On the nature of Bose-Einstein condensation in disordered systems

TL;DR

This paper investigates Bose-Einstein condensation in disordered systems, establishing a link between condensation in random eigenstates and free states, and providing explicit formulas for particle distribution.

Contribution

It demonstrates the equivalence of condensation in random and kinetic eigenstates and introduces a method to analyze particle distribution in such systems.

Findings

Condensation in random eigenstates occurs iff in kinetic eigenstates.

The condensate densities in both states are equal.

Method applies to weak non-random potentials, yielding similar results.

Abstract

We study the perfect Bose gas in random external potentials and show that there is generalized Bose-Einstein condensation in the random eigenstates if and only if the same occurs in the one-particle kinetic-energy eigenstates, which corresponds to the generalized condensation of the free Bose gas. Moreover, we prove that the amounts of both condensate densities are equal. Our method is based on the derivation of an explicit formula for the occupation measure in the one-body kinetic-energy eigenstates which describes the repartition of particles among these non-random states. This technique can be adapted to re-examine the properties of the perfect Bose gas in the presence of weak (scaled) non-random potentials, for which we establish similar results.