D-Dimensional ideal gas in parastatistics: Thermodynamic properties

Abstract

We consider a parastatistics ideal gas with energy spectrumɛ ∞ ¦k¦α (α>0) or even more generally in ad-dimensional box with volumeV (periodic boundary conditions), the numberN of the gas particles being well determined (real particles) or not (quasiparticles). We calculate the main thermodynamic quantities (chemical potential, internal energy, specific heatC, equation of state, latent heat, average numbers of particles) for arbitraryd, α,T (temperature), andp (maximal number of particles per state allowed in the parastatistics). The main asymptotic regimes are worked out explicitly. In particular, the Bose-Einstein condensation for fixed densityN/V appears as a nonuniform convergence in thep → ∞ limit, in complete analogy with the standard critical phenomena that appear in interacting systems in theN → ∞ limit. The system behaves essentially like a Fermi-Dirac one forall finite values ofp, and reveals a Bose-Einstein behavioronly in thep → ∞ limit. For instance, at low temperaturesC ∞T ifp<∞ andC ∞ Td/α ifp→∞. Finally, the Sommerfeld integral and its expansion are generalized to an arbitrary, finitep.