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Sample-to-sample fluctuations of power spectrum of a random motion in a periodic Sinai model

hal.structure.identifierLaboratoire Ondes et Matière d'Aquitaine [LOMA]
dc.contributor.authorDEAN, David S.
hal.structure.identifierDipartimento di Fisica [Rome]
hal.structure.identifierDipartimento di Matematica e Fisica [Roma]
dc.contributor.authorIORIO, Antonio
hal.structure.identifierDipartimento di Fisica [Rome]
hal.structure.identifierIstituto Nazionale di Fisica Nucleare [Sezione di Roma 1] [INFN]
dc.contributor.authorMARINARI, Enzo
hal.structure.identifierLaboratoire de Physique Théorique de la Matière Condensée [LPTMC]
dc.contributor.authorOSHANIN, Gleb
dc.date.created2016-07-04
dc.date.issued2016-09
dc.identifier.issn2470-0045
dc.description.abstractEnThe Sinai model of a tracer diffusing in a quenched Brownian potential is a much-studied problem exhibiting a logarithmically slow anomalous diffusion due to the growth of energy barriers with the system size. However, if the potential is random but periodic, the regime of anomalous diffusion crosses over to one of normal diffusion once a tracer has diffused over a few periods of the system. Here we consider a system in which the potential is given by a Brownian bridge on a finite interval (0,L) and then periodically repeated over the whole real line and study the power spectrum S(f) of the diffusive process x(t) in such a potential. We show that for most of realizations of x(t) in a given realization of the potential, the low-frequency behavior is S(f) ∼ A/f 2 , i.e., the same as for standard Brownian motion, and the amplitude A is a disorder-dependent random variable with a finite support. Focusing on the statistical properties of this random variable, we determine the moments of A of arbitrary, negative, or positive order k and demonstrate that they exhibit a multifractal dependence on k and a rather unusual dependence on the temperature and on the periodicity L, which are supported by atypical realizations of the periodic disorder. We finally show that the distribution of A has a log-normal left tail and exhibits an essential singularity close to the right edge of the support, which is related to the Lifshitz singularity. Our findings are based both on analytic results and on extensive numerical simulations of the process x(t).
dc.language.isoen
dc.publisherAmerican Physical Society (APS)
dc.rights.urihttp://creativecommons.org/licenses/by-nc-sa/
dc.title.enSample-to-sample fluctuations of power spectrum of a random motion in a periodic Sinai model
dc.typeArticle de revue
dc.identifier.doi10.1103/PhysRevE.94.032131
dc.subject.halPhysique [physics]/Matière Condensée [cond-mat]/Mécanique statistique [cond-mat.stat-mech]
dc.identifier.arxiv1607.00058
bordeaux.journalPhysical Review E
bordeaux.page032131 (1-8)
bordeaux.volume94
bordeaux.issue3
bordeaux.peerReviewedoui
hal.identifierhal-01396689
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-01396689v1
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