source at (RA, Dec) = 15h 05m 18.03s -14d 39m 33.6s on 2017-02-08.27692 UT. The OT unfiltered magnitude is (limit 19.8m).
MASTER: bright optical transient
Sidorenkov, V. N.; Lipunov, V. M.; Kornilov, V. G.; Chazov, V. V.; Berezhko, E. G.; Klypin, A. A.; Shafer, E. Yu.; Mironova, I. V.; Esin, V. P.; Gundorov, V. L.; Charikov, A. V.; Aitova, G. A.; Gektin, Yu. M.; Trunkovsky, E. M.; Lipunova, N. A.; Popova, A. O.; Gerasimov, I. A.; Gluschenko, Yu. V.
2017-02-01
MASTER-IAC auto-detection system ( Lipunov et al., "MASTER Global Robotic Net", Advances in Astronomy, 2010, 30L ) discovered OT source at (RA, Dec) = 01h 44m 50.47s +45d 32m 42.9s on 2017-01-29.03010 UT. The OT unfiltered magnitude is (mlim=19.5m).
Master of science as change masters
DEFF Research Database (Denmark)
2006-01-01
Engineers are the driving forces of technological development – how do engineers obtain the relevant skills in order to fulfil this position? In this chapter, we ask whether the concept of change master could be a possible future direction for engineering skills. Developed by Kanter, the change...
Memory-effect-induced macroscopic-microscopic entanglement
Mu, Qingxia; Zhao, Xinyu; Yu, Ting
2016-07-01
We study optomechanical entanglement between an optical cavity field and a movable mirror coupled to a non-Markovian environment. The non-Markovian quantum-state diffusion approach and the non-Markovian master equation are shown to be useful in investigating entanglement generation between the cavity field and the movable mirror. The simple model presented in this paper demonstrates several interesting properties of optomechanical entanglement that are associated with environment memory effects. It is evident that the effective environment central frequency can be used to modulate the optomechanical entanglement. In addition, we show that the maximum entanglement may be achieved by properly choosing the effective detuning, which is significantly dependent on the strength of the memory effect of the environment.
Cébron, Guillaume; Dahlqvist, Antoine; Gabriel, Franck
2017-09-01
The master field is the large N limit of the Yang-Mills measure on the Euclidean plane. It can be viewed as a non-commutative process indexed by loops on the plane. We construct and study generalized master fields, called free planar Markovian holonomy fields which are versions of the master field where the law of a simple loop can be as more general as it is possible. We prove that those free planar Markovian holonomy fields can be seen as well as the large N limit of some Markovian holonomy fields on the plane with unitary structure group.
Master of science as change masters
DEFF Research Database (Denmark)
2006-01-01
master concept stresses the importance of creativity, innovation, leadership, and change. In this chapter, this concept will be analyzed and elaborated on partly in relation to the concepts of Bildung and Skill and partly to three different notions of engineering practice in technological innovation......Engineers are the driving forces of technological development – how do engineers obtain the relevant skills in order to fulfil this position? In this chapter, we ask whether the concept of change master could be a possible future direction for engineering skills. Developed by Kanter, the change...... process must be managed is together with the dynamic and comprehensive perspective on engineering practice used to shape the engineer of tomorrow, and by that we hint at overall trajectories in the design of engineering education. These trajectories call for exemplarity, inter-disciplinarily, integration...
DEFF Research Database (Denmark)
2006-01-01
Development and content of an international Master in Urban Quality development and management. The work has been done in a cooperation between Berlage institut, Holland; Chulalongkorn University, Thailand; Mahidol University, Thailand; University Kebangsaan Malaysia, Malaysia; og Aalborg...
DEFF Research Database (Denmark)
2006-01-01
Development and content of an international Master in Urban Quality development and management. The work has been done in a cooperation between Berlage institut, Holland; Chulalongkorn University, Thailand; Mahidol University, Thailand; University Kebangsaan Malaysia, Malaysia; og Aalborg...
Cardoso, Ciro
2014-01-01
This book is designed for all levels of Lumion users; from beginner to advanced, you will find useful insights and professional techniques to improve and develop your skills in order to fully control and master Lumion.
Energy Technology Data Exchange (ETDEWEB)
NONE
1995-06-01
This document is a master list of acronyms and other abbreviations that are used by or could be useful to, the personnel at Los Alamos National Laboratory. Many specialized and well-known abbreviations are not included in this list.
Energy Technology Data Exchange (ETDEWEB)
Clifford, David J.; Harris, James M.
2014-12-01
This is the IDC Re-Engineering Phase 2 project Integrated Master Plan (IMP). The IMP presents the major accomplishments planned over time to re-engineer the IDC system. The IMP and the associate Integrated Master Schedule (IMS) are used for planning, scheduling, executing, and tracking the project technical work efforts. REVISIONS Version Date Author/Team Revision Description Authorized by V1.0 12/2014 IDC Re- engineering Project Team Initial delivery M. Harris
Hierarchically Organized Iterative Solutions of the Evolution Equations in QCD
Jadach, S; Was, Z
2007-01-01
The task of Monte Carlo simulation of the evolution of the parton distributions in QCD and of constructing new parton shower Monte Carlo algorithms requires new way of organizing solutions of the QCD evolution equations, in which quark-gluon transitions on one hand and quark-quark or gluon-gluon transitions (pure gluonstrahlung) on the other hand, are treated separately and differently. This requires certain reorganization of the iterative solutions of the QCD evolution equations and leads to what we refer to as a hierarchic iterative solutions of the evolution equations. We present three formal derivations of such a solution. Results presented here are already used in the other recent works to formulate new MC algorithms for the parton-shower-like implementations of the QCD evolution equations. They are primarily of the non-Markovian type. However, such a solution can be used for the Markovian-type MCs as well. We also comment briefly on the relation of the presented formalism to similar methods used in othe...
2013-01-01
Desarrollo de una aplicación en Android que sea totalmente funcional. En este caso nos hemos propuesto desarrollar el juego MasterMind, un clásico de los juegos de mesa, pero adaptándolo a las nuevas tecnologías que nos permitirán darle una orientación social al estilo de Apalabrados o Mezcladitos. Desenvolupament d'una aplicació en Android que sigui totalment funcional. En aquest cas ens hem proposat desenvolupar el joc MasterMind, un clàssic dels jocs de taula, però adaptant-lo a les nov...
Directory of Open Access Journals (Sweden)
Vladimir Lipunov
2010-01-01
Full Text Available The main goal of the MASTER-Net project is to produce a unique fast sky survey with all sky observed over a single night down to a limiting magnitude of 19-20. Such a survey will make it possible to address a number of fundamental problems: search for dark energy via the discovery and photometry of supernovae (including SNIa, search for exoplanets, microlensing effects, discovery of minor bodies in the Solar System, and space-junk monitoring. All MASTER telescopes can be guided by alerts, and we plan to observe prompt optical emission from gamma-ray bursts synchronously in several filters and in several polarization planes.
Energy Technology Data Exchange (ETDEWEB)
Plane, J. M. C.; Whalley, C. L.; Goddard, A. [School of Chemistry, University of Leeds, Leeds LS2 9JT (United Kingdom); Frances-Soriano, L. [School of Chemistry, University of Leeds, Leeds LS2 9JT (United Kingdom); Department of Physical Chemistry, University of Valencia, Valencia 46100 (Spain); Harvey, J. N.; Glowacki, D. R. [Centre for Computational Chemistry, University of Bristol, Bristol BS8 1TS (United Kingdom); Viggiano, A. A. [Air Force Research Laboratory, Kirtland AFB, New Mexico 87117 (United States)
2012-07-07
complex, suggesting that this reaction proceeds mostly by near-resonant electronic energy transfer to Fe(a{sup 5}F) + O{sub 2}(X). The reaction of Ca + O{sub 2}(a) occurs in an intermediate regime with two competing pressure dependent channels: (1) a recombination to produce CaO{sub 2}({sup 1}A{sub 1}), and (2) a singlet/triplet non-adiabatic hopping channel leading to CaO + O({sup 3}P). In order to interpret the Ca + O{sub 2}(a) results, we utilized density functional theory along with multireference and explicitly correlated CCSD(T)-F12 electronic structure calculations to examine the lowest lying singlet and triplet surfaces. In addition to mapping stationary points, we used a genetic algorithm to locate minimum energy crossing points between the two surfaces. Simulations of the Ca + O{sub 2}(a) kinetics were then carried out using a combination of both standard and non-adiabatic Rice-Ramsperger-Kassel-Marcus (RRKM) theory implemented within a weak collision, multiwell master equation model. In terms of atmospheric significance, only in the case of Ca does reaction with O{sub 2}(a) compete with O{sub 3} during the daytime between 85 and 110 km.
Bendisch, J.; Bunte, K.; Klinkrad, H.; Krag, H.; Martin, C.; Sdunnus, H.; Walker, R.; Wegener, P.; Wiedemann, C.
