Finite Temperature Behaviors of q-deformed Fermi Gases

TL;DR

This paper develops a q-deformed extension of BCS theory for ultracold Fermi gases, revealing a tunable crossover between fermionic and bosonic behaviors influenced by the deformation parameter.

Contribution

It introduces a novel q-deformed BCS-Leggett theory for ultracold gases, exploring new quantum statistical behaviors and crossover phenomena.

Findings

Fermionic features emerge in Bose-Einstein Condensation regime due to q-deformation

Observation of a q-induced Bose-Fermi crossover

Weak Fermi-Bose crossover signs in fermionic regimes

Abstract

During the last three decades, non-standard statistics for indistinguishable quantum particles has attracted broad attentions and research interests from many institutions. Among these new types of statistics, the q-deformed Bose and Fermi statistics, originated from the study of quantum algebra, are being applied in more and more physical systems. In this paper, we construct a q-deformed generalization of the BCS-Leggett theory for ultracold Fermi gases based on our previously constructed q-deformed BCS theory. Some interesting features of this q-deformed interacting quantum gas are obtained by numerical analysis. For example, in the ordinary Bose-Einstein Condensation regime, the gas presents a fermionic feature instead of bosonic feature if the deformation parameter is tuned suitably, which might be referred to as the q-induced ``Bose-Fermi'' crossover. Conversely, a weak sign of the ``Fermi-Bose'' crossover is also found in the ordinary weak fermionic regime.