# Superfluids, Fluctuations and Disorder

## TL;DR

This paper develops a field-theory framework to study how disorder affects ultracold bosonic atoms, revealing that disorder can destroy superfluidity even when perturbative analysis applies.

## Contribution

It introduces a novel field-theory approach incorporating disorder effects on superfluid and condensate properties in ultracold bosonic systems.

## Key findings

- Disorder modifies condensate depletion and superfluid response.
- Superfluid phase can be destroyed by disorder in perturbative regimes.
- Implementation of replica trick for disordered ultracold bosons.

## Abstract

We present a field-theory description of ultracold bosonic atoms in presence of a disordered external potential. By means of functional integration techniques, we aim to investigate and review the interplay between disordered energy landscapes and fluctuations, both thermal and quantum ones. Within the broken-symmetry phase, up to the Gaussian level of approximation, the disorder contribution crucially modifies both the condensate depletion and the superfluid response. Remarkably, it is found that the ordered (i.e. superfluid) phase can be destroyed also in regimes where the random external potential is suitable for a perturbative analysis. We analyze the simplest case of quenched disorder and then we move to present the implementation of the replica trick for ultracold bosonic systems. In both cases, we discuss strengths and limitations of the reviewed approach, paying specific attention to possible extensions and the most recent experimental outputs.