Non-Markovian effects in electronic and spin transport

TL;DR

This paper develops a non-Markovian master equation framework for quadratic fermionic systems coupled to reservoirs, enabling analysis of complex non-Markovian effects in quantum transport.

Contribution

It introduces an explicit link between master equations and Green's functions, allowing the study of non-Markovian dynamics in quantum transport models.

Findings

Identifies regimes with negative decoherence rates.

Analyzes real-time dynamics and steady states of specific models.

Extends phase diagrams of XY-spin chains to non-Markovian regimes.

Abstract

We derive a non-Markovian master equation for the evolution of a class of open quantum systems consisting of quadratic fermionic models coupled to wide-band reservoirs. This is done by providing an explicit correspondence between master equations and non-equilibrium Green's functions approaches. Our findings permit to study non-Markovian regimes characterized by negative decoherence rates. We study the real-time dynamics and the steady-state solution of two illustrative models: a tight-binding and an XY-spin chains. The rich set of phases encountered for the non-equilibrium XY model extends previous studies to the non-Markovian regime.