2004-01-01
Meteoroid and Space Debris Terrestrial Reference model (MASTER) is the European particulate environment and risk assessment model. It is based on quasi-deterministic principles, using comprehensive orbit propagation theories and volume discretisation techniques, to derive spatial density and velocity distributions in a three-dimensional control volume ranging from LEO to GEO altitudes. The new release, MASTER-2001, incorporates new modelling and validation approaches and enables the calculation of fluxes on targets operating between the year 1957 and 2050, using detailed simulation results. This could be achieved by using not only the POEM simulation tool for the past to present debris populations, but also applying the long term prediction tool DELTA to obtain future populations. The paper describes the features and results of the MASTER-2001 model, and the updated modelling approach (e.g., the use of a new fragmentation model). The historical and future evolution of the space debris environment in terms of spatial density and object fluxes as given by MASTER-2001 are presented and discussed.
Thorn, Alan
2015-01-01
Mastering Unity Scripting is an advanced book intended for students, educators, and professionals familiar with the Unity basics as well as the basics of scripting. Whether you've been using Unity for a short time or are an experienced user, this book has something important and valuable to offer to help you improve your game development workflow.
Hvorfor master i medborgerskab?
DEFF Research Database (Denmark)
Korsgaard, Ove
2002-01-01
Danmarks Pædagogiske Universitet planlægger i samarbejde med Syddansk Universitet at udbyde en master i medborgerskab: etisk og demokratisk dannelse. Artiklens forfatter gør rede for nogle af de tanker, der ligger bag uddannelsen, og belyser, hvorfor medborgerskab er blevet et nøglebegreb i nyere...
Hvorfor master i medborgerskab?
DEFF Research Database (Denmark)
Korsgaard, Ove
2002-01-01
Danmarks Pædagogiske Universitet planlægger i samarbejde med Syddansk Universitet at udbyde en master i medborgerskab: etisk og demokratisk dannelse. Artiklens forfatter gør rede for nogle af de tanker, der ligger bag uddannelsen, og belyser, hvorfor medborgerskab er blevet et nøglebegreb i nyere...
Groner, Loiane
2013-01-01
Designed to be a structured guide, Mastering Ext JS is full of engaging examples to help you learn in a practical context.This book is for developers who are familiar with using Ext JS who want to augment their skills to create even better web applications.
Allegra, Carmen J.
2015-01-01
During the past decade, biomedical technologies have undergone an explosive evolution---from the publication of the first complete human genome in 2003, after more than a decade of effort and at a cost of hundreds of millions of dollars---to the present time, where a complete genomic sequence can be available in less than a day and at a small fraction of the cost of the original sequence. The widespread availability of next generation genomic sequencing has opened the door to the development of precision oncology. The need to test multiple new targeted agents both alone and in combination with other targeted therapies, as well as classic cytotoxic agents, demand the development of novel therapeutic platforms (particularly Master Protocols) capable of efficiently and effectively testing multiple targeted agents or targeted therapeutic strategies in relatively small patient subpopulations. Here, we describe the Master Protocol concept, with a focus on the expected gains and complexities of the use of this design. An overview of Master Protocols currently active or in development is provided along with a more extensive discussion of the Lung Master Protocol (Lung-MAP study). PMID:26433553
From Markovian semigroup to non-Markovian quantum evolution
Chruściński, D.; Kossakowski, A.
2012-01-01
We provided a class of legitimate memory kernels leading to completely positive trace-preserving dynamical maps. Our construction is based on a simple normalization procedure. Interestingly, when applied to a classical system it gives rise to semi-Markov evolution. Therefore, it may be considered as a quantum version of semi-Markov dynamics which is much more general than Markovian dynamics.
Non-Markovian State-Dependent Networks in Critical Loading
2015-02-04
waiting times. Queueing Syst. Theory Appl. 1990, 6, 335–351. 21. Yamada, K. Diffusion approximation for open state-dependent queueing networks in the heavy...Critical Loading We establish a heavy traffic limit theorem for the queue -length process in a critically loaded single class queueing network with state...Title We establish a heavy traffic limit theorem for the queue -length process in a critically loaded single class queueing network with state
Non-Markovian quantum feedback networks II: Controlled flows
Gough, John E.
2017-06-01
The concept of a controlled flow of a dynamical system, especially when the controlling process feeds information back about the system, is of central importance in control engineering. In this paper, we build on the ideas presented by Bouten and van Handel [Quantum Stochastics and Information: Statistics, Filtering and Control (World Scientific, 2008)] and develop a general theory of quantum feedback. We elucidate the relationship between the controlling processes, Z, and the measured processes, Y, and to this end we make a distinction between what we call the input picture and the output picture. We should note that the input-output relations for the noise fields have additional terms not present in the standard theory but that the relationship between the control processes and measured processes themselves is internally consistent—we do this for the two main cases of quadrature measurement and photon-counting measurement. The theory is general enough to include a modulating filter which post-processes the measurement readout Y before returning to the system. This opens up the prospect of applying very general engineering feedback control techniques to open quantum systems in a systematic manner, and we consider a number of specific modulating filter problems. Finally, we give a brief argument as to why most of the rules for making instantaneous feedback connections [J. Gough and M. R. James, Commun. Math. Phys. 287, 1109 (2009)] ought to apply for controlled dynamical networks as well.
Characterization of the degree of Musical non-Markovianity
Mannone, Maria; Compagno, Giuseppe
2013-01-01
Recently, as an aid for musical analysis, in computational musicology mathematical and informatics tools have been developed to quantitatively characterize some aspects of musical compositions. To a musical composition can be attributed by ear a certain amount of memory. This results associated to repetitions and similarities of the patterns in musical scores. To higher variations, a lower amount of memory is perceived. However musical memory of a score has never been quantitatively defined. ...
Non-Markovian State-Dependent Networks in Critical Loading
2013-01-23
Stochastics Rep., 40(1-2):43–76, 1992. [11] T. G. Kurtz. Strong approximation theorems for density dependent Markov chains . Stochastic Processes Appl., 6(3...for queue -length processes in critically loaded single class queueing networks with state-dependent arrival and service rates. A distinguishing...loading Report Title ABSTRACT We establish heavy traffic limit theorems for queue -length processes in critically loaded single class queueing networks
c -number quantum generalized Langevin equation for an open system
Kantorovich, L.; Ness, H.; Stella, L.; Lorenz, C. D.
2016-11-01
We derive a c -number generalized Langevin equation (GLE) describing the evolution of the expectation values xixit of the atomic position operators xi of an open system. The latter is coupled linearly to a harmonic bath kept at a fixed temperature. The equations of motion contain a non-Markovian friction term with the classical kernel [L. Kantorovich, Phys. Rev. B 78, 094304 (2008), 10.1103/PhysRevB.78.094304] and a zero mean non-Gaussian random force with correlation functions that depend on the initial preparation of the open system. We used a density operator formalism without assuming that initially the combined system was decoupled. The only approximation made in deriving quantum GLE consists of assuming that the Hamiltonian of the open system at time t can be expanded up to the second order with respect to operators of atomic displacements ui=xi-t (the "harmonization" approximation). The noise is introduced to ensure that sampling many quantum GLE trajectories yields exactly the average one. An explicit expression for the pair correlation function of the noise, consistent with the classical limit, is also proposed. Unlike the usually considered quantum operator GLE, the proposed c -number quantum GLE can be used in direct molecular dynamic simulations of open systems under general equilibrium or nonequilibrium conditions.
Completely positive maps with memory
Daffer, S; Cresser, J D; McIver, J K; Daffer, Sonja; Wodkiewicz, Krzysztof; Cresser, James D.; Iver, John K. Mc
2003-01-01
The prevailing description for dissipative quantum dynamics is given by the Lindblad form of a Markovian master equation, used under the assumption that memory effects are negligible. However, in certain physical situations, the master equation is essentially of a non-Markovian nature. This paper examines master equations that possess a memory kernel, leading to a replacement of white noise by colored noise. The conditions under which this leads to a completely positive, trace-preserving map are discussed for an exponential memory kernel. A physical model that possesses such an exponential memory kernel is presented. This model contains a classical, fluctuating environment based on random telegraph signal stochastic variables.
Podvorotniy, P.; Balanutsa, P.; Lipunov, V.; Shumkov, V.; Gorbovskoy, E.; Tiurina, N.; Kornilov, V.; Belinski, A.; Shatskiy, N.; Chazov, V.; Kuznetsov, A.; Krushinsky, V.; Zimnukhov, D.; Zalozhnih, I.; Ivanov, K.; Popov, A.; Yazev, S.; Budnev, N.; Konstantinov, E.; Chuvalaev, O.; Poleshchuk, V.; Parkhomenko, A.; Gress, O.; Tlatov, A.; Dormidontov, D.; Yurkov, V.; Senik, V.; Sergienko, Y.; Varda, D.; Sinyakov, E.; Shurpakov, S.; Levato, Hugo; Saffe, Carlos; Mallamaci, Claudio; Lopez, Carlos; Podest, Federico
2012-03-01
MASTER163105.47+615548.4 - PSN MASTER-Tunka auto-detection system discovered OT source at (RA, Dec) = 16h 31m 05.47s +61d 55m 48.4s on 2012-03-14.83877 UT. The OT unfiltered magnitude is 18.1m (limit 19.8m). The OT is seen in 5 images. There is no minor planet at this place. There is one nonstar object in The Guide Star Catalog N4HU009709 with 1.3 arcsec offset (jmag=21.9). We have reference image without OT on 2011-05-01.72794 UT with unfiltered magnitude limit 20.1m.
