Fermi Statistics of Partially Populated States

TL;DR

This paper extends Fermi statistics to include partially occupied states, deriving a new distribution that generalizes the traditional Fermi distribution and converges to it at zero temperature.

Contribution

It introduces a formal extension of Fermi statistics to partially occupied states, broadening the applicability of Fermi-Dirac distribution.

Findings

Derived a partial Fermi distribution dependent on partial occupation

At zero temperature, the new distribution reduces to the standard Fermi distribution

The extended distribution maintains similar properties to the original Fermi distribution

Abstract

Fermi statistics is formally extended to the case when energy levels are allowed to be partially occupied, which the Pauli principle does not categorically exclude. The partial Fermi distribution obtained depends on the partial occupation of states but otherwise has similar properties as the (integer) Fermi distribution. In the zero temperature limit both are identical.