# 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 language English 1327-1368 42 Journal of Statistical Physics 159 6 https://doi.org/10.1007/s10955-015-1235-8 Published - 2015 Jun 28

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.
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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.

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