Effect of the Minimal Length on Bose-Einstein Condensation in the Relativistic Ideal Bose Gas

TL;DR

This paper investigates how a minimal length scale, derived from the generalized uncertainty principle, influences the critical temperature and stability of Bose-Einstein condensation in a relativistic ideal Bose gas, revealing quantum gravity effects.

Contribution

It provides analytical and numerical analysis of quantum gravitational effects on BEC critical temperature and stability, a novel exploration in relativistic quantum gases.

Findings

Quantum gravity raises the BEC critical temperature.

Omitting quantum gravitational effects can cause metastability at low densities.

Quantum gravitational effects can destabilize BEC at high densities.

Abstract

Based on the generalized uncertainty principle (GUP), the critical temperature and the Helmholtz free energy of Bose-Einstein condensation (BEC) in the relativistic ideal Bose gas are investigated. At the non-relativistic limit and the ultra-relativistic limit, we calculate the analytical form of the shifts of the critical temperature and the Helmholtz free energy caused by weak quantum gravitational effects. The exact numerical results of these shifts are obtained. Quantum gravity effects lift the critical temperature of BEC. By measuring the shift of the critical temperature, we can constrain the deformation parameter $\beta_0$. Furthermore, at lower densities, omitting quantum gravitational effects may lead to a metastable state while at sufficiently high densities, quantum gravitational effects tend to make BEC unstable. Using the numerical methods, the stable-unstable transition temperature is found.