Clark, Kelly
2004-01-01
In painting and drawing classes, it is typical to ask students to work directly from a master. It is one way to study composition techniques, and to become familiar with classical style firsthand. In museums, easels are set up as artists work, not in an attempt to copy or plagiarize, but in an attempt to be part of history by participating in it.…
Neeraj, Nishant
2013-01-01
Mastering Apache Cassandra is a practical, hands-on guide with step-by-step instructions. The smooth and easy tutorial approach focuses on showing people how to utilize Cassandra to its full potential.This book is aimed at intermediate Cassandra users. It is best suited for startups where developers have to wear multiple hats: programmer, DevOps, release manager, convincing clients, and handling failures. No prior knowledge of Cassandra is required.
Kuc, Rafal
2013-01-01
A practical tutorial that covers the difficult design, implementation, and management of search solutions.Mastering ElasticSearch is aimed at to intermediate users who want to extend their knowledge about ElasticSearch. The topics that are described in the book are detailed, but we assume that you already know the basics, like the query DSL or data indexing. Advanced users will also find this book useful, as the examples are getting deep into the internals where it is needed.
Transparency masters for mathematics revealed
Berman, Elizabeth
1980-01-01
Transparency Masters for Mathematics Revealed focuses on master diagrams that can be used for transparencies for an overhead projector or duplicator masters for worksheets. The book offers information on a compilation of master diagrams prepared by John R. Stafford, Jr., audiovisual supervisor at the University of Missouri at Kansas City. Some of the transparencies are designed to be shown horizontally. The initial three masters are number lines and grids that can be used in a mathematics course, while the others are adaptations of text figures which are slightly altered in some instances. The
Palamar, Todd
2011-01-01
The exclusive, official guide to the very latest version of Maya Get extensive, hands-on, intermediate to advanced coverage of Autodesk Maya 2012, the top-selling 3D software on the market. If you already know Maya basics, this authoritative book takes you to the next level. From modeling, texturing, animation, and visual effects to high-level techniques for film, television, games, and more, this book provides professional-level Maya instruction. With pages of scenarios and examples from some of the leading professionals in the industry, author Todd Palamar will help you master the entire CG
Keller, Eric
2010-01-01
A beautifully-packaged, advanced reference on the very latest version of Maya. If you already know the basics of Maya, the latest version of this authoritative book takes you to the next level. From modeling, texturing, animation, and visual effects to high-level techniques for film, television, games, and more, this book provides professional-level Maya instruction. With pages of scenarios and examples from some of the leading professionals in the industry, this book will help you master the entire CG production pipeline.: Provides professional-level instruction on Maya, the industry-leading
Fractional Chemotaxis Diffusion Equations
Langlands, T A M
2010-01-01
We introduce mesoscopic and macroscopic model equations of chemotaxis with anomalous subdiffusion for modelling chemically directed transport of biological organisms in changing chemical environments with diffusion hindered by traps or macro-molecular crowding. The mesoscopic models are formulated using Continuous Time Random Walk master equations and the macroscopic models are formulated with fractional order differential equations. Different models are proposed depending on the timing of the chemotactic forcing. Generalizations of the models to include linear reaction dynamics are also derived. Finally a Monte Carlo method for simulating anomalous subdiffusion with chemotaxis is introduced and simulation results are compared with numerical solutions of the model equations. The model equations developed here could be used to replace Keller-Segel type equations in biological systems with transport hindered by traps, macro-molecular crowding or other obstacles.
Energy Technology Data Exchange (ETDEWEB)
Antila, E.; Kaario, O.; Lahtinen, T. (and others)
2004-07-01
This is the final report of the research project 'Mastering the Diesel Process'. The project has been a joint research effort of the Helsinki University of Technology, the Tampere University of Technology, the Technical Research Centre of Finland, and the Aabo Akademi University. Moreover, the contribution of the Michigan Technological University has been important. The project 'Mastering the Diesel Process' has been a computational research project on the physical phenomena of diesel combustion. The theoretical basis of the project lies on computational fluid dynamics. Various submodels for computational fluid dynamics have been developed or tested within engine simulation. Various model combinations in three diesel engines of different sizes have been studied. The most important submodels comprise fuel spray drop breakup, fuel evaporation, gas-fuel interaction in the spray, mixing model of combustion, heat transfer, emission mechanisms. The boundary conditions and flow field modelling have been studied, as well. The main simulation tool have been Star-CD. KIVA code have been used in the model development, as well. By the help of simulation, we are able to investigate the effect of various design parameters or operational parameters on diesel combustion and emission formation. (orig.)
What about Master's Students? The Master's Student Persistence Model
Cohen, Kristin E.
2012-01-01
This study was designed to investigate the factors that affect master's student persistence in the United States. More specifically, this study explored whether the following factors: students' background, institution's, academic, environmental and psychological influences, had a significant effect on whether a master's student persisted and/or…
Explorations into quantum state diffusion beyond the Markov approximation
Broadbent, Curtis J.; Jing, Jun; Yu, Ting; Eberly, Joseph H.
2011-05-01
The non-Markovian quantum state diffusion equation is rapidly becoming a powerful tool for both theoretical and numerical investigations into non-trivial problems in quantum optical QED. It has been used to rederive the exact master equation for quantum Brownian motion, as well as an optical cavity or a two-level atom which is either damped or dephased under the rotating wave approximation. The exact quantum state diffusion equations for the spin-1 system have also been found, and general theorems have now been derived for solving the N-cavity, N-qubit, and N-level systems. Here, we build upon the results of Ref. to explore other problems from quantum optical QED using the non-Markovian quantum state diffusion equation.
DEFF Research Database (Denmark)
Laursen, Steffen
2010-01-01
led to a number of insights into the social organization of the mound cemeteries that will be presented in the paper. It is obvious that there existed a close spatial relation between freshwater springs and the compact mounds cemeteries that emerged c.2050 BC. The mound cemeteries appear to have been...... flanked by villages that relied on these water recourses for agricultural production. The springs emerged in the zone separating the cemeteries from the settlements. The freshwater springs were actively incorporated into the religious landscape of the dead, by consistently erecting mounds of a particular...... high status type right above the head of each spring. These tombs of the masters of the springs are distinguished by their larger size and vertical shaft entrance. It is argued that this particular strategy of power was employed after population growth had intensified conflicts over the rights...
DEFF Research Database (Denmark)
Christensen, Andreas Aagaard
2013-01-01
The environmental history of New Zealand is one of the clearest and most recent examples of the way humans make a home for themselves in newly explored territory. New Zealand was the last major land area in the world to be colonised by people and, given its extraordinary natural history, the first...... as Europeans. This fact makes their success in forging cultural landscapes from the new land all the more interesting for students of environmental history. As an example of such processes, New Zealand illustrates the way human newcomers learn to master an environment, change the land and its resources...... resources which change as the society itself changes. Newcomers to any environment meet it with a set of technologies and a culture which they bring with them and which changes continuously, as it aligns with experience gathered in that environment. The environmental histories told from a multiplicity...
Masters change, slaves remain.
Graham, Patricia; Penn, Jill K M; Schedl, Paul
2003-01-01
Sex determination offers an opportunity to address many classic questions of developmental biology. In addition, because sex determination evolves rapidly, it offers an opportunity to investigate the evolution of genetic hierarchies. Sex determination in Drosophila melanogaster is controlled by the master regulatory gene, Sex lethal (Sxl). DmSxl controls the alternative splicing of a downstream gene, transformer (tra), which acts with tra2 to control alternative splicing of doublesex (dsx). DmSxl also controls its own splicing, creating an autoregulatory feedback loop that ensures expression of Sxl in females, but not males. A recent paper has shown that in the dipteran Ceratitis capitata later (downstream) steps in the regulatory hierarchy are conserved, while earlier (upstream) steps are not. Cctra is regulated by alternative splicing and apparently controls the alternative splicing of Ccdsx. However, Cctra is not regulated by CcSxl. Instead it appears to autoregulate in a manner similar to the autoregulation seen with DmSxl.
Bommier, Véronique
2016-06-01
Context. The spectrum of the linear polarization, which is formed by scattering and observed on the solar disk close to the limb, is very different from the intensity spectrum and thus able to provide new information, in particular about anisotropies in the solar surface plasma and magnetic fields. In addition, a large number of lines show far wing polarization structures assigned to partial redistribution (PRD), which we prefer to denote as Rayleigh/Raman scattering. The two-level or two-term atom approximation without any lower level polarization is insufficient for many lines. Aims: In the previous paper of this series, we presented our theory generalized to the multilevel and multiline atom and comprised of statistical equilibrium equations for the atomic density matrix elements and radiative transfer equation for the polarized radiation. The present paper is devoted to applying this theory to model the second solar spectrum of the Na i D1 and D2 lines. Methods: The solution method is iterative, of the lambda-iteration type. The usual acceleration techniques were considered or even applied, but we found these to be unsuccessful, in particular because of nonlinearity or large number of quantities determining the radiation at each depth. Results: The observed spectrum is qualitatively reproduced in line center, but the convergence is yet to be reached in the far wings and the observed spectrum is not totally reproduced there. Conclusions: We need to investigate noniterative resolution methods. The other limitation lies in the one-dimensional (1D) atmosphere model, which is unable to reproduce the intermittent matter structure formed of small loops or spicules in the chromosphere. This modeling is rough, but the computing time in the presence of hyperfine structure and PRD prevents us from envisaging a three-dimensional (3D) model at this instant.
