Quantum Statistics of Fermi Gases.

Neri Merhav

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.

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 \(R\).

Juan Wang, Xiaotian Zhang, Zemao Wu +2 more

In this paper, we study the spatial noise fluctuations of the density distribution of non-interacting 6Li ultracold Fermi gases. For ideal ultracold Fermi gases, the Fermi-Dirac statistics governs its quantum distribution. The suppression of density fluctuations at low temperature, due to Pauli exclusion principle, is observed in a large cloud of fermions. To clearly reveal the density noise fluctuations of the ideal Fermi gases, other noises, such as the background noise, imaging laser noise, CCD photon counting noise, are greatly suppressed. The noise fluctuation shows a sub-Poissonian statistics in excess of 10,000 atoms per spin state. The dependence of the spatial atom noise fluctuation on the quantum degeneracy is also investigated by changing the temperature of the degenerated Fermi gases. The Fermi gases with lower temperature exhibit larger suppression of the noise fluctuations. The results may have great applications in measuring the temperature of strongly correlated many-body physics and observing the phase transition of incompressible quantum phases.

Alexander Bérkovich