### 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 |
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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 |

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### 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