Finite Size Effect on Bose-Einstein Condensation

TL;DR

This paper investigates finite size effects on Bose-Einstein condensation, introducing a generalized statistics correction, applying scaling theory to inhomogeneous systems, and analyzing the thermodynamic Casimir force, aligning theoretical results with experimental observations.

Contribution

It presents a generalized Bose-Einstein statistics for finite systems, applies scaling theory to trapped condensates, and studies the Casimir force, providing new insights into finite size effects on BEC.

Findings

Generalized B-E statistics matches experimental condensate fractions.

Critical particle number increases dramatically near condensation temperature.

Thermodynamic Casimir force varies with temperature in BEC systems.

Abstract

We show various aspects of finite size effects on Bose-Einstein condensation(BEC). In the first section we introduce very briefly the BEC of harmonically trapped ideal Bose gas. In the second section we theoretically argued that Bose-Einstein(B-E) statistics needs a correction for finite system at ultralow temperatures. As a corrected statistics we introduced a Tsallis type of generalized B-E statistics. The condensate fraction calculated with this generalized B-E statistics, is satisfied well with the experimental result. In the third section we show how to apply the scaling theory in an inhomogeneous system like harmonically trapped Bose condensate at finite temperatures. We calculate the temperature dependence of the critical number of particles by a scaling theory within the Hartree-Fock approximation and find that there is a dramatic increase in the critical number of particles as the condensation point is approached. Our results support the experimental result which was obtained well below the condensation temperature. In the fourth section we concentrate on the thermodynamic Casimir force on the Bose-Einstein condensate. We explored the temperature dependence of the Casimir force.