Quantum transport in one-dimensional systems via a master equation approach: Numerics and an exact solution

TL;DR

This paper explores quantum transport in one-dimensional systems using a master equation approach, demonstrating numerical methods and providing an exact solution for specific models to understand nonequilibrium steady states.

Contribution

It introduces a numerical approach with the density matrix renormalization method and presents an exact solution for a particular model in quantum transport.

Findings

Successful use of DMRG to find stationary solutions

Derivation of an exact solution for a specific model

Insights into properties of quantum nonequilibrium steady states

Abstract

We discuss recent findings about properties of quantum nonequilibrium steady states. In particular we focus on transport properties. It is shown that the time dependent density matrix renormalization method can be used successfully to find a stationary solution of Lindblad master equation. Furthermore, for a specific model an exact solution is presented.