Exact master equation and general non-Markovian dynamics in open quantum systems

Zhang, Wei Min

doi:10.1140/epjst/e2018-800047-4

Cited by 28 publications

(38 citation statements)

References 82 publications

(189 reference statements)

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“…We expect that by coupling the system with the environment, it is possible to explore the microscopical quantum origins of work and heat from the dynamics of open quantum systems, which are manifested by dissipation dynamics and fluctuation dynamics, respectively. We will explore these fundamental concepts in the further research within our exact master equation theory [21][22][23][24][25] .…”

Section: (6)mentioning

confidence: 99%

“…In all these investigations, thermalization is demonstrated mainly in quantum Brownian motion with initial Gaussian wave packets at high temperature limit 29,34,35 . In the last decade, we have also derived the exact master equation for a large class of open quantum systems [21][22][23][24][25] and solved the exact master equation with arbitrary initial states at arbitrary initial temperature of the reservoir such that the thermalization process is generally provided [36][37][38] . From such exact solutions for a large class of open quantum systems, we will attempt to understand thermodynamics with the detailed thermalization process determined from the principle of quantum mechanics in this paper.…”

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confidence: 99%

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Quantum thermodynamics of single particle systems

Ali

Huang

Zhang

2020

Sci Rep

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thermodynamics is built with the concept of equilibrium states. However, it is less clear how equilibrium thermodynamics emerges through the dynamics that follows the principle of quantum mechanics. in this paper, we develop a theory of quantum thermodynamics that is applicable for arbitrary small systems, even for single particle systems coupled with a reservoir. We generalize the concept of temperature beyond equilibrium that depends on the detailed dynamics of quantum states. We apply the theory to a cavity system and a two-level system interacting with a reservoir, respectively. The results unravels (1) the emergence of thermodynamics naturally from the exact quantum dynamics in the weak system-reservoir coupling regime without introducing the hypothesis of equilibrium between the system and the reservoir from the beginning; (2) the emergence of thermodynamics in the intermediate system-reservoir coupling regime where the Born-Markovian approximation is broken down; (3) the breakdown of thermodynamics due to the long-time non-Markovian memory effect arisen from the occurrence of localized bound states; (4) the existence of dynamical quantum phase transition characterized by inflationary dynamics associated with negative dynamical temperature. the corresponding dynamical criticality provides a border separating classical and quantum worlds. The inflationary dynamics may also relate to the origin of big bang and universe inflation. And the third law of thermodynamics, allocated in the deep quantum realm, is naturally proved. In the past decade, many efforts have been devoted to understand how, starting from an isolated quantum system evolving under Hamiltonian dynamics, equilibration and effective thermodynamics emerge at long times 1-5. On the other hand, the investigations of open quantum systems initiate interests on the issue of quantum thermodynamics taking place under the quantum evolution of open systems 6-20. The questions of how thermodynamics emerges from quantum dynamics, how do quantum systems dynamically equilibrate and thermalize, and whether thermalization is always reachable in quantum regime, are central and fundamental to research for quantum thermodynamics. However, a general theory of quantum thermodynamics that has conceptually no ambiguity in answering the above questions has not yet been obtained, because investigations in addressing above questions inevitably take various assumptions and approximations. In this paper, we will attempt to answer these questions by rigorously solving the quantum dynamics based on the exact master equation we developed recently for a large class of open quantum systems 21-25. Recall that thermodynamics is built with the hypothesis of equilibrium 26. Macroscopic systems at equilibrium are fully described by the relation between the internal energy E and a set of other extensive parameters, the entropy S, the volume V, and the particle number N i of different components i = 1, 2, ••• , magnetic moment M, etc.,

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Section: (6)mentioning

confidence: 99%

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confidence: 99%

Quantum thermodynamics of single particle systems

Ali

Huang

Zhang

2020

Sci Rep

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“…In the steady state limit t → ∞, the function v can be expressed as v(t, t)| t→∞ ≡ dωχ(ω) [418,420,421]. The non-equilibrium FDT then reads [420,421]…”

Section: A Scale Of Local Thermal Fluctuations and Excitationsmentioning

confidence: 99%

Local temperatures out of equilibrium

2019

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The temperature of a physical system is operationally defined in physics as "that quantity which is measured by a thermometer" weakly coupled to, and at equilibrium with the system. This definition is unique only at global equilibrium in view of the zeroth law of thermodynamics: when the system and the thermometer have reached equilibrium, the "thermometer degrees of freedom" can be traced out and the temperature read by the thermometer can be uniquely assigned to the system. Unfortunately, such a procedure cannot be straightforwardly extended to a system out of equilibrium, where local excitations may be spatially inhomogeneous and the zeroth law of thermodynamics does not hold. With the advent of several experimental techniques that attempt to extract a single parameter characterizing the degree of local excitations of a (mesoscopic or nanoscale) system out of equilibrium, this issue is making a strong comeback to the forefront of research. In this paper, we will review the difficulties to define a unique temperature out of equilibrium, the majority of definitions that have been proposed so far, and discuss both their advantages and limitations. We will then examine a variety of experimental techniques developed for measuring the non-equilibrium local temperatures under various conditions. Finally we will discuss the physical implications of the notion of local temperature, and present the practical applications of such a concept in a variety of nanosystems out of equilibrium. Figure 4: (a) The product of the density of states η(E) times the global distribution function ϕ|ρ|ϕ forms a strongly pronounced peak at the expectation value of the global system energyĒ. (b) The logarithm of the local distribution function a|ρ|a (solid line) and the logarithm of a canonical distribution (dashed line) with the same local temperature for a harmonic chain. (a) and (b) are reprinted with permission from [74].

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“…In the past decades, several types of master equations have been developed to study different fields, e.g. Nakajima-Zwanzig equation 7 , 8 , Redfield master equation 9 , Lindblad master equation 10 , Hu-Paz-Zhang master equation 11 , general non-Markovian time-local master equation 12 – 16 , etc. With the master equation, the evolution of time-dependant expectation values for arbitrary operator in the Hilbert space of the system S, defined as , can be obtained by solving a set of ordinary differential equations.…”

Section: Introductionmentioning

confidence: 99%

Stochastic Schrödinger equation derivation of non-Markovian two-time correlation functions

Carballeira

Dolgitzer

Zhao

et al. 2021

Sci Rep

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We derive the evolution equations for two-time correlation functions of a generalized non-Markovian open quantum system based on a modified stochastic Schrödinger equation approach. We find that the two-time reduced propagator, an object that used to be characterized by two independent stochastic processes in the Hilbert space of the system, can be simplified and obtained by taking ensemble average over one single noise. This discovery can save the cost of computation, and accelerate the converging process when taking the average over noisy trajectories. As a result, our method can be widely applied to many open quantum models, especially large-scale systems and extend the quantum regression theory to the non-Markovian case. In the short-time simulations, it is observed a significant difference between Markovian and non-Markovian cases, which can be applied to realize the environmental spectrum detection and enhance the measurement sensitivity in varying open quantum systems.

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Exact master equation and general non-Markovian dynamics in open quantum systems

Cited by 28 publications

References 82 publications

Quantum thermodynamics of single particle systems

Quantum thermodynamics of single particle systems

Local temperatures out of equilibrium

Stochastic Schrödinger equation derivation of non-Markovian two-time correlation functions

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