Exact calculation of the time convolutionless master equation generator: Application to the nonequilibrium resonant level model

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.

Random quantum operations

International Nuclear Information System (INIS)

Bruzda, Wojciech; Cappellini, Valerio; Sommers, Hans-Juergen; Zyczkowski, Karol

2009-01-01

We define a natural ensemble of trace preserving, completely positive quantum maps and present algorithms to generate them at random. Spectral properties of the superoperator Φ associated with a given quantum map are investigated and a quantum analogue of the Frobenius-Perron theorem is proved. We derive a general formula for the density of eigenvalues of Φ and show the connection with the Ginibre ensemble of real non-symmetric random matrices. Numerical investigations of the spectral gap imply that a generic state of the system iterated several times by a fixed generic map converges exponentially to an invariant state

Stochastic wave-function unravelling of the generalized Lindblad equation using correlated states

International Nuclear Information System (INIS)

Moodley, Mervlyn; Nsio Nzundu, T; Paul, S

2012-01-01

We perform a stochastic wave-function unravelling of the generalized Lindblad master equation using correlated states, a combination of the system state vectors and the environment population. The time-convolutionless projection operator method using correlated projection superoperators is applied to a two-state system, a qubit, that is coupled to an environment consisting of two energy bands which are both populated. These results are compared to the data obtained from Monte Carlo wave-function simulations based on the unravelling of the master equation. We also show a typical quantum trajectory and the average time evolution of the state vector on the Bloch sphere. (paper)

The Weyl law for contractive maps

Science.gov (United States)

Spina, Maria E.; Rivas, Alejandro M. F.; Carlo, Gabriel

2013-11-01

We find an empirical Weyl law followed by the eigenvalues of contractive maps. An important property is that it is mainly insensitive to the dimension of the corresponding invariant classical set, the strange attractor. The usual explanation for the fractal Weyl law emergence in scattering systems (i.e., having a projective opening) is based on the classical phase space distributions evolved up to the quantum to classical correspondence (Ehrenfest) time. In the contractive case this reasoning fails to describe it. Instead, we conjecture that the support for this behavior is essentially given by the strong non-orthogonality of the eigenvectors of the contractive superoperator. We test the validity of the Weyl law and this conjecture on two paradigmatic systems, the dissipative baker and kicked top maps.

The Weyl law for contractive maps

International Nuclear Information System (INIS)

Spina, Maria E; Rivas, Alejandro M F; Carlo, Gabriel

2013-01-01

We find an empirical Weyl law followed by the eigenvalues of contractive maps. An important property is that it is mainly insensitive to the dimension of the corresponding invariant classical set, the strange attractor. The usual explanation for the fractal Weyl law emergence in scattering systems (i.e., having a projective opening) is based on the classical phase space distributions evolved up to the quantum to classical correspondence (Ehrenfest) time. In the contractive case this reasoning fails to describe it. Instead, we conjecture that the support for this behavior is essentially given by the strong non-orthogonality of the eigenvectors of the contractive superoperator. We test the validity of the Weyl law and this conjecture on two paradigmatic systems, the dissipative baker and kicked top maps. (paper)

Stochastic representation of a class of non-Markovian completely positive evolutions

International Nuclear Information System (INIS)

Budini, Adrian A.

2004-01-01

By modeling the interaction of an open quantum system with its environment through a natural generalization of the classical concept of continuous time random walk, we derive and characterize a class of non-Markovian master equations whose solution is a completely positive map. The structure of these master equations is associated with a random renewal process where each event consist in the application of a superoperator over a density matrix. Strong nonexponential decay arise by choosing different statistics of the renewal process. As examples we analyze the stochastic and averaged dynamics of simple systems that admit an analytical solution. The problem of positivity in quantum master equations induced by memory effects [S. M. Barnett and S. Stenholm, Phys. Rev. A 64, 033808 (2001)] is clarified in this context

Chaos, entropy, and life-time in classical and quantum systems; Chaos, entropie et duree de vie dans les systemes classiques et quantiques

Energy Technology Data Exchange (ETDEWEB)

