Modeling heat transport through completely positive maps

Wichterich, Hannu; Henrich, Markus J.; Breuer, Heinz‐Peter; Gemmer, Jochen; Michel, M.

doi:10.1103/physreve.76.031115

Cited by 216 publications

(281 citation statements)

References 30 publications

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“…This setup provides a fully coherent bulk dynamics and incoherent boundary conditions, which is particularly suited for studying nonequilibrium heat transport in a setup similar to the classical case [151]. The Quantum Master Equation (QME) approach can be used to study not only heat transport, but also nonequilibrium processes in general (particle transport, spin transport, etc.).…”

Section: Fourier Law In Quantum Mechanicsmentioning

confidence: 99%

From Thermal Rectifiers to Thermoelectric Devices

Benenti

Casati

Mejía‐Monasterio

et al. 2016

Thermal Transport in Low Dimensions

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We discuss thermal rectification and thermoelectric energy conversion from the perspective of nonequilibrium statistical mechanics and dynamical systems theory. After preliminary considerations on the dynamical foundations of the phenomenological Fourier law in classical and quantum mechanics, we illustrate ways to control the phononic heat flow and design thermal diodes. Finally, we consider the coupled transport of heat and charge and discuss several general mechanisms for optimizing the figure of merit of thermoelectric efficiency.

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Section: Fourier Law In Quantum Mechanicsmentioning

confidence: 99%

From Thermal Rectifiers to Thermoelectric Devices

Benenti

Casati

Mejía‐Monasterio

et al. 2016

Thermal Transport in Low Dimensions

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“…However, Floquet theory has the drawback of converting a finitedimensional problem to an infinite dimensional one. Consequently, most interesting results from Floquet theory are often obtained as a perturbation expansion in terms of inverse drive frequency, giving results primarily for high frequency driving.Moreover, from calculations in the absence of timeperiodic modulations, the commonly used phenomenological Lindblad Quantum Master Equations are known to have several drawbacks, especially in an out-ofequilibrium situation [63][64][65][66]. It has been recently shown that microscopically derived Redfield Quantum Master Equation (RQME) under Born-Markov approximation can be used to overcome the drawbacks of phenomenological Lindblad equations and to obtain correct results up-to leading order in system-bath coupling [63].…”

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confidence: 99%

Quantum transport under ac drive from the leads: A Redfield quantum master equation approach

Purkayastha

2017

Phys. Rev. B

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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 non-interacting 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 Redfield quantum master equation under Born-Markov approximation, we derive a linear differential equation for equal time two-point correlation matrix, sometimes also called 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 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. Two most important experimentally relevant insights from this are : (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. A. IntroductionThe dynamics of a quantum system coupled to an external environment (so-called "open" quantum system) are a result of the intricate interplay between the coherent evolution of the quantum degrees of freedom, the structure of the environment and the form and strength of the system-environment coupling. From quantum cavities [1-3] and superconducting qubits [4][5][6][7][8][9] , through quantum dots [10][11][12][13][14][15], molecular junctions [16][17][18][19][20][21][22][23][24][25][26][27] and cold atoms [28][29][30][31] , to excitons traveling in photosynthetic complexes [32][33][34][35], open quantum systems show dynamics which can be far richer and more surprising than their coherent (environment-free) counterparts.Recent ideas of designing a quantum state by engineering a specific environment [36][37][38][39][40][41][42] or by a periodic modulation of the open system's Hamiltonian [16,43,44] open a path to new forms of control over quantum systems. Combining these two concepts of time-periodic modulations and environment (bath) engineering, here we study the dynamics of open quantum systems where the environment thermodynamic parameters are periodically modulated. Even though there exists formally exact methods of treating such set-ups...

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“…The SA is an approximation that extracts a slow part of the dynamics; one can obtain L SA by averaging L in time in the interaction picture or by omitting the fast oscillating terms in L in the interaction picture. However, it is known that the internal current vanishes in the NESS of the SA-QME [9]. Therefore, the SA-QME is not appropriate for analyzing the steady state itself (however, note Ref.…”

Section: Decomposition Of Qmementioning

confidence: 99%

“…Therefore, the SA-QME is not appropriate for analyzing the steady state itself (however, note Ref. [46]), and one often uses any of the original Redfield QME, alternatively approximated Lindblad QME [9], or axiomatic Lindblad QME [44,45] for nonequilibrium situations.…”

Section: Decomposition Of Qmementioning

confidence: 99%

“…In quantum systems, one of the theoretical frameworks widely used for open systems is the quantum master equation (QME) [1], an equation of motion for the density matrix of the system. In fact, the QME is used in various fields of physics: e.g., quantum optics [1,2], nuclear magnetic resonance [3], electron transfer in chemical physics and biophysics [4,5], heat transport [6,7,8,9,10,11,12,13,14], electronic transport in mesoscopic conductors [15,16,17,18,19], spin transport [20], and nonequilibrium thermodynamics and statistical physics [21,22,23,24,25]. Therefore, the QME is a reliable approach to investigating NESS in various systems (c.f.…”

Section: Introductionmentioning

confidence: 99%

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A Perturbative Method for Nonequilibrium Steady State of Open Quantum Systems

Yuge

Sugita

2015

J. Phys. Soc. Jpn.

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We develop a method of calculating the nonequilibrium steady state (NESS) of an open quantum system that is weakly coupled to reservoirs in different equilibrium states. We describe the system using a Redfield-type quantum master equation (QME). We decompose the Redfield QME into a Lindblad-type QME and the remaining part R. Regarding the steady state of the Lindblad QME as the unperturbed solution, we perform a perturbative calculation with respect to R to obtain the NESS of the Redfield QME. The NESS thus determined is exact up to the first order in the system-reservoir coupling strength (pump/loss rate), which is the same as the order of validity of the QME. An advantage of the proposed method in numerical computation is its applicability to systems larger than those in methods of directly solving the original Redfield QME. We apply the method to a noninteracting fermion system to obtain an analytical expression of the NESS density matrix. We also numerically demonstrate the method in a nonequilibrium quantum spin chain.

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Modeling heat transport through completely positive maps

Cited by 216 publications

References 30 publications

From Thermal Rectifiers to Thermoelectric Devices

From Thermal Rectifiers to Thermoelectric Devices

Quantum transport under ac drive from the leads: A Redfield quantum master equation approach

A Perturbative Method for Nonequilibrium Steady State of Open Quantum Systems

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