Bose-Einstein condensation in finite noninteracting systems: A relativistic gas with pair production. II

Abstract

An asymptotic evaluation of the specific heat of an ideal relativistic Bose gas confined to a cuboidal enclosure ($L_1\times L_2\times L_3$) is carried out, under periodic boundary conditions, taking into account the possibility of particle-antiparticle pair production in the system. Finite-size corrections to the standard bulk behavior are calculated explicitly in the regions $t>\mathrm{}0\mathrm{}$ and $t<\mathrm{}0\mathrm{}$, where $t=\frac{(T-T_c)}{T_c}$, such that $\left|t\right|\ll 1$ and $\left|L_{i}t\right|\gg 1$. While for $t>\mathrm{}0\mathrm{}$ finite-size corrections turn out to be exponential for all geometries, for $t<\mathrm{}0\mathrm{}$ this is true only in the case of a film; for other geometries, such as a cuboid or a rectangular channel, these corrections conform to a power law instead. Finally, we consider the situation in the core region, where $\left|L_{i}t\mathrm{}\right|=O\left(1\mathrm{}\right)\mathrm{}$, and examine the location $t^{*}$ and the height $c_{\rho }^{*}$ of the specific-heat maximum; finite-size corrections in this region turn out to be $O\left(L_{<}^{-1\mathrm{}}\right)$, where $L_{<}$ denotes the shortest side of the enclosure.