Thermodynamics of ideal Fermi gas under generic power law potential in $d$-dimension

TL;DR

This paper systematically analyzes the thermodynamics of an ideal Fermi gas in arbitrary dimensions under a generic power law potential, revealing zero-temperature properties and the influence of trapping potentials on thermodynamic behavior.

Contribution

It provides a comprehensive theoretical framework for the thermodynamics of trapped Fermi gases in arbitrary dimensions with generic power law potentials, highlighting zero-temperature properties and volume-dependent zero point pressure.

Findings

Pressure and energy are non-zero at absolute zero temperature.

Zero point pressure depends on volume, not just a constant.

Thermodynamic properties are dominated by Pauli exclusion in the degenerate limit.

Abstract

Thermodynamics of ideal Fermi gas trapped in an external generic power law potential $U=\sum_{i=1} ^d c_i |\frac{x_i}{a_i}|^{n_i}$ are investigated systematically from the grand thermodynamic potential in $d$ dimensional space. These properties are explored deeply in the degenerate limit ($\mu>> K_BT$), where the thermodynamic properties are greatly dominated by Pauli exclusion principle. Pressure and energy along with the isothermal compressibilty is non zero at $T=0K$, denoting trapped Fermi system is quite live even at absolute zero temperature. The nonzero value of compressibilty denotes zero point pressure is not just a constant but depends on volume.