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Acta Physica Sinica

THE THEORY OF LINEAR TRANSPORT COEFFICIENTS IN QUANTUM STATISTICS

CHEN SHI-KANG

Published Jan 1, 1963• 0 citations
Publisher

Abstract

摘要 本文利用van Hove的趋向平衡理论讨论了Kubo的输运系数表达式,得到了没有任何无规相位假设的结果,并将其与玻耳兹曼方程作了比较。由本文的讨论,我们期望在强作用系统的高频现象中能观测到相位关联效应。高频线性输运系数的宏观测量不会破坏这种相位关联。 Abstract Using the method of van Hove in the theory of approach to equilibrium, we analyse Kubo's formula of transport coefficients. The results of dynamical theory are obtained without using the assumption of random phase and compared with the solution of Boltzmann equation. We expect that the phase interference effect may be observed in the high-frequency phenomena of strongly interacting system. The macroscopic measurement of high-frequency linear transport process does not destroy this interference effect. 作者及机构信息 陈式刚 Authors and contacts CHEN SHI-KANG 参考文献 [1] 施引文献

DOI
10.7498/aps.19.456

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摘要 本文指出杨诺赛波动方程作为电子的个体理论的困难;指出这一类型波动方程可以作为原子核系综理论的数学形式,也可以作为元粒子系综理论的数学形式。本文并讨论了这一类型波动方程的第二级量子化问题。 Abstract It is shown that the modified Schr?dinger equation proposed by Janossy cannot describe the behavior of the electron correctly. However, it is further shown that the equation can be regarded as a model of a possible phenomenalogical theory of nuclei or as a model of a possible theory of elementary particles. The quantization of the equation is discussed. 作者及机构信息 朱洪元 1. 中国科学院物理研究所 Authors and contacts TZU HUNG-YUAN 1. 中国科学院物理研究所 参考文献 [1] 施引文献

Acta Physica Sinica•Jan 1, 1956•0 citations
摘要 本文利用van Hove的趋向平衡理论讨论了Kubo的输运系数表达式,得到了没有任何无规相位假设的结果,并将其与玻耳兹曼方程作了比较。由本文的讨论,我们期望在强作用系统的高频现象中能观测到相位关联效应。高频线性输运系数的宏观测量不会破坏这种相位关联。 Abstract Using the method of van Hove in the theory of approach to equilibrium, we analyse Kubo's formula of transport coefficients. The results of dynamical theory are obtained without using the assumption of random phase and compared with the solution of Boltzmann equation. We expect that the phase interference effect may be observed in the high-frequency phenomena of strongly interacting system. The macroscopic measurement of high-frequency linear transport process does not destroy this interference effect. 作者及机构信息 陈式刚 Authors and contacts CHEN SHI-KANG 参考文献 [1] 施引文献
We consider a system of weakly interacting Fermions which satisfies all those requirements necessary for the derivation of Van Hove’s weak coupling master equation. We show how the Boltzmann equation can be derived with the help of a Factorisation Theorem which we then prove, in the limit of an infinite system. We then use this Factorisation Theorem to show that the electrical conductivity derived from the Kubo formula is equivalent to the conductivity derived from the Boltzmann equation, for the same system of Fermions. Finally, we illustrate how the theory must be modified for a weakly interacting system of electrons and phonons.
摘要 提出了一种新的变分解的方法求解极化子问题，并归结为解一个非线性的微分积分方程。其数值计算的结果正是过去工作所预期的。 Abstract A new variational method for solving polaron problem is suggested, and the nonlinear differential-integral equation satisfied by variational solution of plolaron has been derived, the numerical result of which is as anticipated by earlier. works. 作者及机构信息 汪克林, 陈庆虎, 完绍龙 1. 中国科学技术大学基础物理中心 基金项目: 国家攀登计划资助课题. Authors and contacts WANG KE-LIN, CHEN QING-HU, WAN SHAO-LONG 1. 中国科学技术大学基础物理中心 参考文献 施引文献
We have given in two previous chapters a first introduction to non-equilibrium phenomena. The present chapter is devoted to a presentation of more general approaches, in which time dependence will be made explicit, whereas in practice we had to limit ourselves to stationary situations in Chapters 6 and 8. In the first part of the chapter, we examine the relaxation toward equilibrium of a system that has been brought out of equilibrium by an external perturbation. The main result is that, for small deviations from equilibrium, this relaxation is described by equilibrium time correlation functions, called Kubo (or relaxation) functions: this result is also known as ‘Onsager's regression law’. The Kubo functions turn out to be basic objects of non-equilibrium statistical mechanics. First they allow one to compute the dynamical susceptibilities, which describe the response of the system to an external time dependent perturbation: the dynamical susceptibilities are, within a multiplicative constant, the time derivatives of Kubo functions. A second crucial property is that transport coefficients can be expressed in terms of time integrals of Kubo functions. As we limit ourselves to small deviations from equilibrium, our theory is restricted to a linear approximation and is known as linear response theory . The classical version of linear reponse is somewhat simpler than the quantum one, and will be described first in Section 9.1. We shall turn to the quantum theory in Section 9.2, where one of our main results will be the proof of the fluctuationdissipation theorem.
Nonequilibrium transport properties of quantum systems have recently become experimentally accessible in a number of platforms in so-called full-counting experiments that measure transient and steady-state nonequilibrium transport dynamics. We show that the effect of the measurement back-action can be exploited to establish general relationships between transport coefficients in the transient regime which take the form of fluctuation-dissipation theorems in the steady state. This result becomes most conspicuous in the transient dynamics of open quantum systems under strong-coupling to non-Markovian environments in nonequilibrium settings. In order to explore this regime, a new simulation method based in a hierarchy of equations of motion has been developed. We instantiate our proposal with the study of energetic conductance between two baths connected via a few level system.
摘要 本文指出杨诺赛波动方程作为电子的个体理论的困难;指出这一类型波动方程可以作为原子核系综理论的数学形式,也可以作为元粒子系综理论的数学形式。本文并讨论了这一类型波动方程的第二级量子化问题。 Abstract It is shown that the modified Schr?dinger equation proposed by Janossy cannot describe the behavior of the electron correctly. However, it is further shown that the equation can be regarded as a model of a possible phenomenalogical theory of nuclei or as a model of a possible theory of elementary particles. The quantization of the equation is discussed. 作者及机构信息 朱洪元 1. 中国科学院物理研究所 Authors and contacts TZU HUNG-YUAN 1. 中国科学院物理研究所 参考文献 [1] 施引文献