# Finite-Size Effects with Boundary Conditions on Bose-Einstein Condensation

## TL;DR

This paper studies how boundary conditions and finite size influence Bose-Einstein condensation in ideal gases, revealing that smaller systems and certain boundary conditions can enhance the transition temperature and condensate fraction.

## Contribution

It provides a numerical analysis of finite-size effects and boundary conditions on Bose-Einstein condensation, highlighting the impact of system size and boundary choices.

## Key findings

- Smaller system sizes increase the characteristic temperature and condensate fraction.
- Antiperiodic boundary conditions induce a singularity in the system.
- Boundary conditions significantly affect Bose-Einstein condensation properties.

## Abstract

We investigate the statistical distribution for ideal Bose gases with constant particle density in the 3D box of volume $V=L^{3}$. By changing linear size $L$ and imposing different boundary conditions on the system, we present a numerical analysis on the characteristic temperature and condensate fraction, and find that the smaller linear size is efficient to increase the characteristic temperature and condensate fraction. Moreover, there is a singularity under the antiperiodic boundary condition.