Finite temperature current densities and Bose-Einstein condensation in topologically nontrivial spaces

TL;DR

This paper analyzes how finite temperature, topology, and gauge fields influence charge and current densities, revealing effects like Bose-Einstein condensation and Aharonov-Bohm phenomena in a scalar field theory.

Contribution

It provides new analytical representations for charge and current densities in topologically nontrivial spaces with gauge fields, including effects of Bose-Einstein condensation.

Findings

Current density is nonzero only along compact dimensions.

High-temperature limit shows linear dependence of densities on temperature.

Gauge field tuning can control phase transition parameters.

Abstract

We investigate the finite temperature expectation values of the charge and current densities for a complex scalar field with nonzero chemical potential in background of a flat spacetime with spatial topology $R^{p}\times (S^{1})^{q}$. Along compact dimensions quasiperiodicity conditions with general phases are imposed on the field. In addition, we assume the presence of a constant gauge field which, due to the nontrivial topology of background space, leads to Aharonov-Bohm-like effects on the expectation values. By using the Abel-Plana-type summation formula and zeta function techniques, two different representations are provided for both the current and charge densities. The current density has nonzero components along the compact dimensions only and, in the absence of a gauge field, it vanishes for special cases of twisted and untwisted scalar fields. In the high-temperature limit, the current density and the topological part in the charge density are linear functions of the temperature. The Bose-Einstein condensation for a fixed value of the charge is discussed. The expression for the chemical potential is given in terms of the lengths of compact dimensions, temperature and gauge field. It is shown that the parameters of the phase transition can be controlled by tuning the gauge field. The separate contributions to the charge and current densities coming from the Bose-Einstein condensate and from excited states are also investigated.