On the nature of Bose-Einstein condensation enhanced by localization

TL;DR

This paper investigates how external potentials influence Bose-Einstein condensation, showing that under certain conditions, the condensate can be distributed over many low-energy states without any single state being macroscopically occupied.

Contribution

It establishes a criterion for the absence of condensation in kinetic energy states and applies it to specific classes of random and weak potentials.

Findings

Condensate can be spread over many low-energy states without macroscopic occupation.

External potentials can suppress condensation in kinetic energy states under certain conditions.

The criterion is satisfied for specific classes of random and weak potentials.

Abstract

In a previous paper we established that for the perfect Bose gas and the mean-field Bose gas with an external random or weak potential, whenever there is generalized Bose-Einstein condensation in the eigenstates of the single particle Hamiltonian, there is also generalized condensation in the kinetic energy states. In these cases Bose-Einstein condensation is produced or enhanced by the external potential. In the present paper we establish a criterion for the absence of condensation in single kinetic energy states and prove that this criterion is satisfied for a class of random potentials and weak potentials. This means that the condensate is spread over an infinite number of states with low kinetic energy without any of them being macroscopically occupied.