From Normal Diffusion to Superdiffusion of Energy in the Evanescent Flip Noise Limit

Cédric Bernardin, Patrícia Gonçalves, Milton Jara, Makiko Sasada, Marielle Simon

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

We consider a harmonic chain perturbed by a stochastic noise which conserves the energy and a second quantity called the volume, and destroys all the other ones. We then add to this model a second energy conserving noise depending on a parameter $$\gamma $$γ, that annihilates the volume conservation. When $$\gamma $$γ is of order one, the energy diffuses according to the standard heat equation after a space-time diffusive scaling. On the other hand, when $$\gamma =0$$γ=0, the energy superdiffuses according to a $$3/4$$3/4-fractional heat equation after a subdiffusive space-time scaling. In this paper, we study the existence of a crossover between these two regimes as a function of $$\gamma $$γ.

Original languageEnglish
Pages (from-to)1327-1368
Number of pages42
JournalJournal of Statistical Physics
Volume159
Issue number6
DOIs
Publication statusPublished - 2015 Jun 28

Fingerprint

Superdiffusion
Flip
Energy
Heat Equation
Space-time
Scaling
scaling
thermodynamics
energy
Conserve
Crossover
Conservation
conservation
crossovers
Fractional
Harmonic
harmonics

Keywords

  • Anomalous diffusion
  • Equilibrium fluctuations
  • Fourier’s law

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

From Normal Diffusion to Superdiffusion of Energy in the Evanescent Flip Noise Limit. / Bernardin, Cédric; Gonçalves, Patrícia; Jara, Milton; Sasada, Makiko; Simon, Marielle.

In: Journal of Statistical Physics, Vol. 159, No. 6, 28.06.2015, p. 1327-1368.

Research output: Contribution to journalArticle

Bernardin, Cédric ; Gonçalves, Patrícia ; Jara, Milton ; Sasada, Makiko ; Simon, Marielle. / From Normal Diffusion to Superdiffusion of Energy in the Evanescent Flip Noise Limit. In: Journal of Statistical Physics. 2015 ; Vol. 159, No. 6. pp. 1327-1368.
@article{706724cd80db46e28842e12c4f9b005e,
title = "From Normal Diffusion to Superdiffusion of Energy in the Evanescent Flip Noise Limit",
abstract = "We consider a harmonic chain perturbed by a stochastic noise which conserves the energy and a second quantity called the volume, and destroys all the other ones. We then add to this model a second energy conserving noise depending on a parameter $$\gamma $$γ, that annihilates the volume conservation. When $$\gamma $$γ is of order one, the energy diffuses according to the standard heat equation after a space-time diffusive scaling. On the other hand, when $$\gamma =0$$γ=0, the energy superdiffuses according to a $$3/4$$3/4-fractional heat equation after a subdiffusive space-time scaling. In this paper, we study the existence of a crossover between these two regimes as a function of $$\gamma $$γ.",
keywords = "Anomalous diffusion, Equilibrium fluctuations, Fourier’s law",
author = "C{\'e}dric Bernardin and Patr{\'i}cia Gon{\cc}alves and Milton Jara and Makiko Sasada and Marielle Simon",
year = "2015",
month = "6",
day = "28",
doi = "10.1007/s10955-015-1235-8",
language = "English",
volume = "159",
pages = "1327--1368",
journal = "Journal of Statistical Physics",
issn = "0022-4715",
publisher = "Springer New York",
number = "6",

}

TY - JOUR

T1 - From Normal Diffusion to Superdiffusion of Energy in the Evanescent Flip Noise Limit

AU - Bernardin, Cédric

AU - Gonçalves, Patrícia

AU - Jara, Milton

AU - Sasada, Makiko

AU - Simon, Marielle

PY - 2015/6/28

Y1 - 2015/6/28

N2 - We consider a harmonic chain perturbed by a stochastic noise which conserves the energy and a second quantity called the volume, and destroys all the other ones. We then add to this model a second energy conserving noise depending on a parameter $$\gamma $$γ, that annihilates the volume conservation. When $$\gamma $$γ is of order one, the energy diffuses according to the standard heat equation after a space-time diffusive scaling. On the other hand, when $$\gamma =0$$γ=0, the energy superdiffuses according to a $$3/4$$3/4-fractional heat equation after a subdiffusive space-time scaling. In this paper, we study the existence of a crossover between these two regimes as a function of $$\gamma $$γ.

AB - We consider a harmonic chain perturbed by a stochastic noise which conserves the energy and a second quantity called the volume, and destroys all the other ones. We then add to this model a second energy conserving noise depending on a parameter $$\gamma $$γ, that annihilates the volume conservation. When $$\gamma $$γ is of order one, the energy diffuses according to the standard heat equation after a space-time diffusive scaling. On the other hand, when $$\gamma =0$$γ=0, the energy superdiffuses according to a $$3/4$$3/4-fractional heat equation after a subdiffusive space-time scaling. In this paper, we study the existence of a crossover between these two regimes as a function of $$\gamma $$γ.

KW - Anomalous diffusion

KW - Equilibrium fluctuations

KW - Fourier’s law

UR - http://www.scopus.com/inward/record.url?scp=84929944821&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84929944821&partnerID=8YFLogxK

U2 - 10.1007/s10955-015-1235-8

DO - 10.1007/s10955-015-1235-8

M3 - Article

AN - SCOPUS:84929944821

VL - 159

SP - 1327

EP - 1368

JO - Journal of Statistical Physics

JF - Journal of Statistical Physics

SN - 0022-4715

IS - 6

ER -