A finite temperature study of ideal quantum gases in the presence of one dimensional quasi-periodic potential

TL;DR

This paper investigates the thermodynamics and transport properties of ideal quantum gases in a one-dimensional quasi-periodic Aubry-André potential at finite temperature, revealing universal behaviors and localization phenomena.

Contribution

It provides a detailed analysis of BEC crossover, superfluidity, and localization in quasi-periodic potentials, highlighting universal scaling and the impact on persistent currents.

Findings

Non-monotonic BEC crossover temperature with potential strength

Power-law vanishing of BEC temperature at the critical point

Decay of persistent current indicating localization at Fermi energy

Abstract

We study the thermodynamics of ideal Bose gas as well as the transport properties of non interacting bosons and fermions in a one dimensional quasi-periodic potential, namely Aubry-Andr\'e (AA) model at finite temperature. For bosons in finite size systems, the effect of quasi-periodic potential on the crossover phenomena corresponding to Bose-Einstein condensation (BEC), superfluidity and localization phenomena at finite temperatures are investigated. From the ground state number fluctuation we calculate the crossover temperature of BEC which exhibits a non monotonic behavior with the strength of AA potential and vanishes at the self-dual critical point following power law. Appropriate rescaling of the crossover temperatures reveals universal behavior which is studied for different quasi-periodicity of the AA model. Finally, we study the temperature and flux dependence of the persistent current of fermions in presence of a quasi-periodic potential to identify the localization at the Fermi energy from the decay of the current.