Hartree-Fock Mean-Field Theory for Trapped Dirty Bosons

TL;DR

This paper develops a non-perturbative Hartree-Fock and replica method approach to analyze a trapped weakly interacting Bose gas with disorder at finite temperature, deriving self-consistent equations for various density components.

Contribution

It introduces a detailed Hartree-Fock mean-field framework combined with the replica method to study disordered Bose gases, providing a basis for understanding density distributions.

Findings

Derived self-consistency equations for condensate, thermal, and fragmented densities.

Analyzed how densities evolve with increasing disorder strength in 1D and 3D.

Established a non-perturbative approach applicable to trapped dirty bosons.

Abstract

Here we work out in detail a non-perturbative approach to the dirty boson problem, which relies on the Hartree-Fock theory and the replica method. For a weakly interacting Bose gas within a trapped confinement and a delta-correlated disorder potential at finite temperature, we determine the underlying free energy. From it we determine via extremization self-consistency equations for the three components of the particle density, namely the condensate density, the thermal density, and the density of fragmented local Bose-Einstein condensates within the respective minima of the random potential landscape. Solving these self-consistency equations in one and three dimensions in two other publications has revealed how these three densities change for increasing disorder strength.