Wigner-Weyl calculus in description of non-dissipative transport phenomena

Precise Wigner-Weyl calculus for the honeycomb lattice

In this paper we propose the precise Wigner-Weyl calculus for the lattice models defined on the honeycomb lattice. We construct two symbols of operators: the $\mathscr{B}$-symbol, which is similar to the symbol introduced by F. Buot, and the $W$ (or, Weyl) symbol. The latter possesses the set of useful properties. These identities allow us to use it in physical applications. In particular, we derive topological expression for the Hall conductivity through the Wigner transformed Green function. This expression may be used for the description of quantum Hall effect in the systems with artificial…

Wigner-Weyl calculus in Keldysh technique

We discuss the non-equilibrium dynamics of condensed matter/quantum field systems in the framework of Keldysh technique. In order to deal with the inhomogeneous systems we use the Wigner-Weyl formalism. Unification of the mentioned two approaches is demonstrated on the example of Hall conductivity. We express Hall conductivity through the Wigner transformed two-point Green's functions. We demonstrate how this expression is reduced to the topological number in thermal equilibrium at zero temperature. At the same time both at finite temperature and out of equilibrium the topological invariance i…

Precise Wigner-Weyl calculus for lattice models

We propose a new version of Wigner-Weyl calculus for tight-binding lattice models. It allows to express various physical quantities through Weyl symbols of operators and Green's functions. In particular, Hall conductivity in the presence of varying and arbitrarily strong magnetic field is represented using the proposed formalism as a topological invariant.

有限晶格的离散维格纳-外尔演算

Discrete Wigner-Weyl calculus for the finite lattice

该研究发展Felix Buot的方法，修正其算子符号定义，构建适用于有限晶格的新型离散外尔符号，推导二维非平衡非均匀系统电导率表达式，完善晶格模型的Keldysh技术。

Dissipative transport in superlattices within the Wigner function formalism

We employ the Wigner function formalism to simulate partially coherent, dissipative electron transport in biased semiconductor superlattices. We introduce a model collision integral with terms that describe energy dissipation, momentum relaxation, and the decay of spatial coherences (localization). Based on a particle-based solution to the Wigner transport equation with the model collision integral, we simulate quantum electronic transport at 10 K in a GaAs/AlGaAs superlattice and accurately reproduce its current density vs field characteristics obtained in experiment.

开放量子系统的三次量子化：新的耗散对称性及其与相空间和Keldysh场论表述的联系

Third quantization of open quantum systems: new dissipative symmetries and connections to phase-space and Keldysh field theory formulations

本文重新表述三次量子化技术，统一连接Lindblad主方程、Wigner函数和Keldysh作用量三种开放量子系统方法，揭示二次Lindblad算符中的基本耗散对称性，并将其应用于耗散非线性振子获得新的精确结果。