QmeQ 1.0: An open-source Python package for calculations of transport through quantum dot devices

QmeQ is an open-source Python package for numerical modeling of transport through quantum dot devices with strong electron–electron interactions using various approximate master equation approaches. The package provides a framework for calculating stationary particle or energy currents driven by differences in chemical potentials or temperatures between the leads which are tunnel coupled to the quantum dots. The electronic structures of the quantum dots are described by their single-particle states and the Coulomb matrix elements between the states. When transport is treated perturbatively to lowest order in the tunneling couplings, the possible approaches are Pauli (classical), first-order Redfield, and first-order von Neumann master equations, and a particular form of the Lindblad equation. When all processes involving two-particle excitations in the leads are of interest, the second-order von Neumann approach can be applied. All these approaches are implemented in QmeQ. We here give an overview of the basic structure of the package, give examples of transport calculations, and outline the range of applicability of the different approximate approaches.QmeQ是一款开源Python软件包，可采用多种近似主方程（master equation）方法，对存在强电子-电子相互作用的量子点器件的输运过程开展数值建模。该软件包提供了一套标准化计算框架，用于计算由隧穿耦合至量子点的引线间化学势差或温度差所驱动的定态粒子流或能量流。量子点的电子结构可通过其单粒子态以及态间的库仑矩阵元进行表征。当采用隧穿耦合项下的最低阶微扰论处理输运过程时，可选用的近似方法包括泡利（经典）主方程、一阶雷德菲尔德主方程、一阶冯·诺依曼主方程，以及一类特殊形式的林德布拉德（Lindblad）方程。当需要考虑引线中所有涉及双粒子激发的过程时，则可采用二阶冯·诺依曼方法。上述所有近似方法均已在QmeQ中实现。本文概述了该软件包的基本结构，给出了输运计算的典型实例，并梳理了不同近似方法的适用范围。