Two characteristic temperatures for a Bose-Einstein condensate of a finite number of particles

TL;DR

This paper investigates two key temperatures related to Bose-Einstein condensates with finite particles, showing their convergence to the critical temperature as particle number increases, aiding phase transition studies.

Contribution

It introduces and calculates two characteristic temperatures for finite Bose-Einstein condensates in power-law traps, linking them to phase transition indicators.

Findings

Characteristic temperatures approach the critical temperature with increasing particle number

The temperatures are related to properties of condensate statistics

Results are applicable to finite-atom Bose-Einstein condensates

Abstract

We consider two characteristic temperatures for a Bose-Einstein condensate, that are related to certain properties of the condensate statistics. We calculate them for an ideal gas confined in power-law traps and show that they approach the critical temperature in the limit of large number of particles. The considered characteristic temperatures can be useful in the studies of Bose-Einstein condensates of a finite number of atoms, indicating the point of a phase transition.