Fluctuations of a weakly interacting Bose-Einstein condensate

TL;DR

This paper investigates the fluctuations in the number of condensed atoms in a finite-size, weakly interacting Bose-Einstein condensate, highlighting the effects of interactions and particle-number constraints near the critical temperature.

Contribution

It introduces a combined recursive and saddle-point approach to evaluate partition functions for realistic system sizes and emphasizes the role of interactions and constraints in fluctuation behavior.

Findings

Crossover from anomalous to normal fluctuation scaling observed in large systems

Interactions and particle-number constraints significantly affect fluctuation statistics near criticality

Self-consistent Bogoliubov-Popov and Hartree-Fock methods effectively describe excitations and interactions

Abstract

Fluctuations of the number of condensed atoms in a finite-size, weakly interacting Bose gas confined in a box potential are investigated for temperatures up to the critical region. The canonical partition functions are evaluated using a recursive scheme for smaller systems, and a saddle-point approximation for larger samples, that allows to treat realistic size systems containing up to $N \sim 10^5$ particles. We point out the importance of particle-number constrain and interactions between out of condensate atoms for the statistics near the critical region. For sufficiently large systems the crossover from the anomalous to normal scaling of the fluctuations is observed. The excitations are described in a self-consistent way within the Bogoliubov-Popov approximation, and the interactions between thermal atoms are described by means of the Hartree-Fock method.