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

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 γ , that annihilates the volume conservation. When γ i...

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Bibliographic Details
Published in:Journal of statistical physics 2015-06, Vol.159 (6), p.1327-1368
Main Authors: Bernardin, Cédric, Gonçalves, Patrícia, Jara, Milton, Sasada, Makiko, Simon, Marielle
Format: Article
Language:English
Subjects:
Mathematical and Computational Physics
Mathematics
Physical Chemistry
Physics
Physics and Astronomy
Probability
Quantum Physics
Statistical Physics and Dynamical Systems
Theoretical
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Summary: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 γ , that annihilates the volume conservation. When 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 γ = 0 , the energy superdiffuses according to a 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 γ .
ISSN:0022-4715
1572-9613
DOI:10.1007/s10955-015-1235-8