On master integrals for two loop Bhabha scattering
Czakon, M; Riemann, Tord
2004-01-01
All scalar master integrals (MIs) for massive 2-loop QED Bhabha scattering are identified. The 2- and 3-point MIs have been calculated in terms of harmonic polylogarithms with the differential equation method. The calculation of 4-point MIs is underway. We sketch some alternative methods which help to solve (mainly) singularities of some MIs.
On master integrals for two loop Bhabha scattering
Energy Technology Data Exchange (ETDEWEB)
Czakon, M.; Gluza, J. [Uniwersytet Slaski, Katowice (Poland). Inst. Fizyki; Riemann, T.
2004-09-01
All scalar master integrals (MIs) for massive 2-loop QED Bhabha scattering are identified. The 2- and 3-point MIs have been calculated in terms of harmonic polylogarithms with the differential equation method. The calculation of 4-point MIs is underway. We sketch some alternative methods which help to solve (mainly) singularities of some MIs. (orig.)
Lambert, Chip
2015-01-01
You've started down the path of jQuery Mobile, now begin mastering some of jQuery Mobile's higher level topics. Go beyond jQuery Mobile's documentation and master one of the hottest mobile technologies out there. Previous JavaScript and PHP experience can help you get the most out of this book.
Paga Marrero, Hector Jose
2013-01-01
The Master Console oversees the function of Computer Systems in Firing room 1 (FR1). Master Console Operators, MCOs' for short, are our customer. I was integrated into the System Monitoring and Control (SMC) software team that is under the guidance of David Slaiman, who is the product group lead. I have been brought up to speed with System Monitoring and Control. The initial time spent reading SMC software design description and understanding how it works. The current Firing Room 1 Console Display is a floor layout giving the MCO two essential pieces of information which are Health and Status. When an issue arises, the MCO has to look on the display to find which console is affected and then the MCO must use the Reference designator from the display to manually search for the Portal Workstation (PWS) installed in the console using the hardware map; which is a long process to lookup a PWS if an issue is present. My project is to make the FR1 Console Display easier for the MCO's to pinpoint PWS's without having to lookup additional resources in the process. My project also includes updating Firing Room 1 Console Display to include the F1R Non-Redundant Set. The display does not have good use of space and functionality. PWS numbers were not present in the previous design and are the critical component in efficient understanding and administration of the consoles. Part of the process includes getting feedback from the customer, instead of just emailing them with a question, we made a proposal with changes so they could respond and give us their input; which proved to be an effective method for engaging them. In order to do this I had to use the Display Editor (DE) tool developed by NASA, Paint.Net and Visio. The process I have been using has been Visio to alter the floor layout of Firing Room and take advantage of the white areas, and then I take the altered floor plan into Paint.Net. Once in Paint.Net I put the new floor plan as a background to the standard console
``Mastering`` the global commons
Energy Technology Data Exchange (ETDEWEB)
Stehr, N. [British Columbia Univ., Vancouver, BC (Canada). Peter Wall Inst. for Advanced Studies and Green Coll.
1999-11-01
The question of ``mastering`` the global commons will increasingly become a central socio-political issue, if it has not already attained this status. For example, the dilemmas brought about by anthropogenic climate change are in many ways unprecedented. They call for massive efforts to plan global climate change. In this context, knowledge about the physical nature of global climate changes is adequate in order to move from a comprehension to a solution of the problem. The record shows that past generations, too, have been fascinated with and concerned about the impact of climate on society, as well as, anthropogenic climate change. But these efforts have, for the most part, been informed by the doctrine of climate determinism. In much the same vein, the concept of climate policies as an ``optimal control problem`` is inadequate. Impact research has to be cognizant of the social construct of climate, as well as, fundamental secular societal changes that profoundly alter modern societies and the value orientations of its citizens. Climate policies as a form of large-scale and deliberate climate change, therefore, have to draw extensively on social science expertise. (orig.) 53 refs.
Learning profiles of Master students
DEFF Research Database (Denmark)
Sprogøe, Jonas; Hemmingsen, Lis
2005-01-01
at DPU in 2001 several evaluations and research have been carried out on several topics relating to form, content, and didactics, but one important focus is missing: the research about the psychological profile and learning style of the master student. Knowledge is lacking on how teaching methods...... and programme designs relate to and support the learning profiles and learning styles of the master students. In other words: What are the consequences of the students' learning styles in terms of planning and teaching in the master programme?...
2011-01-01
750 x 1159 pixels. 300 ppi. RGB Poster for a production of Carlo Goldoni's "A Servant of Two Masters," directed by David Johnson, and produced at Virginia Tech's Squires Studio Theatre for the 2011-2012 season.
Enhanced Master Station History Report
National Oceanic and Atmospheric Administration, Department of Commerce — The Enhanced Master Station History Report (EMSHR) is a compiled list of basic, historical information for every station in the station history database, beginning...
STS-107 Master Experiment List
2002-12-01
A master list of the various experiments conducted aboard the STS-107 Space Mission is presented. The topics include: 1) Biology; 2) Earth and Space Sciences; 3) Physical Sciences; 4) Space Product Development; and 6) Technology Development.
Masters in clinical veterinary research.
Barr, Frances
2016-08-20
A new masters qualification from the BSAVA aims to encourage and support clinical research in practice. As Frances Barr explains, it is aimed at those looking for a professional challenge. British Veterinary Association.
DEFF Research Database (Denmark)
Danielsen, Oluf
2004-01-01
The Master in ICT and Learning (MIL)was started in 2000, and it is owned in collaboration by five Danish universities. It is an accredited virtual part-time 2-year education. MIL is unique in that it builds on the pedagogical framework of project pedagogy and is based in virtual collaboration....... It is organized around ICT and Learning. This is illustrated through a presentation of the study program, the four modules, the projects and the master thesis....
Dual arm master controller concept
Energy Technology Data Exchange (ETDEWEB)
Kuban, D.P.; Perkins, G.S.
1984-01-01
The Advanced Servomanipulator (ASM) slave was designed with an anthropomorphic stance, gear/torque tube power drives, and modular construction. These features resulted in increased inertia, friction, and backlash relative to tape-driven manipulators. Studies were performed which addressed the human factors design and performance trade-offs associated with the corresponding master controller best suited for the ASM. The results of these studies, as well as the conceptual design of the dual arm master controller, are presented. 6 references, 3 figures.
2010-10-01
... 46 Shipping 1 2010-10-01 2010-10-01 false Master. 15.805 Section 15.805 Shipping COAST GUARD....805 Master. (a) There must be an individual holding an appropriate license as or a valid MMC with endorsement as master master in command of each of the following vessels: (1) Every self-propelled,...
Enhanced Master Controller Unit Tester
Benson, Patricia; Johnson, Yvette; Johnson, Brian; Williams, Philip; Burton, Geoffrey; McCoy, Anthony
2007-01-01
The Enhanced Master Controller Unit Tester (EMUT) software is a tool for development and testing of software for a master controller (MC) flight computer. The primary function of the EMUT software is to simulate interfaces between the MC computer and external analog and digital circuitry (including other computers) in a rack of equipment to be used in scientific experiments. The simulations span the range of nominal, off-nominal, and erroneous operational conditions, enabling the testing of MC software before all the equipment becomes available.
Mastering IDEAScript the definitive guide
Mueller, John Paul
2011-01-01
With approximately 44,000 users in the U.S. and Canada, as well as 42,000 in Europe, IDEA software has become a leading provider of data analysis software for use by auditors and accountants. Written to provide users with a quick access guide for optimal use of IDEAScript, Mastering IDEAScript: The Definitive Guide is IDEA's official guide to mastering IDEAScript, covering essential topics such as Introducing IDEAScript, Understanding the Basics of IDEAScript Editor, Designing Structured Applications, Understanding IDEA Databases and much more. For auditors, accountants and controllers.
Dual arm master controller development
Energy Technology Data Exchange (ETDEWEB)
Kuban, D.P.; Perkins, G.S.
1985-01-01
The advanced servomanipulator (ASM) slave was designed with an anthropomorphic stance, gear/torque tube power drives, and modular construction. These features resulted in increased inertia, friction, and backlash relative to tape-driven manipulators. Studies were performed which addressed the human factors design and performance trade-offs associated with the corresponding master controller best suited for the ASM. The results of these studies, as well as the conceptual design of the dual arm master controller, are presented. This work was performed as part of the Consolidated Fuel Reprocessing Program at the Oak Ridge National Laboratory. 5 refs., 7 figs., 1 tab.
Hood River Production Master Plan.
Energy Technology Data Exchange (ETDEWEB)
O' Toole, Patty
1991-07-01
The Northwest Power Planning Council's 1987 Columbia River Fish and Wildlife Program authorizes the development of artificial production facilities to raise chinook salmon and steelhead for enhancement in the Hood, Umatilla, Walla Walla, Grande Ronde and Imnaha rivers and elsewhere. On February 26, 1991 the Council agreed to disaggregate Hood River from the Northeast Oregon Hatchery Project, and instead, link the Hood River Master Plan (now the Hood River Production Plan) to the Pelton Ladder Project (Pelton Ladder Master Plan 1991).
