Condensation and symmetry-breaking in the zero-range process with weak site disorder

Cécile Mailler, Peter Mörters and Daniel Ueltschi

Stochastic Processes and their Applications, 2016, vol. 126, issue 11, 3283-3309

Abstract: Condensation phenomena in particle systems typically occur as one of two distinct types: either as a spontaneous symmetry breaking in a homogeneous system, in which particle interactions enforce condensation in a randomly located site, or as an explicit symmetry breaking in a system with background disorder, in which particles condensate in the site of extremal disorder. In this paper we confirm a recent conjecture by Godrèche and Luck by showing, for a zero range process with weak site disorder, that there exists a phase where condensation occurs with an intermediate type of symmetry-breaking, in which particles condensate in a site randomly chosen from a range of sites favoured by disorder. We show that this type of condensation is characterised by the occurrence of a Gamma distribution in the law of the disorder at the condensation site. We further investigate fluctuations of the condensate size and confirm a phase diagram, again conjectured by Godrèche and Luck, showing the existence of phases with normal and anomalous fluctuations.

Keywords: Condensation; Symmetry-breaking; Extended condensate; Interacting particle system; Zero-range process; Disordered system; Weak disorder; Grand canonical ensemble; Extremes; Gamma distribution; Central limit theorem (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1016/j.spa.2016.04.028

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