Fluctuations of a weakly interacting Bose-Einstein condensate

¹  Institute of Theoretical Physics, University of Warsaw - 00-681 Warsaw, Poland, EU
²  Center for Theoretical Physics, Polish Academy of Sciences - Aleja Lotników 32/46, 02-668 Warsaw, Poland, EU
³  Institute of Physics, Polish Academy of Sciences - Aleja Lotników 32/46, 02-668 Warsaw, Poland, EU
⁴  Faculty of Mathematics and Sciences, Cardinal Stefan Wyszyński University - Warsaw, Poland, EU

Corresponding author: idziaszek@fuw.edu.pl

Received: 6 March 2009
Accepted: 15 March 2009

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 ~ 10⁵ particles. We point out the importance of particle-number constraint 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.