Discrete nature of thermodynamics in confined ideal Fermi gases

TL;DR

This paper reveals that thermodynamic properties of confined ideal Fermi gases exhibit discrete behaviors and oscillatory peaks under strong confinement, which could enable the development of novel nano devices.

Contribution

It provides exact summation formulas for thermodynamic properties of ideal Fermi gases in rectangular nano domains, highlighting their discrete and oscillatory nature.

Findings

Number of particles and internal energy per particle show discrete dependence on chemical potential.

Heat capacity exhibits sharp oscillatory peaks under strong confinement.

Discrete thermodynamic behaviors could be harnessed for nano device development.

Abstract

Intrinsic discrete nature in thermodynamic properties of Fermi gases appears under strongly confined and degenerate conditions. For a rectangular confinement domain, thermodynamic properties of an ideal Fermi gas are expressed in their exact summation forms. For 1D, 2D and 3D nano domains, variations of both number of particles and internal energy per particle with chemical potential are examined. It is shown that their relation with chemical potential exhibits a discrete nature which allows them to take only some definite values. Furthermore, quasi-irregular oscillatory-like sharp peaks are observed in heat capacity. New nano devices can be developed based on these behaviors.