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arXiv 2008.01275cond-mat.mes-hallquant-ph
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非平衡格林函数(NEGF)方法

The Non-Equilibrium Green Function (NEGF) Method

Kerem Y. Camsari, Shuvro Chowdhury, Supriyo Datta

摘要:

非平衡格林函数(NEGF)方法是在20世纪60年代通过Schwinger、Kadanoff、Baym、Keldysh等人的经典工作,使用多体微扰理论(MBPT)和非平衡过程的图解理论建立的。许多文献是基于最初的MBPT为基础的方法,这使得它无法访问那些不熟悉先进的量子统计力学。我们从单电子薛定谔方程出发,用比较基本的参数直接得到了NEGF方程。这些方程已被用来讨论许多有趣的问题,如量子化电导,(整数)量子霍尔效应,安德森局域化,共振隧穿和自旋输运没有多体效应的系统处理。但它超越了纯粹的相干输运,使我们能够在自洽玻恩近似中包括相破缺相互作用(动量弛豫和动量守恒以及自旋守恒和自旋弛豫)。我们相信NEGF方程的范围和实用性超越了最初用于推导它的基于MBPT的方法。NEGF教会我们如何将量子动力学与“接触”结合起来,就像玻尔兹曼教会我们如何将经典动力学与“接触”结合起来一样,使用广泛的比喻意义上的接触一词来表示各种熵驱动的过程。我们相信,这种“接触”薛定谔方程的方法应该对任何从事器件物理或一般非平衡统计力学工作的人都有广泛的兴趣。

英文摘要:

The Non-Equilibrium Green Function (NEGF) method was established in the 1960's through the classic work of Schwinger, Kadanoff, Baym, Keldysh and others using many-body perturbation theory (MBPT) and the diagrammatic theory for non-equilibrium processes. Much of the literature is based on the original MBPT-based approach and this makes it inaccessible to those unfamiliar with advanced quantum statistical mechanics. We obtain the NEGF equations directly from a one-electron Schrödinger equation using relatively elementary arguments. These equations have been used to discuss many problems of great interest such as quantized conductance, (integer) quantum Hall effect, Anderson localization, resonant tunneling and spin transport without a systematic treatment of many-body effects. But it goes beyond purely coherent transport allowing us to include phase-breaking interactions (both momentum-relaxing and momentum-conserving as well as spin-conserving and spin-relaxing) within a self-consistent Born approximation. We believe that the scope and utility of the NEGF equations transcend the MBPT-based approach originally used to derive it. NEGF teaches us how to combine quantum dynamics with "contacts" much as Boltzmann taught us how to combine classical dynamics with "contacts", using the word contacts in a broad, figurative sense to denote all kinds of entropy-driven processes. We believe that this approach to "contact-ing" the Schrödinger equation should be of broad interest to anyone working on device physics or non-equilibrium statistical mechanics in general.

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