Energy fluctuation of ideal Fermi gas trapped under generic power law potential $U=\sum_{i=1} ^d c_i |\frac{x_i}{a_i}|^{n_i}$ in d dimension

TL;DR

This paper derives a general formula for the energy fluctuation of an ideal Fermi gas in arbitrary dimensions under a broad class of power law trapping potentials, extending previous specific cases.

Contribution

It provides a unified analytical framework for energy fluctuations of Fermi gases in arbitrary dimensions and potentials, reproducing known results as special cases.

Findings

Energy fluctuation depends on dimensionality and potential parameters.

Analytical expressions valid in degenerate limit using Sommerfeld expansion.

Reproduces known results for specific cases like free and harmonic traps.

Abstract

Energy fluctuation of ideal Fermi gas trapped under generic power law potential $U=\sum_{i=1} ^d c_i |\frac{x_i}{a_i}|^{n_i}$ have been calculated in arbitrary dimension. Energy fluctuation is scrutinized further in the degenerate limit $\mu>> K_BT$ with the help of Sommerfeld expansion. The dependence of energy fluctuation on dimensionality and power law potential is studied in detail. Most importantly our general result can exactly reproduce the recently published result regarding free and harmonically trapped ideal Fermi gas in d=3 (S Biswas, J Mitra, S Bhattacharyya, J. Stat. Mech. P03013, 2015.)