Anomalous Statistics of Bose-Einstein Condensate in an Interacting Gas: An Effect of the Trap's Form and Boundary Conditions in the Thermodynamic Limit

Sergey Tarasov; Vladimir Kocharovsky; Vitaly Kocharovsky

doi:10.3390/e20030153

Anomalous Statistics of Bose-Einstein Condensate in an Interacting Gas: An Effect of the Trap's Form and Boundary Conditions in the Thermodynamic Limit

Entropy (Basel). 2018 Feb 27;20(3):153. doi: 10.3390/e20030153.

Authors

Sergey Tarasov¹, Vladimir Kocharovsky^{1

2}, Vitaly Kocharovsky³

Affiliations

¹ Institute of Applied Physics, Russian Academy of Science, Nizhny Novgorod 603950, Russia.
² Department of the Advanced School of General and Applied Physics, Lobachevsky State University, Nizhny Novgorod 603950, Russia.
³ Department of Physics and Astronomy, Texas A&M University, College Station, TX 77843-4242, USA.

Abstract

We analytically calculate the statistics of Bose-Einstein condensate (BEC) fluctuations in an interacting gas trapped in a three-dimensional cubic or rectangular box with the Dirichlet, fused or periodic boundary conditions within the mean-field Bogoliubov and Thomas-Fermi approximations. We study a mesoscopic system of a finite number of trapped particles and its thermodynamic limit. We find that the BEC fluctuations, first, are anomalously large and non-Gaussian and, second, depend on the trap's form and boundary conditions. Remarkably, these effects persist with increasing interparticle interaction and even in the thermodynamic limit-only the mean BEC occupation, not BEC fluctuations, becomes independent on the trap's form and boundary conditions.

Keywords: Bogoliubov coupling; Bose-Einstein condensation; interacting Bose gas; mesoscopic system; statistics of Bose-Einstein condensate.