Transport in a periodically driven tilted lattice via the extended reservoir approach: Stability criterion for recovering the continuum limit

TL;DR

This paper investigates the extended reservoir approach for quantum transport in periodically driven systems, establishing a stability criterion to recover the continuum limit and demonstrating its effectiveness through a tilted lattice model.

Contribution

It introduces a simple stability criterion for selecting relaxation rates in the extended reservoir approach applied to periodically driven quantum systems.

Findings

The approach captures the physical continuum limit response.

It recovers known behavior in weak coupling regimes.

It enables analysis of strong coupling and nonlinear responses.

Abstract

Extended reservoirs provide a framework for capturing macroscopic, continuum environments, such as metallic electrodes driving a current through a nanoscale contact, impurity, or material. We examine the application of this approach to periodically driven systems, specifically in the context of quantum transport. As with non--equilibrium steady states in time--independent scenarios, the current displays a Kramers' turnover including the formation of a plateau region that captures the physical, continuum limit response. We demonstrate that a simple stability criteria identifies an appropriate relaxation rate to target this physical plateau. Using this approach, we study quantum transport through a periodically driven tilted lattice coupled to two metallic reservoirs held at a finite bias and temperature. We use this model to benchmark the extended reservoir approach and assess the stability criteria. The approach recovers well--understood physical behavior in the limit of weak system--reservoir coupling. Extended reservoirs enable addressing strong coupling and non--linear response as well, where we analyze how transport responds to the dynamics inside the driven lattice. These results set the foundations for the use of extended reservoir approach for periodically driven, quantum systems, such as many--body Floquet states.