Seyed Majid Saberi Fathi

2007-07-15

In this thesis, we first study Lorentz gas as a billiard ball with elastic collision with the obstacles and a system of hard spheres in 2-dimensions. We study a numerical simulation of the dynamical system and we investigate the entropy increasing in non-equilibrium with time under the effect of collisions and its relation to positive Lyapunov exponents. Then, we study a decay model in a quantum system called Friedrichs model. We consider coupling of the kaons and environment with continuous energies. Then, we show that this model is well adapted to describe oscillation, regeneration, decay and CP violation of a kaonic system. In addition, we apply in the Friedrichs model, the time super-operator formalism that predicts the resonance, i.e. the survival probability of the instable states. (author)

A new quantum statistical evaluation method for time correlation functions

International Nuclear Information System (INIS)

Loss, D.; Schoeller, H.

1989-01-01

Considering a system of N identical interacting particles, which obey Fermi-Dirac or Bose-Einstein statistics, the authors derive new formulas for correlation functions of the type C(t) = i= 1 N A i (t) Σ j=1 N B j > (where B j is diagonal in the free-particle states) in the thermodynamic limit. Thereby they apply and extend a superoperator formalism, recently developed for the derivation of long-time tails in semiclassical systems. As an illustrative application, the Boltzmann equation value of the time-integrated correlation function C(t) is derived in a straight-forward manner. Due to exchange effects, the obtained t-matrix and the resulting scattering cross section, which occurs in the Boltzmann collision operator, are now functionals of the Fermi-Dirac or Bose-Einstein distribution

Chaos, entropy, and life-time in classical and quantum systems

International Nuclear Information System (INIS)

Seyed Majid Saberi Fathi

2007-07-01

In this thesis, we first study Lorentz gas as a billiard ball with elastic collision with the obstacles and a system of hard spheres in 2-dimensions. We study a numerical simulation of the dynamical system and we investigate the entropy increasing in non-equilibrium with time under the effect of collisions and its relation to positive Lyapunov exponents. Then, we study a decay model in a quantum system called Friedrichs model. We consider coupling of the kaons and environment with continuous energies. Then, we show that this model is well adapted to describe oscillation, regeneration, decay and CP violation of a kaonic system. In addition, we apply in the Friedrichs model, the time super-operator formalism that predicts the resonance, i.e. the survival probability of the instable states. (author)

Quantum operations that cannot be implemented using a small mixed environment

International Nuclear Information System (INIS)

Zalka, Christof; Rieffel, Eleanor

2002-01-01

To implement any quantum operation (a.k.a. ''superoperator'' or ''CP map'') on a d-dimensional quantum system, it is enough to apply a suitable overall unitary transformation to the system and a d 2 -dimensional environment which is initialized in a fixed pure state. It has been suggested that a d-dimensional environment might be enough if we could initialize the environment in a mixed state of our choosing. In this note we show with elementary means that certain explicit quantum operations cannot be realized in this way. Our counterexamples map some pure states to pure states, giving strong and easily manageable conditions on the overall unitary transformation. Everything works in the more general setting of quantum operations from d-dimensional to d ' -dimensional spaces, so we place our counterexamples within this more general framework

Quantum computer with mixed states and four-valued logic

International Nuclear Information System (INIS)

Tarasov, Vasily E.

2002-01-01

In this paper we discuss a model of quantum computer in which a state is an operator of density matrix and gates are general quantum operations, not necessarily unitary. A mixed state (operator of density matrix) of n two-level quantum systems is considered as an element of 4 n -dimensional operator Hilbert space (Liouville space). It allows us to use a quantum computer model with four-valued logic. The gates of this model are general superoperators which act on n-ququat state. Ququat is a quantum state in a four-dimensional (operator) Hilbert space. Unitary two-valued logic gates and quantum operations for an n-qubit open system are considered as four-valued logic gates acting on n-ququats. We discuss properties of quantum four-valued logic gates. In the paper we study universality for quantum four-valued logic gates. (author)

Quantum-statistical kinetic equations

International Nuclear Information System (INIS)

Loss, D.; Schoeller, H.

