Nonequilibrium distribution functions for quantum transport: Universality and approximation for the steady state regime

Ness, H.

doi:10.1103/physrevb.89.045409

Cited by 14 publications

(16 citation statements)

References 68 publications

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“…Moreover, for systems far from equilibrium, the FDT which characterizes the balance between the environment fluctuations and dissipation is no longer rigorous. Instead, various forms of approximate FDR have been proposed [187][188][189][190][191][192][193], from which a local temperature can be extracted [139, 187-189, 193, 194]. For instance, Cugliandolo [194] and Puglisi et al [139] have determined the local temperatures of non-equilibrium classical systems by scrutinizing the deviation of non-equilibrium FDR from equilibrium FDT.…”

Section: General Remarksmentioning

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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Section: General Remarksmentioning

confidence: 99%

Local temperatures out of equilibrium

2019

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“…The celebrated Anderson-Holstein model, with a single electronic orbital coupled to a local phonon mode, exposes an intricate interplay between the electronic and nuclear degrees of freedom. The model has been extensively studied to reveal the behavior of the current and its fluctuations in different regimes of electron-phonon coupling, see for example [14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30] . An extension of the Anderson-Holstein model with a secondary phonon bath was examined in many studies, see e.g.…”

Section: Introductionmentioning

confidence: 99%

Full counting statistics of vibrationally assisted electronic conduction: Transport and fluctuations of thermoelectric efficiency

2015

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We study the statistical properties of charge and energy transport in electron conducting junctions with electron-phonon interactions, specifically, the thermoelectric efficiency and its fluctuations. The system comprises donor and acceptor electronic states, representing a two-site molecule or a double quantum dot system. Electron transfer between metals through the two molecular sites is coupled to a particular vibrational mode which is taken to be either harmonic or anharmonic-a truncated (twostate) spectrum. Considering these models we derive the cumulant generating function in steady state for charge and energy transfer, correct to second-order in the electron-phonon interaction, but exact to all orders in the metal-molecule coupling strength. This is achieved by using the nonequilibrium Green's function approach (harmonic mode) and a kinetic quantum master equation method (anharmonic mode). From the cumulant generating function we calculate the charge current and its noise and the large deviation function for the thermoelectric efficiency. We demonstrate that at large bias the charge current, differential conductance, and the current noise can identify energetic and structural properties of the junction. We further examine the operation of the junction as a thermoelectric engine and show that while the macroscopic thermoelectric efficiency is indifferent to the nature of the mode (harmonic or anharmonic), efficiency fluctuations do reflect this property.

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“…For the purpose of the present section, we then use the NEGF approach as the calculations are more straightforward in the non-interacting case. We also note that the NEGF formalism permits us to include local interaction in the central region in a compact and self-consistent scheme, as we have done in [22,[61][62][63][64][65][66][67].…”

Section: An Examplementioning

confidence: 99%

“…For example, in [22,[61][62][63]65], we have studied the effect of electron-vibration interaction on the electron current. For Gibbs-von Neumann NE entropy, one can also define an NE distribution function f NE C which contains all the effects of the interactions as shown in [66]. The interactions will affect the entropy production; however, we expect that, with the so-called conservative approximations for the interaction, the positiveness of the entropy will be conserved.…”

Section: An Example For the Entropy Of The Central Regionmentioning

confidence: 99%

“…We have shown that the NE steady state can be considered as a pseudo equilibrium state with a corresponding generalised Gibbs ensemble given by ρ NE . Following the same principles of equilibrium statistical mechanics, one can define from the generalised Gibbs ensemble a local NE distribution functions [66] in the L, C, R regions. From these NE distribution functions, one can also define the corresponding Gibbs-von Neumann entropies.…”

Section: An Example For the Entropy Of The Central Regionmentioning

confidence: 99%

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Nonequilibrium Thermodynamics and Steady State Density Matrix for Quantum Open Systems

Ness

2017

Entropy

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Abstract:We consider the generic model of a finite-size quantum electron system connected to two (temperature and particle) reservoirs. The quantum open system is driven out of equilibrium by the presence of both potential temperature and chemical differences between the two reservoirs. The nonequilibrium (NE) thermodynamical properties of such a quantum open system are studied for the steady state regime. In such a regime, the corresponding NE density matrix is built on the so-called generalised Gibbs ensembles. From different expressions of the NE density matrix, we can identify the terms related to the entropy production in the system. We show, for a simple model, that the entropy production rate is always a positive quantity. Alternative expressions for the entropy production are also obtained from the Gibbs-von Neumann conventional formula and discussed in detail. Our results corroborate and expand earlier works found in the literature.

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Nonequilibrium distribution functions for quantum transport: Universality and approximation for the steady state regime

Cited by 14 publications

References 68 publications

Local temperatures out of equilibrium

Local temperatures out of equilibrium

Full counting statistics of vibrationally assisted electronic conduction: Transport and fluctuations of thermoelectric efficiency

Nonequilibrium Thermodynamics and Steady State Density Matrix for Quantum Open Systems

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