Statistical mechanics of the magnetized pair quantum gases

The quantum statistical mechanics of an ideal relativistic Bose gas of massive particles is discussed. The thermodynamic functions of the system are obtained from the exact expression for the logarithm of the grand partition function. The correct procedure for carrying out the non-relativistic and ultra-relativistic limits is presented. The limitations and errors of previous calculations which relied on the binomial expansion of the density of states are pointed out. It is shown that the behaviour of the system in the limit of zero temperature is dominated by the non-relativistic effects.

https://iopscience.iop.org/article/10.1088/0305-4470/13/10/020/pdf

The relativistic Bose gas

Simple criterion for the occurrence of Bose-Einstein condensation

The scaling hypothesis on the 'singular' part of the free-energy density of a finite system is examined in the context of a relativistic Bose gas confined to an Einstein universe of radius R. Finite-size effects in the various thermodynamic properties of the system, such as the free energy, the specific heat, the isothermal compressibility and the condensate density, are predicted in the regions of both first-order (T<Tc) and second-order (T approximately=Tc) phase transitions. To test these predictions, a detailed analytical study is carried out which includes the possibility of particle-antiparticle pair production in the system. The various predictions of the scaling hypothesis are fully borne out and the scaling functions governing the critical behaviour of the system are found to be universal, irrespective of the severity of the relativistic effects.

Finite-size scaling for a relativistic Bose gas in an Einstein universe

Relativistic superfluids are of interest in extreme astrophysical or cosmological situations. Some of their properties, ultrabaricity in particular, are studied by means of exact solutions of Einstein’s equations. Those found are almost invariably characterized by equations of state of the typeP = αϱ + const with 0 ≤ α ≤ 1 and ϱ proportional to the square of the number density. They are therefore neither ultrabaric (P > ϱ nor superluminal (vS > 1). Exceptions are, however, represented by the generalized interior Schwarzschild solution, the Stephani solution and a new conformally flat solution also of the Stephani type. For these superluminality is allowed if no assumptions are introduced regarding the mechanism of propagation of sound waves. In the one with Stephani metric, transitions can occur in principle from evolutionary stages withvS > 1 to others withvS < 1, andvice versa.

V.A. Kuzmin

Papers

Photon condensation in the big bang cosmology and longitudinal background radiation of the universe