Large Deviations in the Superstable Weakly Imperfect Bose Gas

TL;DR

This paper applies large deviations theory to analyze the phase transition behavior of the superstable Weakly Imperfect Bose Gas, revealing a continuous onset of Bose condensate density and detailed thermodynamic properties at critical densities.

Contribution

It introduces a large deviations framework to study phase transitions in the WIBG, providing new insights into condensate behavior at critical points.

Findings

Discontinuity in condensate density disappears at the phase transition

Condensate density starts continuously at the first critical density

Free energy per particle remains constant until the second critical density

Abstract

The superstable Weakly Imperfect Bose Gas {(WIBG)} was originally derived to solve the inconsistency of the Bogoliubov theory of superfluidity. Its grand-canonical thermodynamics was recently solved but not at {point of} the {(first order)} phase transition. This paper proposes to close this gap by using the large deviations formalism and in particular the analysis of the Kac distribution function. It turns out that, as a function of the chemical potential, the discontinuity of the Bose condensate density at the phase transition {point} disappears as a function of the particle density. Indeed, the Bose condensate continuously starts at the first critical particle density and progressively grows but the free-energy per particle stays constant until the second critical density is reached. At higher particle densities, the Bose condensate density as well as the free-energy per particle both increase {monotonously}.