Mastering Ninject for dependency injection
Baharestani, Daniel
2013-01-01
Mastering Ninject for Dependency Injection teaches you the most powerful concepts of Ninject in a simple and easy-to-understand format using lots of practical examples, diagrams, and illustrations.Mastering Ninject for Dependency Injection is aimed at software developers and architects who wish to create maintainable, extensible, testable, and loosely coupled applications. Since Ninject targets the .NET platform, this book is not suitable for software developers of other platforms. Being familiar with design patterns such as singleton or factory would be beneficial, but no knowledge of depende
Balanutsa, P.; Gorbovskoy, E.; Lipunov, V.; Denisenko, D.; Tiurina, N.; Kornilov, V.; Belinski, A.; Shatskiy, N.; Chazov, V.; Kuznetsov, A.; Zimnukhov, D.; Krushinsky, V.; Zalozhnih, I.; Popov, A.; Bourdanov, A.; Punanova, A.; Ivanov, K.; Yazev, S.; Budnev, N.; Konstantinov, E.; Chuvalaev, O.; Poleshchuk, V.; Gress, O.; Parkhomenko, A.; Tlatov, A.; Dormidontov, D.; Senik, V.; Yurkov, V.; Sergienko, Y.; Varda, D.; Sinyakov, E.; Shumkov, V.; Shurpakov, S.; Levato, H.; Saffe, C.; Mallamaci, C.; Lopez, C.; Podest, F.
2012-09-01
OT MASTER J005552.55+261100.8 discovery MASTER-Amur auto-detection system discovered OT source at (RA, Dec) = 00h 55m 52.55s +26d 11m 00.8s on 2012-08-30.77359 UT by two tube simultaneously during 3 min exposition. The OT unfiltered magnitude is 14.2m (limit 18.0m). There is no minor planet at this place. There is no known satellite around 4 degrees at this time. There is one non star object NBKY021338 (jmag~ 22.3) in the Guide Star Catalog with 3.6 arcsec offset.
Master-slave micromanipulator apparatus
Morimoto, Alan K.; Kozlowski, David M.; Charles, Steven T.; Spalding, James A.
1999-01-01
An apparatus based on precision X-Y stages that are stacked. Attached to arms projecting from each X-Y stage are a set of two axis gimbals. Attached to the gimbals is a rod, which provides motion along the axis of the rod and rotation around its axis. A dual-planar apparatus that provides six degrees of freedom of motion precise to within microns of motion. Precision linear stages along with precision linear motors, encoders, and controls provide a robotics system. The motors can be positioned in a remote location by incorporating a set of bellows on the motors and can be connected through a computer controller that will allow one to be a master and the other one to be a slave. Position information from the master can be used to control the slave. Forces of interaction of the slave with its environment can be reflected back to the motor control of the master to provide a sense of force sensed by the slave. Forces import onto the master by the operator can be fed back into the control of the slave to reduce the forces required to move it.
Master-slave micromanipulator method
Morimoto, Alan K.; Kozlowski, David M.; Charles, Steven T.; Spalding, James A.
1999-01-01
A method based on precision X-Y stages that are stacked. Attached to arms projecting from each X-Y stage are a set of two axis gimbals. Attached to the gimbals is a rod, which provides motion along the axis of the rod and rotation around its axis. A dual-planar apparatus that provides six degrees of freedom of motion precise to within microns of motion. Precision linear stages along with precision linear motors, encoders, and controls provide a robotics system. The motors can be remotized by incorporating a set of bellows on the motors and can be connected through a computer controller that will allow one to be a master and the other one to be a slave. Position information from the master can be used to control the slave. Forces of interaction of the slave with its environment can be reflected back to the motor control of the master to provide a sense of force sensed by the slave. Forces import onto the master by the operator can be fed back into the control of the slave to reduce the forces required to move it.
El Camino College Master Plan.
El Camino Coll., Torrance, CA.
This document is the educational Master Plan for El Camino Community College District. The purpose of the plan is to develop a research-based document that will be used as a foundation for decisions regarding instructional programs, support services, staffing and facilities. It is intended to serve as the basic foundation for all other plans of…
Nutrition recommendations for masters athletes.
Rosenbloom, Christine A; Dunaway, Ann
2007-01-01
"More than 3000 masters athletes from 62 countries compete in Linz, Austria, in March of 2006." In 2005, 9000 "silver-haired Americans go for the gold." The National Senior Games Association announced a "major change in the NSGA rules affecting the game of basketball; a new age division of 80+ has been added for 2007."
Kawai, Shinnosuke; Komatsuzaki, Tamiki
2010-12-21
A framework recently developed for the extraction of a dynamic reaction coordinate to mediate reactions buried in a multidimensional Langevin equation is extended to the generalized Langevin equations without a priori assumption of the forms of the potential (in general, nonlinearly coupled systems) and the friction kernel. The equation of motion with memory effect can be transformed into an equation without memory at the cost of an increase in the dimensionality of the system, and hence the theoretical framework developed for the (nonlinear) Langevin formulation can be generalized to the non-Markovian process with colored noise. It is found that the increased dimension can be physically interpreted as effective modes of the fluctuating environment. As an illustrative example, we apply this theory to a multidimensional generalized Langevin equation for motion on the Müller-Brown potential surface with an exponential friction kernel. Numerical simulations find a boundary between the highly reactive region and the less reactive region in the space of initial conditions. The location of the boundary is found to depend significantly on both the memory kernel and the nonlinear couplings. The theory extracts a reaction coordinate whose sign determines the fate of the reaction taking into account thermally fluctuating environments, memory effect, and nonlinearities. It is found that the location of the boundary of reactivity is satisfactorily reproduced as the zero of the statistical average of the new reaction coordinate, which is an analytical functional of both the original position coordinates and velocities of the system, and of the properties of the environment.
Adequate bases of phase space master integrals for $gg \\to h$ at NNLO and beyond
Höschele, Maik; Ueda, Takahiro
2014-01-01
We study master integrals needed to compute the Higgs boson production cross section via gluon fusion in the infinite top quark mass limit, using a canonical form of differential equations for master integrals, recently identified by Henn, which makes their solution possible in a straightforward algebraic way. We apply the known criteria to derive such a suitable basis for all the phase space master integrals in afore mentioned process at next-to-next-to-leading order in QCD and demonstrate that the method is applicable to next-to-next-to-next-to-leading order as well by solving a non-planar topology. Furthermore, we discuss in great detail how to find an adequate basis using practical examples. Special emphasis is devoted to master integrals which are coupled by their differential equations.
Adequate bases of phase space master integrals for gg → h at NNLO and beyond
Höschele, Maik; Hoff, Jens; Ueda, Takahiro
2014-09-01
We study master integrals needed to compute the Higgs boson production cross section via gluon fusion in the infinite top quark mass limit, using a canonical form of differential equations for master integrals, recently identified by Henn, which makes their solution possible in a straightforward algebraic way. We apply the known criteria to derive such a suitable basis for all the phase space master integrals in afore mentioned process at next-to-next-to-leading order in QCD and demonstrate that the method is applicable to next-to-next-to-next-to-leading order as well by solving a non-planar topology. Furthermore, we discuss in great detail how to find an adequate basis using practical examples. Special emphasis is devoted to master integrals which are coupled by their differential equations.
Testing the Master Constraint Programme for Loop Quantum Gravity I. General Framework
Dittrich, B; Dittrich, Bianca; Thiemann, Thomas
2004-01-01
Recently the Master Constraint Programme for Loop Quantum Gravity (LQG) was proposed as a classically equivalent way to impose the infinite number of Wheeler -- DeWitt constraint equations in terms of a single Master Equation. While the proposal has some promising abstract features, it was until now barely tested in known models. In this series of five papers we fill this gap, thereby adding confidence to the proposal. We consider a wide range of models with increasingly more complicated constraint algebras, beginning with a finite dimensional, Abelean algebra of constraint operators which are linear in the momenta and ending with an infinite dimensional, non-Abelean algebra of constraint operators which closes with structure functions only and which are not even polynomial in the momenta. In all these models we apply the Master Constraint Programme successfully, however, the full flexibility of the method must be exploited in order to complete our task. This shows that the Master Constraint Programme has a w...
Analyzing a stochastic time series obeying a second-order differential equation.
Lehle, B; Peinke, J
2015-06-01
The stochastic properties of a Langevin-type Markov process can be extracted from a given time series by a Markov analysis. Also processes that obey a stochastically forced second-order differential equation can be analyzed this way by employing a particular embedding approach: To obtain a Markovian process in 2N dimensions from a non-Markovian signal in N dimensions, the system is described in a phase space that is extended by the temporal derivative of the signal. For a discrete time series, however, this derivative can only be calculated by a differencing scheme, which introduces an error. If the effects of this error are not accounted for, this leads to systematic errors in the estimation of the drift and diffusion functions of the process. In this paper we will analyze these errors and we will propose an approach that correctly accounts for them. This approach allows an accurate parameter estimation and, additionally, is able to cope with weak measurement noise, which may be superimposed to a given time series.
