Quantum master equation approach to quantum transport through mesoscopic systems

TL;DR

This paper develops a quantum master equation framework for mesoscopic quantum transport, extending previous approaches to finite temperature and bias, providing a versatile tool for analyzing transport phenomena.

Contribution

It introduces a generalized quantum master equation approach applicable at finite temperature and bias, extending Gurvitz's method for broader transport analysis.

Findings

Formalism applicable for a wide range of transport problems

Validates approach with multiple examples

Provides compact expressions for current and density matrix

Abstract

For quantum transport through mesoscopic system, a quantum master equation approach is developed in terms of compact expressions for the transport current and the reduced density matrix of the system. The present work is an extension of Gurvitz's approach for quantum transport and quantum measurement, namely, to finite temperature and arbitrary bias voltage. Our derivation starts from a second-order cummulant expansion of the tunneling Hamiltonian, then follows conditional average over the electrode reservoir states. As a consequence, in the usual weak tunneling regime, the established formalism is applicable for a wide range of transport problems. The validity of the formalism and its convenience in application are well illustrated by a number of examples.