Bose-Einstein condensation in a rigidly rotating relativistic boson gas

TL;DR

This paper investigates how rigid rotation influences Bose-Einstein condensation in a relativistic boson gas, revealing modifications in transition temperature, condensate fraction, and phase transition nature due to rotation effects.

Contribution

It provides analytical expressions for thermodynamic quantities of a rotating Bose gas and explores the impact of rotation on BEC transition properties in relativistic regimes.

Findings

Rotation lowers the critical exponent of the BE transition.

Rotation can change the phase transition from continuous to discontinuous in nonrelativistic gases.

Rotation affects the temperature dependence of fugacity and heat capacity in Bose gases.

Abstract

We study the Bose-Einstein condensation (BEC) of a free Bose gas under rigid rotation. The aim is to explore the impact of rotation on the thermodynamic quantities associated with BEC, including the Bose-Einstein (BE) transition temperature and condensate fraction. We begin by introducing the rotation in the Lagrangian density of free charged Klein-Gordon fields and determine the corresponding grand canonical partition function at finite temperature, chemical potential, and finite angular velocity. Assuming slow rotation, we derive analytical expressions for the pressure, energy, number, and angular momentum densities of a free Bose gas in nonrelativistic and ultrarelativistic limits in terms of the corresponding fugacities. We then focus on the phenomenon of BEC. We calculate the critical temperature of BEC transition and the condensate fraction in a slowly rotating Bose gas including only particles. Our findings indicate that the critical exponent associated with the BE transition in a rotating gas is lower compared to that in a nonrotating Bose gas. We also determine the fugacity in a rotating Bose gas in the aforementioned limits and examine how rotation affects its temperature dependence, both below and above the critical temperature. By analyzing the behavior of heat capacity at these temperatures, we demonstrate that in a nonrelativistic Bose gas, the rotation transforms the nature of the BE phase transition from a continuous to a discontinuous transition. In general, we find that a nonrelativistic Bose gas under rotation behaves similarly to a nonrotating Bose gas in ultrarelativistic limit.