Anomalous fluctuations of the condensate in interacting Bose gases

TL;DR

This paper investigates the unusual volume-dependent fluctuations of the condensate in interacting Bose gases, revealing anomalous behavior caused by infrared divergences from phonon excitations, applicable to both box and harmonic trap confinements.

Contribution

It demonstrates the presence of anomalous condensate fluctuations in interacting Bose gases due to infrared divergences, extending previous understanding to confined geometries.

Findings

Condensate fluctuations scale as V^{4/3} in a box.

Anomalous fluctuations also occur in harmonic traps.

Infrared divergences from phonons cause the anomalies.

Abstract

We find that the fluctuations of the condensate in a weakly interacting Bose gas confined in a box of volume $V$ follow the law $<\delta N_0^2>\sim V^{4/3}$. This anomalous behaviour arises from the occurrence of infrared divergencies due to phonon excitations and holds also for strongly correlated Bose superfluids. The analysis is extended to an interacting Bose gas confined in a harmonic trap where the fluctuations are found to exhibit a similar anomaly.