Thermodynamic and magnetic properties of nonrelativistic "para-Fermi gas"

Abstract

The equation of state, the magnetic moment, as well as a Curie-type law for the susceptibility parameter of a system of particles of spin 1/2 in the presence of an external magnetic field are calculated assuming that these particles obey generalized statistics. Here one assumes that the occupation number of an energy state can take the values 0, 1, 2,...,l and no more, where l is an integer greater than unity. This is a direct consequence of the generalized method of field quantization originally due to Green. Exact expressions for the thermodynamic and magnetic properties due to the generalized nature of the statistics are given, and the characteristic departures of the present results from those of the Fermi-Dirac case are pointed out. Our results are useful for investigating the thermodynamic state and spontaneous magnetization of the highly compressed state of matter, presumably of quarks, obtained in a star in gravitational collapse. The quarks are assumed to obey generalized Fermi statistics known in the literature as para-Fermi statistics.