Absence of charged pion condensation in a magnetic field with parallel rotation

Abstract

We investigate the critical temperature of a relativistic Bose-Einstein condensate of charged bosons driven by rotation in a parallel magnetic field [Y. Liu and I. Zahed, Phys. Rev. Lett. 120, 032001 (2018)]. For non-interacting bosons, the critical temperature can only be determined for a system with fixed angular momentum. We find that the critical temperature of the non-interacting system vanishes due to the fact that the system is quasi-one-dimensional, indicating that non-interacting bosons cannot undergo Bose-Einstein condensation. For interacting bosons, we investigate a system with quartic self-interaction. We show that the order parameter vanishes and the off-diagonal long-range order is absent at any nonzero temperature because of the quasi-one-dimensional feature, in accordance with the Coleman-Mermin-Wagner-Hohenberg theorem.

Figures (1)

• Figure 1: The angular speed $\Omega$ as a function of $T$ for different values of the angular momentum $L_{z}$ at $\mu=0$. In the numerical calculation, we set $m^{2}=qB$ and $N=100$.