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Diffusion in Energy Conserving Coupled Maps

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Abstract

We consider a dynamical system consisting of subsystems indexed by a lattice. Each subsystem has one conserved degree of freedom (“energy”) the rest being uniformly hyperbolic. The subsystems are weakly coupled together so that the sum of the subsystem energies remains conserved. We prove that the subsystem energies satisfy the diffusion equation in a suitable scaling limit.

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Authors and Affiliations

  1. UCLouvain, IRMP, Chemin du Cyclotron 2, 1348, Louvain-la-Neuve, Belgium

    Jean Bricmont

  2. Department of Mathematics and Statistics, University of Helsinki, P.O. Box 68, 00014, Helsinki, Finland

    Antti Kupiainen

Authors
  1. Jean Bricmont
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  2. Antti Kupiainen
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Corresponding author

Correspondence to Jean Bricmont.

Additional information

Communicated by G. Gallavotti

Partially supported by the Belgian IAP program P6/02.

Supported by the Academy of Finland and European Research Council.

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Bricmont, J., Kupiainen, A. Diffusion in Energy Conserving Coupled Maps. Commun. Math. Phys. 321, 311–369 (2013). https://doi.org/10.1007/s00220-013-1687-0

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  • DOI: https://doi.org/10.1007/s00220-013-1687-0

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