Quantum rearrangement and self-consistent BCS-BEC crossover thermodynamics

TL;DR

This paper develops an analytical, self-consistent approach to the thermodynamics of strongly interacting fermions, specifically addressing the BCS-BEC crossover and unitary limit, ensuring thermodynamic consistency and calculating a universal energy ratio.

Contribution

It introduces an exact analytical method for strongly interacting fermions using a medium-dependent potential and self-consistent equations, advancing understanding of the BCS-BEC crossover.

Findings

Derived a universal energy ratio $\xi= ext{0.49}$ at T=0.

Ensured thermodynamic consistency through additional correlation potential contributions.

Provided a self-consistent framework applicable to the unitary limit regime.

Abstract

Based on previous works, analytical calculational procedures for dealing with the strongly interacting fermions ground state are further developed through a medium dependent potential in terms of the Bethe-Peierls contact interaction model. The methods are exact in the unitary limit regime and they lead to the self-consistent equations analogous to the Hartree ones. The single particle energy spectrum rearrangement effects on the thermodynamics due to the Hugenholtz-van Hove theorem constraint are addressed. These effects lead to an additional instantaneous correlation potential contribution to the system physical chemical potential and pressure, i.e., equation of state, which enforces the classical thermodynamic consistency. The Dyson-Schwinger equations represent implicitly the various Bethe-Goldstone expansion ones. In a thermodynamically self-consistent way, the universal dimensionless factor is analytically calculated to be $\xi=\049$, which defines the ratio of the unitary fermions energy density to that of the ideal non-interacting ones at T=0.