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Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics

Bose-Einstein condensation in a system ofq-bosons

Mario Salerno

Published Dec 1, 1994• 19 citations
Publisher

Abstract

We introduce a q-boson system with infinite range interaction which exhibits in the thermodynamic limit a Bose-Einstein condensation. Young tableaux analysis is used to solve the quantum problem of the system and to show that for a particular value of the deformation parameter the system behaves as a Bose gas with hard-core repulsion on a full graph. The method used to solve our system is of general validity and can be applied to other Hamiltonians with infinite range interactions.

DOI
10.1103/physreve.50.4528

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We introduce a q-boson system with infinite range interaction which exhibits in the thermodynamic limit a Bose-Einstein condensation. Young tableaux analysis is used to solve the quantum problem of the system and to show that for a particular value of the deformation parameter the system behaves as a Bose gas with hard-core repulsion on a full graph. The method used to solve our system is of general validity and can be applied to other Hamiltonians with infinite range interactions.
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In this paper, we propose quantum graphs as one-dimensional models with a complex topology to study Bose-Einstein condensation and phase transitions in a rigorous way. We first investigate non-interacting many-particle systems on quantum graphs and provide a complete classification of systems that exhibit Bose-Einstein condensation. We then consider models of interacting particles that can be regarded as a generalisation of the well-known Tonks-Girardeau gas. Here, our principal result is that no phase transitions occur in bosonic systems with repulsive hardcore interactions, indicating an absence of Bose-Einstein condensation.