Non-adiabatic elimination of auxiliary modes in continuous quantum measurements
Yang, Huan; Chen, Yanbei
2011-01-01
When measuring a complex quantum system, we are often interested in only a few degrees of freedom-the plant, while the rest of them are collected as auxiliary modes-the bath. The bath can have finite memory (non-Markovian), and simply ignoring its dynamics, i.e., adiabatically eliminating it, is inadequate to predict the true quantum behavior of the plant. We generalize the technique introduced by Strunz et. al. [Phys. Rev. Lett 82, 1801 (1999)], and develop a formalism that allows us to eliminate the bath non-adiabatically in continuous quantum measurements, and derive a non-Markovian stochastic master equation for the plant alone. We apply this formalism to two interesting examples in cavity QED: (i) a two-level atom (a qubit) coupled to a cavity and (ii) linear optomechanical interaction, both of which can be exactly solved.
2010-10-01
... 46 Shipping 1 2010-10-01 2010-10-01 false Master (OSV). 11.493 Section 11.493 Shipping COAST GUARD... Professional Requirements for Deck Officers § 11.493 Master (OSV). (a) Except as provided by paragraph (b) of this section, to qualify for an endorsement as Master (OSV), an applicant shall present evidence...
2010-07-01
... 33 Navigation and Navigable Waters 1 2010-07-01 2010-07-01 false Master. 104.205 Section 104.205... SECURITY: VESSELS Vessel Security Requirements § 104.205 Master. (a) Nothing in this part is intended to permit the Master to be constrained by the Company, the vessel owner or operator, or any other...
Evolution of Master Planning of Tianjin
Institute of Scientific and Technical Information of China (English)
2008-01-01
<正>1.Review on previous master planning of Tianjin From 1953 to 1999,with thanks to the great attention of the Municipal Government of Tianjin to the work of master planning,there had been 21 draft master plans finished successively for Tianjin,
14 CFR 27.1361 - Master switch.
2010-01-01
... 14 Aeronautics and Space 1 2010-01-01 2010-01-01 false Master switch. 27.1361 Section 27.1361... STANDARDS: NORMAL CATEGORY ROTORCRAFT Equipment Electrical Systems and Equipment § 27.1361 Master switch. (a) There must be a master switch arrangement to allow ready disconnection of each electric power...
MASTER: 2 short optical transients
Balanutsa, P.; Lipunov, V.; Rebolo, R.; Serra-Ricart, M.; Buckley, D.; Gorbovskoy, E.; Tiurina, N.; Kuznetsov, A.; Popova, E.; Gress, O.; Kornilov, V.; Vladimirov, V.
2017-02-01
MASTER-IAC auto-detection system ( Lipunov et al., "MASTER Global Robotic Net", Advances in Astronomy, 2010, 30L ) discovered OT source at (RA, Dec) = 13h 30m 17.28s +78d 09m 51.8s on 2017-02-02.96362 UT. The OT is seen on 3 images with the following m_OT: 2017-02-02 23:03:55.905 18.57 2017-02-02 23:05:36.496 14.48 2017-02-02 23:07:37.042 14.92 We have reference image without OT on 2016-06-10.89789 UT with unfiltered magnitude limit 19.1m.
[Master course in biomedical engineering].
Jobbágy, Akos; Benyó, Zoltán; Monos, Emil
2009-11-22
The Bologna Declaration aims at harmonizing the European higher education structure. In accordance with the Declaration, biomedical engineering will be offered as a master (MSc) course also in Hungary, from year 2009. Since 1995 biomedical engineering course has been held in cooperation of three universities: Semmelweis University, Budapest Veterinary University, and Budapest University of Technology and Economics. One of the latter's faculties, Faculty of Electrical Engineering and Informatics, has been responsible for the course. Students could start their biomedical engineering studies - usually in parallel with their first degree course - after they collected at least 180 ECTS credits. Consequently, the biomedical engineering course could have been considered as a master course even before the Bologna Declaration. Students had to collect 130 ECTS credits during the six-semester course. This is equivalent to four-semester full-time studies, because during the first three semesters the curriculum required to gain only one third of the usual ECTS credits. The paper gives a survey on the new biomedical engineering master course, briefly summing up also the subjects in the curriculum.
Master classes - What do they offer?
Hanken, Ingrid Maria; Long, Marion
2012-01-01
Master classes are a common way to teach music performance, but how useful are they in helping young musicians in their musical development? Based on his experiences of master classes Lali (2003:24) states that “For better or for worse, master classes can be life-changing events.” Anecdotal evidence confirm that master classes can provide vital learning opportunities, but also that they can be of little use to the student, or worse, detrimental. Since master classes are a common component in ...
Fokker-Planck approach to stochastic delay differential equations
Guillouzic, Steve
2001-10-01
Models written in terms of stochastic delay differential equations (SDDE's) have recently appeared in a number of fields, such as physiology, optics, and climatology. Unfortunately, the development of a Fokker-Planck approach for these equations is being hampered by their non-Markovian nature. In this thesis, an exact Fokker- Planck equation (FPE) is formulated for univariate SDDE's involving Gaussian white noise. Although this FPE is not self-sufficient, it is found to be helpful in at least two different contexts: with a short delay approximation and under an appropriate separation of time scales. In the short delay approximation, a Taylor expansion is applied to an SDDE with nondelayed diffusion and yields a nondelayed stochastic differential equation. The aforementioned FPE then allows the derivation of an alternate and complementary approximation of the original SDDE. This method is illustrated with linear and logistic SDDE's. Under the separation of time scales assumption, the FPE of a bistable system is reduced to a form that is uniquely determined by the steady-state probability density when the diffusion term of the SDDE is nondelayed. In the context of an overdamped particle with delayed coupling to a symmetrical and stochastically driven potential, the resulting FPE is used with standard techniques to express the transition rate between wells in terms of the noise amplitude and of the steady-state probability density. The same is also accomplished for the mean first passage time from one point to another. This whole approach is then applied to the case of a quartic potential, for which all realisations eventually stabilise on an oscillatory trajectory with an ever increasing amplitude. Although this latter phenomenon prevents the existence of a steady-state limit, a pseudo- steady-state probability density can be defined and used instead of the non-existent steady-state one when the transition rate to these unbounded oscillatory trajectories is
Mansfield, Richard
2010-01-01
A comprehensive guide to the language used to customize Microsoft Office. Visual Basic for Applications (VBA) is the language used for writing macros, automating Office applications, and creating custom applications in Word, Excel, PowerPoint, Outlook, and Access. This complete guide shows both IT professionals and novice developers how to master VBA in order to customize the entire Office suite for specific business needs.: Office 2010 is the leading productivity suite, and the VBA language enables customizations of all the Office programs; this complete guide gives both novice and experience
Institute of Scientific and Technical Information of China (English)
王良华
2007-01-01
Mr Smith was a boss of a butcher's shop(肉店). One day a hungry dog came to the shop. The dog wagged(摇动) its tail again and again. The boss gave it some meat to eat. So later on, the dog always stayed with the owner and looked upon him as its own master. When the people found that the boss was friendly(友好) to the dog, they thought Mr Smith could be trusted. As time passed by, more and more customers(顾客) came to buy fresh meat(鲜肉). And he was getting richer and richer.
Directory of Open Access Journals (Sweden)
Uroš Lobnik
1999-01-01
Full Text Available The Maribor Town plan project began in 1995. The elaborate analytical part was directed into recognising and establishing key problems in the town and guidelines for their solution. Expert guidelines were elaborated and presented as conceptual ideas, easily understood by professionals and lay-people. The concept of the master plan or town plan as such is based on the division and connection of the four parts of the town. In the concluding remarks certain ideas on improving the planning system are presented.
Mastering Microsoft Azure infrastructure services
Savill, John
2015-01-01
Understand, create, deploy, and maintain a public cloud using Microsoft Azure Mastering Microsoft Azure Infrastructure Services guides you through the process of creating and managing a public cloud and virtual network using Microsoft Azure. With step-by-step instruction and clear explanation, this book equips you with the skills required to provide services both on-premises and off-premises through full virtualization, providing a deeper understanding of Azure's capabilities as an infrastructure service. Each chapter includes online videos that visualize and enhance the concepts presented i
Magnus, Wilhelm
2004-01-01
The hundreds of applications of Hill's equation in engineering and physics range from mechanics and astronomy to electric circuits, electric conductivity of metals, and the theory of the cyclotron. New applications are continually being discovered and theoretical advances made since Liapounoff established the equation's fundamental importance for stability problems in 1907. Brief but thorough, this volume offers engineers and mathematicians a complete orientation to the subject.""Hill's equation"" connotes the class of homogeneous, linear, second order differential equations with real, period
Diophantine approximations and Diophantine equations
Schmidt, Wolfgang M
1991-01-01
"This book by a leading researcher and masterly expositor of the subject studies diophantine approximations to algebraic numbers and their applications to diophantine equations. The methods are classical, and the results stressed can be obtained without much background in algebraic geometry. In particular, Thue equations, norm form equations and S-unit equations, with emphasis on recent explicit bounds on the number of solutions, are included. The book will be useful for graduate students and researchers." (L'Enseignement Mathematique) "The rich Bibliography includes more than hundred references. The book is easy to read, it may be a useful piece of reading not only for experts but for students as well." Acta Scientiarum Mathematicarum
EVALUATION OF THE MASTER MARKETER NEWSLETTER
McCorkle, Dean A.; Waller, Mark L.; Amosson, Stephen H.; Smith, Jackie; Bevers, Stanley J.; Borchardt, Robert
2001-01-01
Several support programs have been developed to help support, reinforce, enhance, and improve the effectiveness of the educational experience of Master Marketer graduates and other marketing club participants. One of those products, the Master Marketer Newsletter, is currently mailed to over 700 Master Marketer graduates and Extension faculty on a quarterly basis. In the June 2000 newsletter, a questionnaire was sent to newsletter recipients asking them to evaluate the various sections of the...
