# Einstein relation for a driven disordered quantum chain in subdiffusive regime

## TL;DR

This paper demonstrates a generalized Einstein relation for a quantum particle in a disordered chain exhibiting subdiffusive behavior, linking its spread to a time-dependent drift under electric fields, valid beyond linear response.

## Contribution

It introduces a generalized Einstein relation for subdiffusive quantum transport in disordered systems, extending its validity to strong driving regimes and nonlinear effects.

## Key findings

- GER relates subdiffusive spread to drift velocity under electric field.
- GER remains valid beyond linear response, up to Stark-like localization.
- Numerical results are supported by simplified rate equations.

## Abstract

A quantum particle propagates subdiffusively on a strongly disordered chain when it is coupled to itinerant hard-core bosons. We establish a generalized Einstein relation (GER) that relates such subdiffusive spread to an unusual time-dependent drift velocity, which appears as a consequence of a constant electric field. We show that GER remains valid much beyond the regime of the linear response. Qualitatively, it holds true up to strongest drivings when the nonlinear field-effects lead to the Stark-like localization. Numerical calculations based on full quantum evolution are substantiated by much simpler rate equations for the boson-assisted transitions between localized Anderson states.