Zubarev's Method of a Nonequilibrium Statistical Operator and Some Challenges in the Theory of Irreversible Processes

Morozov,; Ropke,

doi:10.5488/cmp.1.4.673

Cited by 23 publications

(23 citation statements)

References 37 publications

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“…The entropy minimization principle which is the core of the present work has previously been used to derive quantum hydrodynamic models in [27] and [28]. A different, but related approach, can be found in [55], [58], [71]. All these approaches rely on methods which, in the classical setting, have been developped in [53], [60].…”

Section: Introductionmentioning

confidence: 99%

Quantum Energy-Transport and Drift-Diffusion Models

2005

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We show that Quantum Energy-Transport and Quantum Drift-Diffusion models can be derived through diffusion limits of a collisional Wigner equation. The collision operator relaxes to an equilibrium defined through the entropy minimization principle. Both models are shown to be entropic and exhibit fluxes which are related with the state variables through spatially non-local relations. Thanks to an expansion of these models, 2 perturbations of the Classical Energy-Transport and Drift-Diffusion models are found. In the DriftDiffusion case, the quantum correction is the Bohm potential and the model is still entropic. In the Energy-Transport case however, the quantum correction is a rather complex expression and the model cannot be proven entropic.

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Section: Introductionmentioning

confidence: 99%

Quantum Energy-Transport and Drift-Diffusion Models

2005

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“…We refer the reader to these papers for more detail. Although different in the details, the approach developed in section 4 and in [20], [21] bears strong analogies with the so-called NESOM theory (Non-Equilibrium Statistical Operator Mechanics) [39], [42], [51].…”

Section: Introductionmentioning

confidence: 99%

Quantum hydrodynamic models derived from the entropy principle

Degond¹,

Méhats²,

Ringhofer³

2005

Nonlinear Partial Differential Equations and Related Analysis

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In this work, we give an overview of recently derived quantum hydrodynamic and diffusion models. A quantum local equilibrium is defined as a minimizer of the quantum entropy subject to local moment constraints (such as given local mass, momentum and energy densities). These equilibria relate the thermodynamic parameters (such as the temperature or chemical potential) to the densities in a non-local way. Quantum hydrodynamic models are obtained through moment expansions of the quantum kinetic equations closed by quantum equilibria. We also derive collision operators for quantum kinetic models which decrease the quantum entropy and relax towards quantum equilibria. Then, through diffusion limits of the quantum kinetic equation, we establish various classes of models which are quantum extensions of the classical energy-transport and drift-diffusion models.1991 Mathematics Subject Classification. 82C10, 82C70, 82D37, 81Q05, 81S05, 81S30, 81V70.Key words and phrases. Density matrix, quantum entropy, quantum moments, local quantum equilibria, quantum Boltzmann operator, quantum BGK operator, quantum hydrodynamics, quantum drift-diffusion, quantum energy-transport.

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“…The construction of such Gibbslike ensembles for the NE steady state can be obtained either by using the MacLennan-Zubarev approaches 12,[17][18][19][20][21][22][23] or the NE density matrix approach developed by Hershfield in Ref. [24].…”

Section: Steady State Quantum Transportmentioning

confidence: 99%

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

Ness

2014

Phys. Rev. B

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We derive a general expression for the electron nonequilibrium (NE) distribution function in the context of steady state quantum transport through a two-terminal nanodevice with interaction. The central idea for the use of NE distributions for open quantum systems is that both the NE and many-body (MB) effects are taken into account in the statistics of the finite size system connected to reservoirs. We develop an alternative scheme to calculate the NE steady state properties of such systems. The method, using NE distribution and spectral functions, presents several advantages, and is equivalent to conventional steady-state NE Green's functions (NEGF) calculations when the same level of approximation for the MB interaction is used. The advantages of our method resides in the fact that the NE distribution and spectral functions have better analytic behaviour for numerical calculations. Furthermore our approach offer the possibility of introducing further approximations, not only at the level of the MB interaction as in NEGF, but also at the level of the functional form used for the NE distributions. For the single level model with electron-phonon coupling we have considered, such approximations provide a good representation of the exact results, for either the NE distributions themselves or the transport properties. We also derive the formal extensions of our method for systems consisting of several electronic levels and several vibration modes.

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Zubarev's Method of a Nonequilibrium Statistical Operator and Some Challenges in the Theory of Irreversible Processes

Abstract: We give a brief review of applications of the method of the nonequilibrium statistical operator developed by D.N.Zubarev to some problems of nonequilibrium statistical mechanics.

Cited by 23 publications

References 37 publications

Quantum Energy-Transport and Drift-Diffusion Models

Quantum Energy-Transport and Drift-Diffusion Models

Quantum hydrodynamic models derived from the entropy principle

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

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