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

Run Cheng,Hong-Shi Zong,Qian-Yi Wang,Yong-Long Wang

doi:10.3390/sym13020300

Run Cheng, Hong-Shi Zong + Show 2 more

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https://doi.org/10.3390/sym13020300

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Abstract

We investigate the statistical distribution for ideal Bose gases with constant particle density in the 3D box of volume V=L3. 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 a smaller linear size is efficient to increase the characteristic temperature and condensate fraction. Moreover, there is a singularity under the antiperiodic boundary condition.

Highlights

The use of twisted boundary conditions for the Bose–Einstein condensation (BEC) in the cubic box, which is equivalent to realizing the BEC in the presence of a constant background magnetic potential coupled with bosons
In a system of small volume, the characteristic temperature and condensate fraction are sensitive to boundary conditions, especially in the case of antiperiodic boundary condition
We study ideal Bose gases with fixed particle density confined in the cubic box

Summary

Introduction

From the theoretical point of view, the only requirement is that the Hamiltonian of the finite system should be Hermitian, and the above boundary conditions are just some special cases. These inspire us to explore the physics of BEC in finite volume systems by focusing on the finite-size behaviors and twisted boundary conditions [37]. We characterize BEC phase transition with characteristic temperature and condensate fraction, and numerically calculate them under different linear sizes and boundary conditions.

The Ideal Bose Gases in the Cubic Box

Finite-Size Effects on Bose–Einstein Condensation in the Cubic Box

The Influences of Boundary Conditions on Bose–Einstein Condensation in a

Conclusions