1989-01-01

Considering a homogeneous normal quantum fluid consisting of identical interacting fermions or bosons, the authors derive an exact quantum-statistical generalized kinetic equation with a collision operator given as explicit cluster series where exchange effects are included through renormalized Liouville operators. This new result is obtained by applying a recently developed superoperator formalism (Liouville operators, cluster expansions, symmetrized projectors, P q -rule, etc.) to nonequilibrium systems described by a density operator ρ(t) which obeys the von Neumann equation. By means of this formalism a factorization theorem is proven (being essential for obtaining closed equations), and partial resummations (leading to renormalized quantities) are performed. As an illustrative application, the quantum-statistical versions (including exchange effects due to Fermi-Dirac or Bose-Einstein statistics) of the homogeneous Boltzmann (binary collisions) and Choh-Uhlenbeck (triple collisions) equations are derived

Classical and quantum molecular dynamics in NMR spectra

CERN Document Server

Szymański, Sławomir

2018-01-01

The book provides a detailed account of how condensed-phase molecular dynamics are reflected in the line shapes of NMR spectra. The theories establishing connections between random, time-dependent molecular processes and lineshape effects are exposed in depth. Special emphasis is placed on the theoretical aspects, involving in particular intermolecular processes in solution, and molecular symmetry issues. The Liouville super-operator formalism is briefly introduced and used wherever it is beneficial for the transparency of presentation. The proposed formal descriptions of the discussed problems are sufficiently detailed to be implemented on a computer. Practical applications of the theory in solid- and liquid-phase studies are illustrated with appropriate experimental examples, exposing the potential of the lineshape method in elucidating molecular dynamics NMR-observable molecular phenomena where quantization of the spatial nuclear degrees of freedom is crucial are addressed in the last part of the book. As ...

Theory of deep inelastic neutron scattering: Hard-core perturbation theory

International Nuclear Information System (INIS)

Silver, R.N.

1988-01-01

Details are presented of a new many-body theory for deep inelastic neutron scattering (DINS) experiments to measure momentum distributions in quantum fluids and solids. The high-momentum and energy-transfer scattering law in helium is shown to be a convolution of the impulse approximation with a final-state broadening function which depends on the scattering phase shifts and the radial distribution function. The predicted broadening satisfies approximate Y scaling, is neither Lorentzian nor Gaussian, and obeys the f, ω 2 , and ω 3 sum rules. The derivation uses a combination of Liouville perturbation theory, projection superoperators, and semiclassical methods which I term ''hard-core perturbation theory.'' A review is presented of the predictions of prior theories for DINS experiments in relation to the present work. A subsequent paper will present massive numerical predictions and a discussion of DINS experiments on superfluid 4 He

Asymptotic evolution of quantum Markov chains

Energy Technology Data Exchange (ETDEWEB)

Novotny, Jaroslav [FNSPE, CTU in Prague, 115 19 Praha 1 - Stare Mesto (Czech Republic); Alber, Gernot [Institut fuer Angewandte Physik, Technische Universitaet Darmstadt, D-64289 Darmstadt (Germany)

2012-07-01

The iterated quantum operations, so called quantum Markov chains, play an important role in various branches of physics. They constitute basis for many discrete models capable to explore fundamental physical problems, such as the approach to thermal equilibrium, or the asymptotic dynamics of macroscopic physical systems far from thermal equilibrium. On the other hand, in the more applied area of quantum technology they also describe general characteristic properties of quantum networks or they can describe different quantum protocols in the presence of decoherence. A particularly, an interesting aspect of these quantum Markov chains is their asymptotic dynamics and its characteristic features. We demonstrate there is always a vector subspace (typically low-dimensional) of so-called attractors on which the resulting superoperator governing the iterative time evolution of quantum states can be diagonalized and in which the asymptotic quantum dynamics takes place. As the main result interesting algebraic relations are presented for this set of attractors which allow to specify their dual basis and to determine them in a convenient way. Based on this general theory we show some generalizations concerning the theory of fixed points or asymptotic evolution of random quantum operations.

