### 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 |
---|---|

Pages (from-to) | 1327-1368 |

Number of pages | 42 |

Journal | Journal of Statistical Physics |

Volume | 159 |

Issue number | 6 |

DOIs | |

Publication status | Published - 2015 Jun 28 |

### Fingerprint

### Keywords

- Anomalous diffusion
- Equilibrium fluctuations
- Fourier’s law

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics

### Cite this

*Journal of Statistical Physics*,

*159*(6), 1327-1368. https://doi.org/10.1007/s10955-015-1235-8

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

Research output: Contribution to journal › Article

*Journal of Statistical Physics*, vol. 159, no. 6, pp. 1327-1368. https://doi.org/10.1007/s10955-015-1235-8

}

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 -