Localisation determines the optimal noise rate for quantum transport

TL;DR

This paper investigates how eigenstate localisation influences the optimal noise level for energy transport in quantum chains, revealing size-dependent effects and the breakdown of this relationship at low temperatures.

Contribution

It provides a systematic analysis of localisation and noise interplay in quantum transport, incorporating finite temperature effects with a Bloch-Redfield model.

Findings

Optimal transport efficiency depends on both size-independent and size-dependent factors.

A power law describes the interplay between size-dependent and size-independent responses.

The localisation-noise relationship holds at intermediate and high temperatures but fails at low temperatures.

Abstract

Environmental noise plays a key role in determining the efficiency of transport in quantum systems. However, disorder and localisation alter the impact of such noise on energy transport. To provide a deeper understanding of this relationship we perform a systematic study of the connection between eigenstate localisation and the optimal dephasing rate in 1D chains. The effects of energy gradients and disorder on chains of various lengths are evaluated and we demonstrate how optimal transport efficiency is determined by both size-independent, as well as size-dependent factors. By discussing how size-dependent influences emerge from finite size effects we establish when these effects are suppressed, and show that a simple power law captures the interplay between size-dependent and size-independent responses. Moving beyond phenomenological pure dephasing, we implement a finite temperature Bloch-Redfield model that captures detailed balance. We show that the relationship between localisation and optimal environmental coupling strength continues to apply at intermediate and high temperature but breaks down in the low temperature limit.