Tsuchimoto, Masashi; Tanimura, Yoshitaka
2015-08-11
A system with many energy states coupled to a harmonic oscillator bath is considered. To study quantum non-Markovian system-bath dynamics numerically rigorously and nonperturbatively, we developed a computer code for the reduced hierarchy equations of motion (HEOM) for a graphics processor unit (GPU) that can treat the system as large as 4096 energy states. The code employs a Padé spectrum decomposition (PSD) for a construction of HEOM and the exponential integrators. Dynamics of a quantum spin glass system are studied by calculating the free induction decay signal for the cases of 3 × 2 to 3 × 4 triangular lattices with antiferromagnetic interactions. We found that spins relax faster at lower temperature due to transitions through a quantum coherent state, as represented by the off-diagonal elements of the reduced density matrix, while it has been known that the spins relax slower due to suppression of thermal activation in a classical case. The decay of the spins are qualitatively similar regardless of the lattice sizes. The pathway of spin relaxation is analyzed under a sudden temperature drop condition. The Compute Unified Device Architecture (CUDA) based source code used in the present calculations is provided as Supporting Information .
Practice Oriented Master's in Optics
Dimmock, John O.
1998-01-01
The development of an interdisciplinary Masters Program with a concentration in Optics and Photonics Technology has been is described. This program was developed under the U.S. Manufacturing Education and Training Activity of the Technology Reinvestment Project. This development was a collaboration between the University of Alabama in Huntsville (UAH), Alabama A&M University, Northwest Shoals Community College, the NASA Marshall Space Flight Center (MSFC), the U.S. Army Missile Command, Oak Ridge National Laboratory (ORNL), Advanced Optical Systems Inc., Dynetics, Inc., Hughes Danbury Optical Systems, Inc., Nichols Research and Speedring Inc. These organizations as well as the National Institute for Standards and Technology and SCI, Inc. have been participating fully in the design, development and implementation of this program. This goal of the program is to produce highly trained graduates who can also solve practical problems. To this end, the program includes an on-site practicum at a manufacturing location. The broad curriculum of this program emphasizes the fundamentals of optics, optical systems manufacturing and testing, and the principles of design and manufacturing to cost for commercial products. The Master's of Science (MS) in Physics and Master's of Science in Engineering (MSE) in Electrical Engineering Degrees with concentration in Optics and Photonics Technology are offered by the respective UAH academic departments with support from and in consultation with a Steering Committee composed of representatives from each of the participating organizations, and a student representative from UAH. The origins of the programs are described. The curricula of the programs is described. The course outlines of the new courses which were developed for the new curriculum are included. Also included are samples of on-site practicums which the students have been involved in. Also included as attachments are samples of the advertisements, which includes flyers, and
RENEWAL OF BASIC LAWS AND PRINCIPLES FOR POLAR CONTINUUM THEORIES (Ⅹ)--MASTER BALANCE LAW
Institute of Scientific and Technical Information of China (English)
DAI Tian-min
2006-01-01
Through a comparison between the expressions of master balance laws and the conservation laws derived by Noether's theorem, a unified master balance law and six physically possible balance equations for micropolar continuum mechanics are naturally deduced. Among them, by extending the well-known conventional concept of energymomentum tensor, the rather general conservation laws and balance equations named after energy-momentum, energy-angular momentum and energy-energy are obtained. It is clear that the forms of the physical field quantities in the master balance law for the last three cases could not be assumed directly by perceiving through the intuition. Finally,some existing results are reduced immediately as special cases.
Efficient Simulations of Interstellar Gas-Grain Chemistry Using Moment Equations
Barzel, B
2007-01-01
Networks of reactions on dust grain surfaces play a crucial role in the chemistry of interstellar clouds, leading to the formation of molecular hydrogen in diffuse clouds as well as various organic molecules in dense molecular clouds. Due to the sub-micron size of the grains and the low flux, the population of reactive species per grain may be very small and strongly fluctuating. Under these conditions rate equations fail and the simulation of surface-reaction networks requires stochastic methods such as the master equation. However, the master equation becomes infeasible for complex networks because the number of equations proliferates exponentially. Here we introduce a method based on moment equations for the simulation of reaction networks on small grains. The number of equations is reduced to just one equation per reactive specie and one equation per reaction. Nevertheless, the method provides accurate results, which are in excellent agreement with the master equation. The method is demonstrated for the m...
The Master Artisan: A Framework for Master Tradespeople in Australia. Occasional Paper
O'Reilly-Briggs, Karen
2011-01-01
The author explores the prospect of improving pathways and opportunities for tradespeople in Australia through the introduction of a masters-level qualification. The study investigates the views and opinions of senior industry representatives and professional educators to determine whether the introduction of a master trade or master artisan…
Nuclear safety research master plan
Energy Technology Data Exchange (ETDEWEB)
Ha, Jae Joo; Yang, J. U.; Jun, Y. S. and others
2001-06-01
The SRMP (Safety Research Master Plan) is established to cope with the changes of nuclear industry environments. The tech. tree is developed according to the accident progress of the nuclear reactor. The 11 research fields are derived to cover the necessary technologies to ensure the safety of nuclear reactors. Based on the developed tech. tree, the following four main research fields are derived as the main safety research areas: 1. Integrated nuclear safety enhancement, 2. Thermal hydraulic experiment and assessment, 3. Severe accident management and experiment, and 4. The integrity of equipment and structure. The research frame and strategies are also recommended to enhance the efficiency of research activity, and to extend the applicability of research output.
Master of Science in Applied Mathematics, Rensselaer Polytechnic Institute. Final Report.
Boyce, William E.; DiPrima, Richard C.
The purpose of this project was to develop a Master of Science program in Applied Mathematics designed specifically to meet the needs of students wishing to prepare for careers in business, industry, or government. The program emphasizes problem-solving, mathematical modeling, and areas of mathematics such as differential equations, computing, and…
MASTER-OAFA: OT detection during inspection
Gress, O.; Lipunov, V.; Podesta, R.; Levato, H.; Gorbovskoy, E.; Tiurina, N.; Kuznetsov, A.; Balanutsa, P.; Kornilov, V.; Chazov, V.; Gorbunov, I.; Krylov, A.; Lopez, C.; Podesta, F.; Saffe, C.; Shumkov, V.; Pogrosheva, T.
2017-02-01
MASTER-OAFA auto-detection system ( Lipunov et al., "MASTER Global Robotic Net", Advances in Astronomy, 2010, 30L ) discovered OT source at (RA, Dec) = 18h 36m 27.60s -47d 35m 18.1s on 2017-02-02.36706 UT. The OT unfiltered magnitude is 16.2m (mlim=18.1m).
Master's Degree Studies: Expectations versus Reality
Swanepoel, C. H.
2010-01-01
During the past two decades, higher education in South Africa has been affected drastically by transformation. An issue that has specifically been influenced is master's degrees. A significant increase in the demand for access to course work master's degrees has been experienced, while universities themselves have been confronted with a new…
Balanutsa, P.; Lipunov, V.; Buckley, D.; Budnev, N.; Gress, O.; Gorbovskoy, E.; Tiurina, N.; Vladimirov, V.; Kornilov, V.; Kuvshinov, D.; Pogrosheva, T.; Ivanov, K.
2017-02-01
MASTER-SAAO auto-detection system ( Lipunov et al., "MASTER Global Robotic Net", Advances in Astronomy, 2010, 30L ) discovered OT source at (RA, Dec) = 09h 45m 05.87s -65d 43m 43.3s on 2017-02-15.91771 UT. The OT unfiltered magnitude is (mlim=18.6).
MASTER: possible SLSN in SDSS galaxy
Pogrosheva, T.; Lipunov, V.; Rebolo, R.; Serra-Ricart, M.; Gorbovskoy, E.; Tiurina, N.; Kuznetsov, A.; Balanutsa, P.; Kornilov, V.; Gress, O.; Vladimirov, V.
2017-02-01
MASTER-IAC auto-detection system ( Lipunov et al., "MASTER Global Robotic Net", Advances in Astronomy, 2010, 30L ) discovered OT source at (RA, Dec) = 16h 13m 08.18s +26d 09m 53.3s on 2017-02-16.12905 UT. The OT unfiltered magnitude is (mlimit=18.6m).
MASTER: PKS 1142-225 optical flare
Pogrosheva, T.; Lipunov, V.; Podesta, R.; Levato, H.; Gorbovskoy, E.; Tiurina, N.; Balanutsa, P.; Kornilov, V.; Kuznetsov, A.; Gorbunov, I.; Krylov, A.; Lopez, C.; Podesta, F.; Saffe, C.; Kuvshinov, D.; Shumkov, V.
