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

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.

References in corpus (8)

• Universality of Quantum Gravity Corrections
• Minimal Length Uncertainty Relation and gravitational quantum well
• GRBs Neutrinos as a Tool to Explore Quantum Gravity induced Lorentz Violation
• Physics on Smallest Scales - An Introduction to Minimal Length Phenomenology
• Statistical physics in deformed spaces with minimal length
• Constraining the energy-momentum dispersion relation with Planck-scale sensitivity using cold atoms
• Planck-scale effects on Bose-Einstein condensates
• Trapped Bose-Einstein condensates with Planck-scale induced deformation of the energy-momentum dispersion relation

Cited by in corpus (1)

• Weakly interacting Bose gases with generalized uncertainty principle: Effects of quantum gravity