Thermodynamics of two-parameter quantum group Bose and Fermi gases

M. Arık, Jak Kornfilt

Kelly R. Patton, Michael R. Geller, M. P. Blencowe

Wen-Xiang Chen

Bose gases and Fermi gases represent two fundamental particle systems in statistical mechanics, governed by Bose-Einstein and Fermi-Dirac distributions, respectively. This paper provides a comprehensive analysis of the thermodynamic quantities, phase transitions, chemical potentials, and energy level relationships of these gases. The study utilizes Laurent series expansions and group theory analysis to explore the statistical properties and behavior of Bose and Fermi gases under various conditions. Additionally, the paper derives a new energy-mass equation based on metric and curvature \(R\).

Marcelo R. Ubriaco

We study the properties of a thermodynamic system having the symmetry of a quantum group and interacting with a harmonic potential. We calculate the dependence of the chemical potential, heat capacity, and spatial distribution of the gas on the quantum group parameter $q$ and the number of spatial dimensions $D.$ In addition, we consider a fourth-order interaction in the quantum group fields $\ensuremath{\Psi}$ and calculate the ground state energy up to first order.

Shah Mohammad Bahauddin, Mir Mehedi Faruk

Abstract From the unified statistical thermodynamics of quantum gases, the virial coefficients of ideal Bose and Fermi gases, trapped under generic power law potential are derived systematically. From the general result of virial coefficients, one can produce the known results in d = 3 and d = 2. But more importantly we found that, the virial coefficients of Bose and Fermi gases become identical (except the second virial coefficient, where the sign is different) when the gases are trapped under harmonic potential in d = 1. This result suggests the equivalence between Bose and Fermi gases established in d = 1 (J. Stat. Phys. DOI 10.1007/s10955-015-1344-4). Also, it is found that the virial coefficients of two-dimensional free Bose (Fermi) gas are equal to the virial coefficients of one-dimensional harmonically trapped Bose (Fermi) gas.

Frédéric Chevy, Ch Salomon