Bogoliubov Theory of Disordered Bose-Einstein Condensates

TL;DR

This paper develops a Bogoliubov theoretical framework to analyze low-temperature disordered Bose-Einstein condensates, deriving analytical expressions for excitations, sound velocity, and condensate depletion across dimensions.

Contribution

It introduces an analytical approach for weak disorder in disordered Bose-Einstein condensates using Bogoliubov expansion, extending understanding of excitations and depletion.

Findings

Derived analytical formulas for sound velocity in disordered BECs

Calculated zero-temperature condensate depletion in correlated disorder

Applicable across all spatial dimensions

Abstract

We describe interacting bosons at low temperature in spatially correlated random potentials. By a Bogoliubov expansion around the deformed mean-field condensate, the fundamental Hamiltonian for elementary excitations is derived, achieving an analytical formulation in the case of weak disorder. From this, we calculate the sound velocity and true zero-temperature condensate depletion in correlated disorder and all dimensions.