Effect of random on-site energies on the critical temperature of a lattice Bose gas

TL;DR

This paper investigates how random on-site energies influence the critical temperature of a non-interacting Bose gas on a lattice, revealing that disorder can slightly increase the critical temperature at high filling.

Contribution

It provides a perturbative analysis of the critical temperature shift due to Gaussian-distributed disorder in a lattice Bose gas, including the effect of disorder on the chemical potential.

Findings

Disorder slightly enhances the critical temperature at large filling.

Derived the shift in chemical potential caused by disorder.

Calculated the critical temperature for small disorder variance.

Abstract

We study the effect of random on-site energies on the critical temperature of a non-interacting Bose gas on a lattice. In our derivation the on-site energies are distributed according a Gaussian probability distribution function having vanishing average and variance $v_o^2$. By using the replicated action obtained by averaging on the disorder, we perform a perturbative expansion for the Green functions of the disordered system. We evaluate the shift of the chemical potential induced by the disorder and we compute, for $v_o^2 << 1$, the critical temperature for condensation. We find that, for large filling, disorder slightly enhances the critical temperature for condensation.