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

Cecile Mailler, Peter Morters, Daniel Ueltschi

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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 Godreche 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 Godreche and Luck, showing the existence of phases with normal and anomalous fluctuations.
Original languageEnglish
Pages (from-to)3283-3309
Number of pages22
JournalStochastic Processes and their Applications
Volume126
Issue number11
Early online date6 May 2016
DOIs
Publication statusPublished - 1 Nov 2016

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Zero-range Process
Condensation
Symmetry Breaking
Disorder
Condensate
Luck
Fluctuations
Spontaneous Symmetry Breaking
Particle interactions
Gamma distribution
Particle System
Phase Diagram
Anomalous
Phase diagrams
Distinct
Interaction
Range of data

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Condensation and symmetry-breaking in the zero-range process with weak site disorder. / Mailler, Cecile; Morters, Peter; Ueltschi, Daniel.

In: Stochastic Processes and their Applications, Vol. 126, No. 11, 01.11.2016, p. 3283-3309.

Research output: Contribution to journalArticle

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