Weak coupling approximations in non-Markovian Transport

TL;DR

This paper investigates how energy-dependent reservoir densities induce non-Markovian effects in quantum transport, comparing approximate master equations with exact solutions to assess their validity.

Contribution

It demonstrates the limitations of non-Markovian master equations in modeling transport with energy-dependent reservoirs and provides a comparative analysis with exact solutions.

Findings

Non-Markovian effects become significant with strong energy dependence.

Approximate master equations may fail to accurately predict transport properties.

Exact solutions reveal the limitations of common approximations.

Abstract

We study the transport properties of the Fano-Anderson model with a Lorentzian-shaped density of states in one of the electronic reservoirs. We explicitly show that the energy dependence of the density of states can cause non-Markovian effects and that the non-Markovian master equation may fail if these effects are strong. We evaluate the stationary current, the zero frequency current noise and the occupation dynamics of the resonant level by means of a quantum master equation approach within different approximation schemes and compare the results to the exact solution obtained by scattering theory and Green's functions.