Number-resolved master equation approach to quantum measurement and quantum transport

TL;DR

This paper reviews the particle-number-resolved master equation approach for quantum measurement and transport, highlighting its ability to analyze shot noise, full counting statistics, and complex phenomena like the Kondo effect.

Contribution

It systematically discusses the n-resolved master equation approach and introduces a new self-consistent Born approximation method with broad application potential.

Findings

Efficient analysis of shot noise and full counting statistics.

Ability to recover exact results for noninteracting systems.

Potential to study complex phenomena like the Kondo effect.

Abstract

In addition to the well-known Landauer-Buttiker scattering theory and the nonequilibrium Green's function technique for mesoscopic transports, an alternative (and very useful) scheme is quantum master equation approach. In this article, we review the particle-number (n)-resolved master equation (n-ME) approach and its systematic applications in quantum measurement and quantum transport problems. The n-ME contains rich dynamical information, allowing efficient study of topics such as shot noise and full counting statistics analysis. Moreover, we also review a newly developed master equation approach (and its n-resolved version) under self-consistent Born approximation. The application potential of this new approach is critically examined via its ability to recover the exact results for noninteracting systems under arbitrary voltage and in presence of strong quantum interference, and the challenging non-equilibrium Kondo effect.