Bose-Einstein Condensation of Quantum Hard-Spheres as a Deposition Phase Transition and New Relations Between Bosonic and Fermionic Pressures

TL;DR

This paper explores the phase transition of Bose-Einstein particles with hard-core repulsion, revealing their pressure behavior is mathematically similar to nuclear multifragmentation models, and introduces relations linking fermionic and bosonic pressures.

Contribution

It demonstrates a novel equivalence between Bose-Einstein and nuclear multifragmentation pressures and establishes new relations connecting fermionic and bosonic pressures.

Findings

High density Bose-Einstein phase resembles a classical macro-cluster with zero entropy.

Pressure equations of state for Bose-Einstein and nuclear models are mathematically equivalent.

New relations express Fermi-Dirac pressure in terms of Bose-Einstein pressures.

Abstract

We investigate the phase transition of Bose-Einstein particles with the hard-core repulsion in the grand canonical ensemble within the Van der Waals approximation. It is shown that the pressure of non-relativistic Bose-Einstein particles is mathematically equivalent to the pressure of simplified version of the statistical multifragmentation model of nuclei with the vanishing surface tension coefficient and the Fisher exponent $\tau_F = \frac{5}{2}$, which for such parameters has the 1-st order phase transition. The found similarity of these equations of state allows us to show that within the present approach the high density phase of Bose-Einstein particles is a classical macro-cluster with vanishing entropy at any temperature which, similarly to the classical hard spheres, is a kind of solid state. To show this we establish new relations which allow us to identically represent the pressure of Fermi-Dirac particles in terms of pressures of Bose-Einstein particles of two sorts.