2017-02-01
MASTER-OAFA auto-detection system ( Lipunov et al., "MASTER Global Robotic Net", Advances in Astronomy, 2010, 30L ) discovered OT source at (RA, Dec) = 11h 45m 22.02s -22d 50m 31.4s on 2017-02-10.26340 UT. The OT unfiltered magnitude is 16.7m (mlimit=18.0m).
Valuing Initial Teacher Education at Master's Level
Brooks, Clare; Brant, Jacek; Abrahams, Ian; Yandell, John
2012-01-01
The future of Master's-level work in initial teacher education (ITE) in England seems uncertain. Whilst the coalition government has expressed support for Master's-level work, its recent White Paper focuses on teaching skills as the dominant form of professional development. This training discourse is in tension with the view of professional…
Microsoft SQL Server 2012 Master Data Services
Puhakka, Jani
2014-01-01
Insinöörityössä selvitettiin Microsoft SQL Server 2012 Master Data Services -palvelimen toiminnot master datan hallintaan. Tavoitteena oli muodostaa käsitys järjestelmän toiminnallisuuksista ja miten näitä voidaan hyödyntää. Ensimmäisenä työssä tutustuttiin master data -käsitteeseen ja -käyttötarkoitukseen. Tämän jälkeen asennettiin Master Data Services -ympäristö virtuaalikoneelle sekä tutustuttiin käytettävissä oleviin hallintatyökaluihin. Seuraavana käytiin läpi Master Data Serviceen l...
A way to the Photo Master Expert
Inagaki, Toshihiko
After the author presided over the photographer's group for 15 years or more, the author met with the Photo Master certificate examination. And the author took the certificate examination, and was authorized as a Photo Master Expert in 2005. In this report, the outline how photographic technology has been mastered in order to adapt the photographer's group to the great change of photography from film to digital and how the contents of the activity of a photographer's group have changed is described. And the progress which took the Photo Master certificate examination as a good opportunity to prove the achievement level of those activities is described. And as a photographic activity after Photo Master Expert authorization, the shooting method of mural painting in the royal tomb of Amenophis III is described.
Endoscopic Release of Master Knot of Henry.
Lui, Tun Hing
2015-12-01
A post-traumatic partial tear of the flexor hallucis longus tendon at the master knot of Henry and the resultant fibrosis of the knot can result in pain at the medial foot arch or posteromedial ankle pain with trigger hallux. Open debridement of the master knot of Henry is indicated if the symptoms do not improve with nonoperative treatment. The open procedure requires extensive soft-tissue dissection because the master knot of Henry is a deep structure. Endoscopic release of the master knot of Henry is an alternative to the open procedure and has the advantage of less surgical trauma and potential for less chance of recurrence of fibrosis of the master knot of Henry.
Moiseiwitsch, B L
2005-01-01
Two distinct but related approaches hold the solutions to many mathematical problems--the forms of expression known as differential and integral equations. The method employed by the integral equation approach specifically includes the boundary conditions, which confers a valuable advantage. In addition, the integral equation approach leads naturally to the solution of the problem--under suitable conditions--in the form of an infinite series.Geared toward upper-level undergraduate students, this text focuses chiefly upon linear integral equations. It begins with a straightforward account, acco
Collapse-revival of squeezing of two atoms in dissipative cavities
Institute of Scientific and Technical Information of China (English)
邹红梅; 方卯发
2016-01-01
Based on the time-convolutionless master-equation approach, we investigate the squeezing dynamics of two atoms in dissipative cavities. We find that the atomic squeezing is related to initial atomic states, atom–cavity couplings, non-Markovian effects and resonant frequencies of an atom and its cavity. The results show that a collapse–revival phenomenon will occur in the atomic squeezing and this process is accompanied by the buildup and decay of entanglement between two atoms. Enhancing the atom–cavity coupling can increase the frequency of the collapse–revival of the atomic squeezing. The stronger the non-Markovian effect is, the more obvious the collapse–revival phenomenon is. In particular, if the atom–cavity coupling or the non-Markovian effect is very strong, the atomic squeezing will tend to a stably periodic oscillation in a long time. The oscillatory frequency of the atomic squeezing is dependent on the resonant frequency of the atom and its cavity.
PROFESSIONAL MASTER AND ITS CHALLENGES.
Ferreira, Lydia Masako
2015-01-01
To describe the history, origin, objectives, characteristics, implications, the questions of the evaluation form and some examples of the Professional Masters (MP), to differentiate the Academic Master, and identify the challenges for the next quadrennial assessment. The CAPES site on Professional Masters and documents and meeting area of reports from 2004 to 2013 of Medicine III were read as well as the reports and the sub-page of the area in Capes site. The data relating to the evaluation process and the Scoreboard of the other areas were computed and analyzed. From these data it was detected the challenges of Medicine III for the next four years (2013-2016). The creation of the Professional Master is very recent in Medicine III and no Professional Master of Medicine III course was evaluated yet. Were described the objectives, assumptions, characteristics, motivations, the possibilities, the feasibility, the profile of the students, the faculty, the curriculum, funding, intellectual production, social inclusion, the general requirements of Ordinance No. 193/2011 CAPES and some examples of proposals, technological lines of scientific activities, partnerships and counterparties. The evaluation form of the MP was discussed, the need for social, economic and political intellectual production and the differences with the MA. It was also reported the global importance of the MP and its evolution in Brazil. From the understanding of the MP, Medicine III outlined some challenges and goals to be developed in the 2013-2016 quadrennium. Medicine III understood the MP as a new technological scientific horizon within the strict sensu post-graduate and full consistency with the area. Descrever o histórico, a origem, os objetivos, as características, as implicações, os quesitos da ficha de avaliação e alguns exemplos do Mestrado Profissional (MP), sua diferenciação com o Mestrado Acadêmico, e detectar os desafios para o próximo quadriênio de avaliação. O site
Theory of strong turbulence by renormalization
Tchen, C. M.
1981-01-01
The hydrodynamical equations of turbulent motions are inhomogeneous and nonlinear in their inertia and force terms and will generate a hierarchy. A kinetic method was developed to transform the hydrodynamic equations into a master equation governing the velocity distribution, as a function of the time, the position and the velocity as an independent variable. The master equation presents the advantage of being homogeneous and having fewer nonlinear terms and is therefore simpler for the investigation of closure. After the closure by means of a cascade scaling procedure, the kinetic equation is derived and possesses a memory which represents the nonMarkovian character of turbulence. The kinetic equation is transformed back to the hydrodynamical form to yield an energy balance in the cascade form. Normal and anomalous transports are analyzed. The theory is described for incompressible, compressible and plasma turbulence. Applications of the method to problems relating to sound generation and the propagation of light in a nonfrozen turbulence are considered.
Directory of Open Access Journals (Sweden)
Lloyd K. Williams
1987-01-01
Full Text Available In this paper we find closed form solutions of some Riccati equations. Attention is restricted to the scalar as opposed to the matrix case. However, the ones considered have important applications to mathematics and the sciences, mostly in the form of the linear second-order ordinary differential equations which are solved herewith.
Coupled Ito equations of continuous quantum state measurement, and estimation
Diósi, L; Konrad, T; Scherer, A; Audretsch, Juergen; Diosi, Lajos; Konrad, Thomas; Scherer, Artur
2006-01-01
We discuss a non-linear stochastic master equation that governs the time-evolution of the estimated quantum state. Its differential evolution corresponds to the infinitesimal updates that depend on the time-continuous measurement of the true quantum state. The new stochastic master equation couples to the two standard stochastic differential equations of time-continuous quantum measurement. For the first time, we can prove that the calculated estimate almost always converges to the true state, also at low-efficiency measurements. We show that our single-state theory can be adapted to weak continuous ensemble measurements as well.
Prentis, Jeffrey J.
1996-05-01
One of the most challenging goals of a physics teacher is to help students see that the equations of physics are connected to each other, and that they logically unfold from a small number of basic ideas. Derivations contain the vital information on this connective structure. In a traditional physics course, there are many problem-solving exercises, but few, if any, derivation exercises. Creating an equation poem is an exercise to help students see the unity of the equations of physics, rather than their diversity. An equation poem is a highly refined and eloquent set of symbolic statements that captures the essence of the derivation of an equation. Such a poetic derivation is uncluttered by the extraneous details that tend to distract a student from understanding the essential physics of the long, formal derivation.
Energy Technology Data Exchange (ETDEWEB)
Young, C.W. [Applied Research Associates, Inc., Albuquerque, NM (United States)
1997-10-01
In 1967, Sandia National Laboratories published empirical equations to predict penetration into natural earth materials and concrete. Since that time there have been several small changes to the basic equations, and several more additions to the overall technique for predicting penetration into soil, rock, concrete, ice, and frozen soil. The most recent update to the equations was published in 1988, and since that time there have been changes in the equations to better match the expanding data base, especially in concrete penetration. This is a standalone report documenting the latest version of the Young/Sandia penetration equations and related analytical techniques to predict penetration into natural earth materials and concrete. 11 refs., 6 tabs.