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

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• 作者：Cédric Bernardin ; Patrícia Gon?alves ; Milton Jara…
• 关键词：Anomalous diffusion ; Fourier’s law ; Equilibrium fluctuations
• 刊名：Journal of Statistical Physics
• 出版年：2015
• 出版时间：June 2015
• 年：2015
• 卷：159
• 期：6
• 页码：1327-1368
• 全文大小：820 KB
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• 作者单位：Cédric Bernardin (1)
  Patrícia Gon?alves (2) (3)
  Milton Jara (4)
  Makiko Sasada (5)
  Marielle Simon (2) (6)
  
  1. Laboratoire J.A. Dieudonné, UMR CNRS 7351, Université de Nice Sophia-Antipolis, Parc Valrose, 06108, Nice cedex 02, France
  2. Departamento de Matemática, PUC-RIO, Rua Marquês de S?o Vicente, No. 225, Rio de Janeiro, RJ, 22453-900, Brazil
  3. CMAT, Centro de Matemática da Universidade do Minho, Campus de Gualtar, 4710-057, Braga, Portugal
  4. IMPA, Estrada Dona Castorina 110, Jardim Botanico, Rio de Janeiro, CEP 22460-340, Brazil
  5. Department of Mathematics, Keio University, 3-14-1, Hiyoshi, Kohoku-ku, Yokohama-shi, Kanagawa, 223-8522, Japan
  6. UMPA ENS de Lyon, 46 allée d’Italie, 69007, Lyon, France
  
• 刊物类别：Physics and Astronomy
• 刊物主题：Physics
  Statistical Physics
  Mathematical and Computational Physics
  Physical Chemistry
  Quantum Physics
  
• 出版者：Springer Netherlands
• ISSN：1572-9613

文摘

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 \(\gamma \), that annihilates the volume conservation. When \(\gamma \) is of order one, the energy diffuses according to the standard heat equation after a space-time diffusive scaling. On the other hand, when \(\gamma =0\), 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 \(\gamma \).