Ensemble averaged coherent state path integral for disordered bosons with a repulsive interaction (Derivation of mean field equations)

TL;DR

This paper develops an ensemble averaged coherent state path integral approach to analyze disordered bosonic systems with repulsive interactions, providing an alternative to traditional replica or supersymmetric methods for mean field equation derivation.

Contribution

It introduces a novel path integral framework for disordered bosons that enables exact ensemble averaging at finite temperatures, advancing beyond existing replica and supersymmetric techniques.

Findings

Derived mean field equations for disordered bosons

Established exact ensemble averages for static and dynamic disorder

Provided a new methodological approach for disordered quantum systems

Abstract

We consider bosonic atoms with a repulsive contact interaction in a trap potential for a Bose-Einstein condensation and additionally include a random potential. The ensemble averages for two models of static and dynamic disorder are performed and investigated in parallel. The bosonic many body systems of the two disorder models are represented by coherent state path integrals on the Keldysh time contour which allow exact ensemble averages for zero and finite temperatures. These ensemble averages of coherent state path integrals therefore present alternatives to replica field theories or supersymmetric averaging techniques.