# Disordered Bose-Einstein condensate in hard walls trap

## TL;DR

This paper investigates how quenched disorder affects a dilute Bose-Einstein condensate in a hard walls trap, analyzing the free energy, correlation functions, and density profile beyond mean-field approximation.

## Contribution

It introduces a representation for the quenched free energy using integer moments of the partition function and explores effects of disorder and boundary conditions beyond mean-field.

## Key findings

- Derived a series representation for quenched free energy.
- Computed static two-point correlation functions in weak disorder.
- Discussed the emergence of metastable and true ground states under strong disorder.

## Abstract

We discuss the effects of quenched disorder in a dilute Bose-Einstein condensate confined in a hard walls trap. Starting from the disordered Gross-Pitaevskii functional, we obtain a representation for the quenched free energy as a series of integer moments of the partition function. Positive and negative disorder-dependent effective coupling constants appear in the integer moments. Going beyond the mean-field approximation, we compute the static two-point correlation functions at first-order in the positive effective coupling constants. We obtain the combined contributions of effects due to boundary conditions and disorder in this weakly disordered condensate. The ground state renormalized density profile of the condensate is presented. We also discuss the appearance of metastable and true ground states for strong disorder, when the effective coupling constants become negative.