Anomalous behavior of ideal Fermi gas below two dimensions

TL;DR

This paper investigates the unusual thermodynamic behavior of an ideal Fermi gas in dimensions less than two, revealing a hump or trough in properties like specific heat and chemical potential, which intensify as the dimension approaches zero.

Contribution

It uncovers and analyzes the anomalous thermodynamic features of an ideal Fermi gas in fractional dimensions below two, a phenomenon not previously detailed.

Findings

Development of a hump or trough in thermodynamic properties for 0<d<2

Anomalous behavior intensifies as dimension approaches zero

Distinct from phase transition phenomena in Bose gases

Abstract

Normal behavior of the thermodynamic properties of a Fermi gas in $d>2$ dimensions, integer or not, means monotonically increasing or decreasing of its specific heat, chemical potential or isothermal sound velocity, all as functions of temperature. However, for $0<d<2$ dimensions these properties develop a ``hump'' (or ``trough'') which increases (or deepens) as $d\to 0$. Though not the phase transition signaled by the sharp features (``cusp'' or ``jump'') in those properties for the ideal Bose gas in $d>2$ (known as the Bose-Einstein condensation), it is nevertheless an intriguing structural anomaly which we exhibit in detail.