Decay of correlations and absence of superfluidity in the disordered Tonks-Girardeau gas

TL;DR

This paper demonstrates that in a disordered Tonks-Girardeau gas, localization leads to exponential decay of correlations, preventing Bose-Einstein condensation and superfluidity even at zero temperature.

Contribution

It proves the absence of superfluidity and Bose-Einstein condensation in the disordered Tonks-Girardeau gas due to localization effects.

Findings

Exponential decay of correlations in many-body eigenstates

No Bose-Einstein condensation in the disordered system

Absence of superfluidity at zero temperature

Abstract

We consider the Tonks-Girardeau gas subject to a random external potential. If the disorder is such that the underlying one-particle Hamiltonian displays localization (which is known to be generically the case), we show that there is exponential decay of correlations in the many-body eigenstates. Moreover, there is no Bose-Einstein condensation and no superfluidity, even at zero temperature.