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

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:126

Article

Mailler, Cecile¹  Morters, Peter¹  Ueltschi, Daniel² 

[1] Univ Bath, Dept Math Sci, Bath BA2 7AY, Avon, England

[2] Univ Warwick, Dept Math, Coventry CV4 7AL, W Midlands, England

关键词: Condensation;    Symmetry-breaking;    Extended condensate;    Interacting particle system;    Zero-range process;    Disordered system;    Weak disorder;    Grand canonical ensemble;    Extremes;    Gamma distribution;    Central limit theorem;   

DOI  :  10.1016/j.spa.2016.04.028

来源: Elsevier

【 摘 要 】

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. (C) 2016 Elsevier B.V. All rights reserved.

【 授权许可】

Free