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Russian Physics Journal

Thermodynamic characteristics of Fermi gases in a magnetic field

S. S. Lipovetskiǐ, A. A. Olesik, В. С. Секержицкий

Published May 1, 1987• 0 citations
Publisher
DOI
10.1007/bf00900084

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Physical Review A•Jun 1, 1987•1 citation
Based on the Mean Field Theory, the relativistic thermodynamic potential function (RTPF) of interacting Fermi gases in a strong magnetic field is derived. On this basis, by taking the interacting term from the RTPF and using the thermodynamic relations, analytical expressions of the energy, the heat capacity and the chemical potential are calculated at low temperatures. And combined with numerical simulation analysis, the effect of interaction on the thermodynamic properties of the system is analyzed and the regulation mechanisms on the interaction impacts of both the magnetic field and the relativistic effect are discussed.
The spin-polarized ferromagnetic state of a cold Fermi gas is investigated for interacting and noninteracting charge-neutral and $\ensuremath{\beta}$-equilibrated gases. The standard minimal couplings between the magnetic field and the fermions' charges and magnetic dipole moments define the fermions' interaction with the magnetic field. Assuming a variable coupling strength between the magnetic field and the fermion (baryon) dipole moments, it is shown that a ferromagnetized state can be achieved that corresponds to a lower energy spin-polarized state with a magnetic field entirely due to the gas's magnetic response. We find that, depending on the density, a very large increase in the baryon dipole moments is needed to achieve this ferromagnetized state. While the required increase seems unlikely, the induced magnetic field is of the order $\ensuremath{\approx}{10}^{17}$ gauss. Furthermore, while externally magnetized Fermi gases have an anisotropic pressure, the pressure of the ferromagnetized gas is completely isotropic and in the thermodynamically preferred magnetized state.
A two-body-interaction model characterized by the scattering length a is applied to study the thermodynamic and magnetic properties of nonrelativistic interacting systems of spin-(1/2) particles in the presence of an external homogeneous magnetic field under the assumption that the particles obey generalized statistics of order l. Here one assumes that the occupation number of an energy state can take values 0,1,2,3,...,l and no more, where l is an integer greater than unity. Exact expressions for thermodynamic and magnetic properties due to the generalized nature of the statistics are obtained and the characteristic departure of the present results from those of the Fermi-Dirac case are pointed out. Variation of thermodynamic properties with the interaction parameter ${\mathrm{av}}^{\mathrm{\ensuremath{-}}1/3}$ is also obtained.