Relativistic ideal Bose gas in Harmonic traps

TL;DR

This paper investigates the Bose-Einstein condensation of a relativistic ideal boson gas in three-dimensional harmonic traps, analyzing how relativistic effects and antibosons influence the transition temperature and system stability.

Contribution

It introduces a semiclassical approximation method to study relativistic effects and antibosons in BEC within harmonic traps, providing new insights into their impact on critical temperature and stability.

Findings

Relativistic BEC transition temperature T_{c} is higher than nonrelativistic case.

Presence of antibosons lowers Helmholtz free energy at T_{c}, indicating increased stability.

Rest mass of bosons significantly affects system properties.

Abstract

Using semiclassical approximation method, Bose-Einstein condensation (BEC) of a relativistic ideal boson gas (RIBG) with and without antibosons in three-dimensional (3-D) harmonic traps is investigated. The BEC transition temperature T_{c} and the Helmholtz free energy at T_{c} are calculated. The effect of the rest mass of the boson on the properties of the system is also studied. We find that T_{c} of RIBG is higher than that of the nonrelativistic approximation. The RIBG with antibosons is also investigated and it is found that the Helmholtz free energy of the system with antibosons at T_{c} is lower than that of the system without antibosons. It implies that the system with antibosons is more stable.