非平衡量子输运的有效平衡描述I：基本原理和方法
Effective Equilibrium Description of Nonequilibrium Quantum Transport I: Fundamentals and Methodology
摘要：
强关联量子系统的理论描述提出了几个挑战和一些悬而未决的问题。在本文中，我们专注于非线性电子输运通过量子点保持在有限的偏压使用的概念引入Hershfield [物理。70，2134（1993）]，由此可以用系统的Lippmann-Schwinger算子来表示这种非平衡量子杂质模型。这些散射算子允许一个重新制定的非平衡问题作为一个有效的平衡问题与修改后的哈密顿量，从而促进平衡多体技术的实施。我们提供了一个替代推导的有效哈密顿的Hershfield使用“开放系统”的概念。此外，我们证明了使用Schwinger-Keldysh框架和有效平衡方法计算的观测量之间的等价性。对于运输的研究，点的非平衡谱函数被确定为主要利益的数量，我们推导出一般表达式的电流（梅尔-Wingreen公式）和电荷占领的点。我们介绍了一个有限温度的形式主义，这是用来作为计算实时格林函数的工具。在一个配套文件中，我们阐明了一个通用的计划相互作用模型的微扰计算，特别是安德森模型。
英文摘要：
The theoretical description of strongly correlated quantum systems out of equilibrium presents several challenges and a number of open questions persist. In this paper we focus on nonlinear electronic transport through a quantum dot maintained at finite bias using a concept introduced by Hershfield [Phys. Rev. Lett. 70, 2134 (1993)] whereby one can express such nonequilibrium quantum impurity models in terms of the system's Lippmann-Schwinger operators. These scattering operators allow one to reformulate the nonequilibrium problem as an effective equilibrium problem associated with a modified Hamiltonian, thus facilitating the implementation of equilibrium many-body techniques. We provide an alternative derivation of the effective Hamiltonian of Hershfield using the concept of an "open system". Furthermore, we demonstrate the equivalence between observables computed using the Schwinger-Keldysh framework and the effective equilibrium approach. For the study of transport, the non-equilibrium spectral function of the dot is identified as the quantity of principal interest and we derive general expressions for the current (the Meir-Wingreen formula) and the charge occupation of the dot. We introduce a finite temperature formalism which is used as a tool for computing real time Green's functions. In a companion paper we elucidate a generic scheme for perturbative calculations of interacting models, with particular reference to the Anderson model.
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