Resource theory of non-Gaussian operations

Science.gov (United States)

Zhuang, Quntao; Shor, Peter W.; Shapiro, Jeffrey H.

2018-05-01

Non-Gaussian states and operations are crucial for various continuous-variable quantum information processing tasks. To quantitatively understand non-Gaussianity beyond states, we establish a resource theory for non-Gaussian operations. In our framework, we consider Gaussian operations as free operations, and non-Gaussian operations as resources. We define entanglement-assisted non-Gaussianity generating power and show that it is a monotone that is nonincreasing under the set of free superoperations, i.e., concatenation and tensoring with Gaussian channels. For conditional unitary maps, this monotone can be analytically calculated. As examples, we show that the non-Gaussianity of ideal photon-number subtraction and photon-number addition equal the non-Gaussianity of the single-photon Fock state. Based on our non-Gaussianity monotone, we divide non-Gaussian operations into two classes: (i) the finite non-Gaussianity class, e.g., photon-number subtraction, photon-number addition, and all Gaussian-dilatable non-Gaussian channels; and (ii) the diverging non-Gaussianity class, e.g., the binary phase-shift channel and the Kerr nonlinearity. This classification also implies that not all non-Gaussian channels are exactly Gaussian dilatable. Our resource theory enables a quantitative characterization and a first classification of non-Gaussian operations, paving the way towards the full understanding of non-Gaussianity.

Construction of extremal local positive-operator-valued measures under symmetry

International Nuclear Information System (INIS)

Virmani, S.; Plenio, M.B.

2003-01-01

We study the local implementation of positive-operator-valued measures (POVMs) when we require only the faithful reproduction of the statistics of the measurement outcomes for all initial states. We first demonstrate that any POVM with separable elements can be implemented by a separable superoperator, and develop techniques for calculating the extreme points of POVMs under a certain class of constraint that includes separability and positive partial transposition. As examples we consider measurements that are invariant under various symmetry groups (Werner, isotropic, Bell diagonal, local orthogonal), and demonstrate that in these cases separability of the POVM elements is equivalent to implementability via local operations and classical communication (LOCC). We also calculate the extrema of these classes of measurement under the groups that we consider, and give explicit LOCC protocols for attaining them. These protocols are hence optimal methods for locally discriminating between states of these symmetries. One of many interesting consequences is that the best way to locally discriminate Bell-diagonal mixed states is to perform a two-outcome POVM using local von Neumann projections. This is true regardless of the cost function, the number of states being discriminated, or the prior probabilities. Our results give the first cases of local mixed-state discrimination that can be analyzed quantitatively in full, and may have application to other problems such as demonstrations of nonlocality, experimental entanglement witnesses, and perhaps even entanglement distillation

Effects of finite pulse width on two-dimensional Fourier transform electron spin resonance.

Science.gov (United States)

Liang, Zhichun; Crepeau, Richard H; Freed, Jack H

2005-12-01

Two-dimensional (2D) Fourier transform ESR techniques, such as 2D-ELDOR, have considerably improved the resolution of ESR in studies of molecular dynamics in complex fluids such as liquid crystals and membrane vesicles and in spin labeled polymers and peptides. A well-developed theory based on the stochastic Liouville equation (SLE) has been successfully employed to analyze these experiments. However, one fundamental assumption has been utilized to simplify the complex analysis, viz. the pulses have been treated as ideal non-selective ones, which therefore provide uniform irradiation of the whole spectrum. In actual experiments, the pulses are of finite width causing deviations from the theoretical predictions, a problem that is exacerbated by experiments performed at higher frequencies. In the present paper we provide a method to deal with the full SLE including the explicit role of the molecular dynamics, the spin Hamiltonian and the radiation field during the pulse. The computations are rendered more manageable by utilizing the Trotter formula, which is adapted to handle this SLE in what we call a "Split Super-Operator" method. Examples are given for different motional regimes, which show how 2D-ELDOR spectra are affected by the finite pulse widths. The theory shows good agreement with 2D-ELDOR experiments performed as a function of pulse width.

