Wigner Equations for Phonons Transport and Quantum Heat Flux

IF 2.6 2区数学 Q1 MATHEMATICS, APPLIED

Journal of Nonlinear Science Pub Date : 2023-11-03 DOI:10.1007/s00332-023-09993-z

V. D. Camiola, V. Romano, G. Vitanza

引用次数: 0

Abstract

Abstract Starting from the quantum Liouville equation for the density operator and applying the Weyl quantization, Wigner equations for the acoustic, optical and Z phonons are deduced. The equations are valid for any solid, including 2D crystals like graphene. With the use of Moyal’s calculus and its properties, the pseudo-differential operators are expanded up to the second order in $$\hbar $$ ħ . An energy transport model is obtained by using the moment method with closure relations based on a quantum version of the Maximum Entropy Principle by employing a relaxation time approximation for the production terms of energy and energy flux. An explicit form of the thermal conductivity with quantum correction up to $$\hbar ^2$$ ħ 2 order is obtained under a long-time scaling for the most relevant phonon branches.

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声子输运和量子热通量的Wigner方程

摘要从密度算子的量子Liouville方程出发，应用Weyl量子化，推导了声子、光学声子和Z声子的Wigner方程。该方程适用于任何固体，包括石墨烯等二维晶体。利用Moyal微积分及其性质，将伪微分算子扩展到$$\hbar $$的二阶。基于最大熵原理的量子版本，通过对能量和能量通量的产生项采用松弛时间近似，利用具有闭合关系的矩量方法获得了能量输运模型。对于最相关的声子分支，在长时间标度下得到了具有高达$$\hbar ^2$$ ^ 2阶量子修正的显式热导率。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Nonlinear Science 数学-力学

CiteScore

5.00

自引率

3.30%

发文量

审稿时长

4.5 months

期刊介绍： The mission of the Journal of Nonlinear Science is to publish papers that augment the fundamental ways we describe, model, and predict nonlinear phenomena. Papers should make an original contribution to at least one technical area and should in addition illuminate issues beyond that area''s boundaries. Even excellent papers in a narrow field of interest are not appropriate for the journal. Papers can be oriented toward theory, experimentation, algorithms, numerical simulations, or applications as long as the work is creative and sound. Excessively theoretical work in which the application to natural phenomena is not apparent (at least through similar techniques) or in which the development of fundamental methodologies is not present is probably not appropriate. In turn, papers oriented toward experimentation, numerical simulations, or applications must not simply report results without an indication of what a theoretical explanation might be. All papers should be submitted in English and must meet common standards of usage and grammar. In addition, because ours is a multidisciplinary subject, at minimum the introduction to the paper should be readable to a broad range of scientists and not only to specialists in the subject area. The scientific importance of the paper and its conclusions should be made clear in the introduction-this means that not only should the problem you study be presented, but its historical background, its relevance to science and technology, the specific phenomena it can be used to describe or investigate, and the outstanding open issues related to it should be explained. Failure to achieve this could disqualify the paper.