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Geometric and Probabilistic Aspects of Boson Lattice Models

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Book cover In and Out of Equilibrium

Part of the book series: Progress in Probability ((PRPR,volume 51))

Abstract

This review describes quantum systems of bosonic particles moving on a lattice. These models are relevant in statistical physics, and have natural ties with probability theory. The general setting is recalled and the main questions about phase transitions are addressed. A lattice model with Lennard-Jones potential is studied as an example of a system where first-order phase transitions occur.

A major interest of bosonic systems is the possibility of displaying a Bose-Einstein condensation. This is discussed in the light of the main existing rigorous result, namely its occurrence in the hard-core boson model. Finally, we consider another approach that involves the lengths of the cycles formed by the particles in the space-time representation; Bose-Einstein condensation should be related to positive probability of infinite cycles.

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Authors and Affiliations

  1. Department of Physics, Princeton University, Jadwin Hall, Princeton, 08544, NJ

    Daniel Ueltschi

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  1. Daniel Ueltschi
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Editors and Affiliations

  1. IMPA-Instituto de Matemática Pura e Aplicada, Estrada Dona Castorina 110 Jardim Botânico, Rio de Janeiro, RJ 22460-320, Brazil

    Vladas Sidoravicius

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Ueltschi, D. (2002). Geometric and Probabilistic Aspects of Boson Lattice Models. In: Sidoravicius, V. (eds) In and Out of Equilibrium. Progress in Probability, vol 51. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0063-5_17

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  • DOI: https://doi.org/10.1007/978-1-4612-0063-5_17

  • Publisher Name: Birkhäuser, Boston, MA

  • Print ISBN: 978-1-4612-6595-5

  • Online ISBN: 978-1-4612-0063-5

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