Entanglement Dynamics of Linear and Nonlinear Interaction of Two Two-Level Atoms with a Quantized Phase-Damped Field in the Dispersive Regime

Science.gov (United States)

Tavassoly, M. K.; Daneshmand, R.; Rustaee, N.

2018-06-01

In this paper we study the linear and nonlinear (intensity-dependent) interactions of two two-level atoms with a single-mode quantized field far from resonance, while the phase-damping effect is also taken into account. To find the analytical solution of the atom-field state vector corresponding to the considered model, after deducing the effective Hamiltonian we evaluate the time-dependent elements of the density operator using the master equation approach and superoperator method. Consequently, we are able to study the influences of the special nonlinearity function f (n) = √ {n}, the intensity of the initial coherent state field and the phase-damping parameter on the degree of entanglement of the whole system as well as the field and atom. It is shown that in the presence of damping, by passing time, the amount of entanglement of each subsystem with the rest of system, asymptotically reaches to its stationary and maximum value. Also, the nonlinear interaction does not have any effect on the entanglement of one of the atoms with the rest of system, but it changes the amplitude and time period of entanglement oscillations of the field and the other atom. Moreover, this may cause that, the degree of entanglement which may be low (high) at some moments of time becomes high (low) by entering the intensity-dependent function in the atom-field coupling.

Unambiguous discrimination among oracle operators

International Nuclear Information System (INIS)

Chefles, Anthony; Kitagawa, Akira; Takeoka, Masahiro; Sasaki, Masahide; Twamley, Jason

2007-01-01

We address the problem of unambiguous discrimination among oracle operators. The general theory of unambiguous discrimination among unitary operators is extended with this application in mind. We prove that entanglement with an ancilla cannot assist any discrimination strategy for commuting unitary operators. We also obtain a simple, practical test for the unambiguous distinguishability of an arbitrary set of unitary operators on a given system. Using this result, we prove that the unambiguous distinguishability criterion is the same for both standard and minimal oracle operators. We then show that, except in certain trivial cases, unambiguous discrimination among all standard oracle operators corresponding to integer functions with fixed domain and range is impossible. However, we find that it is possible to unambiguously discriminate among the Grover oracle operators corresponding to an arbitrarily large unsorted database. The unambiguous distinguishability of standard oracle operators corresponding to totally indistinguishable functions, which possess a strong form of classical indistinguishability, is analysed. We prove that these operators are not unambiguously distinguishable for any finite set of totally indistinguishable functions on a Boolean domain and with arbitrary fixed range. Sets of such functions on a larger domain can have unambiguously distinguishable standard oracle operators, and we provide a complete analysis of the simplest case, that of four functions. We also examine the possibility of unambiguous oracle operator discrimination with multiple parallel calls and investigate an intriguing unitary superoperator transformation between standard and entanglement-assisted minimal oracle operators

Non-reversible evolution of quantum chaotic system. Kinetic description

International Nuclear Information System (INIS)

Chotorlishvili, L.; Skrinnikov, V.

2008-01-01

It is well known that the appearance of non-reversibility in classical chaotic systems is connected with a local instability of phase trajectories relatively to a small change of initial conditions and parameters of the system. Classical chaotic systems reveal an exponential sensitivity to these changes. This leads to an exponential growth of initial error with time, and as the result after the statistical averaging over this error, the dynamics of the system becomes non-reversible. In spite of this, the question about the origin of non-reversibility in quantum case remains actual. The point is that the classical notion of instability of phase trajectories loses its sense during quantum consideration. The current work is dedicated to the clarification of the origin of non-reversibility in quantum chaotic systems. For this purpose we study a non-stationary dynamics of the chaotic quantum system. By analogy with classical chaos, we consider an influence of a small unavoidable error of the parameter of the system on the non-reversibility of the dynamics. It is shown in the Letter that due to the peculiarity of chaotic quantum systems, the statistical averaging over the small unavoidable error leads to the non-reversible transition from the pure state into the mixed one. The second part of the Letter is dedicated to the kinematic description of the chaotic quantum-mechanical system. Using the formalism of superoperators, a muster kinematic equation for chaotic quantum system was obtained from Liouville equation under a strict mathematical consideration