Noise-induced transport in the Aubry-Andr\'e-Harper model

TL;DR

This paper investigates how coupling a heat bath affects quantum transport in the Aubry-André-Harper model, revealing phase-dependent transport behaviors and proposing a classical master equation to explain the phenomena.

Contribution

It introduces a classical master equation model that qualitatively and sometimes quantitatively explains heat bath effects on transport in the AAH model.

Findings

Localized phase exhibits logarithmic transport due to heat bath coupling.

Increasing coupled sites causes a crossover from ballistic to logarithmic or diffusive transport.

Crossover times grow exponentially with site spacing, and diffusion constants decrease exponentially.

Abstract

We study quantum transport in a quasiperiodic Aubry-Andr\'e-Harper (AAH) model induced by the coupling of the system to a Markovian heat bath. We find that coupling the heat bath locally does not affect transport in the delocalized and critical phases, while it induces logarithmic transport in the localized phase. Increasing the number of coupled sites at the central region introduces a transient diffusive regime, which crosses over to logarithmic transport in the localized phase and in the delocalized regime to ballistic transport. On the other hand, when the heat bath is coupled to equally spaced sites of the system, we observe a crossover from ballistic and logarithmic transport to diffusion in the delocalized and localized regimes, respectively. We propose a classical master equation, which captures our numerical observations for both coupling configurations on a qualitative level and for some parameters, even on a quantitative level. Using the classical picture, we show that the crossover to diffusion occurs at a time that increases exponentially with the spacing between the coupled sites, and the resulting diffusion constant decreases exponentially with the spacing.