Condensation in ideal Fermi gases

TL;DR

This paper explores the theoretical possibility of Bose-like condensation phenomena in ideal Fermi gases across various dimensions by analyzing the probability distribution of particles in the condensate.

Contribution

It introduces a method to determine condensation in ideal Fermi systems by examining the maxima of the condensate probability distribution, revealing potential phase transitions.

Findings

Maxima in condensate probability indicate possible condensation.

In 1D systems, two maxima suggest a first-order phase transition.

The approach offers new insights into ensemble equivalence in Fermi systems.

Abstract

I investigate the possibility of condensation in ideal Fermi systems of general single particle density of states. For this I calculate the probability $w_{N_0}$ of having exactly $N_0$ particles in the condensate and analyze its maxima. The existence of such maxima at macroscopic values of $N_0$ indicates a condensate. An interesting situation occurs for example in 1D systems, where $w_{N_0}$ may have two maxima. One is at $N_0=0$ and another one may exist at finite $N_0$ (for temperatures bellow a certain condensation temperature). This suggests the existence of a first order phase transition. % The calculation of $w_{N_0}$ allows for the exploration of ensemble equivalence of Fermi systems from a new perspective.