Many-particle quantum graphs and Bose-Einstein condensation

Jens Bolte, Joachim Kerner

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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 fist 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
Original languageEnglish
Article number061901
Pages (from-to)1-16
Number of pages16
JournalJournal of Mathematical Physics
Issue number6
Early online date2 Jun 2014
Publication statusE-pub ahead of print - 2 Jun 2014

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