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

arXiv comment8 pages

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Cited by in corpus (1)

• Alternative Formulation of the Induced Surface and Curvature Tensions Approach