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Canonical Analysis of Condensation in Factorised Steady States

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Abstract

We study the phenomenon of real space condensation in the steady state of a class of mass transport models where the steady state factorises. The grand canonical ensemble may be used to derive the criterion for the occurrence of a condensation transition but does not shed light on the nature of the condensate. Here, within the canonical ensemble, we analyse the condensation transition and the structure of the condensate, determining the precise shape and the size of the condensate in the condensed phase. We find two distinct condensate regimes: one where the condensate is gaussian distributed and the particle number fluctuations scale normally as L 1/2 where L is the system size, and a second regime where the particle number fluctuations become anomalously large and the condensate peak is non-gaussian. Our results are asymptotically exact and can also be interpreted within the framework of sums of random variables. We further analyse two additional cases: one where the condensation transition is somewhat different from the usual second order phase transition and one where there is no true condensation transition but instead a pseudocondensate appears at superextensive densities.

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Authors and Affiliations

  1. SUPA, School of Physics, University of Edinburgh, Mayfield Road, Edinburgh, EH9 3JZ, UK

    M. R. Evans

  2. Laboratoire de Physique Théorique et Modèles Statistiques, Université Paris-Sud, Bat 100, 91405, Orsay-Cedex, France

    Satya N. Majumdar

  3. Department of Physics and Center for Stochastic Processes in Science and Engineering, Virginia Tech, Blacksburg, VA, 24061-0435, USA

    R. K. P. Zia

Authors
  1. M. R. Evans
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  2. Satya N. Majumdar
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  3. R. K. P. Zia
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Correspondence to M. R. Evans.

Additional information

PACS numbers: 05.40.-a, 02.50.Ey, 64.60.-i.

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Evans, M.R., Majumdar, S.N. & Zia, R.K.P. Canonical Analysis of Condensation in Factorised Steady States. J Stat Phys 123, 357–390 (2006). https://doi.org/10.1007/s10955-006-9046-6

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  • DOI: https://doi.org/10.1007/s10955-006-9046-6

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