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Energy Transfer in a Fast-Slow Hamiltonian System

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Abstract

We consider a finite region of a lattice of weakly interacting geodesic flows on manifolds of negative curvature and we show that, when rescaling the interactions and the time appropriately, the energies of the flows evolve according to a nonlinear diffusion equation. This is a first step toward the derivation of macroscopic equations from a Hamiltonian microscopic dynamics in the case of weakly coupled systems.

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Authors and Affiliations

  1. Department of Mathematics, University of Maryland, 4417 Mathematics Bldg, College Park, MD, 20742, USA

    Dmitry Dolgopyat

  2. Dipartimento di Matematica, II Università di Roma (Tor Vergata), Via della Ricerca Scientifica, 00133, Roma, Italy

    Carlangelo Liverani

Authors
  1. Dmitry Dolgopyat
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  2. Carlangelo Liverani
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Correspondence to Carlangelo Liverani.

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Communicated by H. Spohn

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Dolgopyat, D., Liverani, C. Energy Transfer in a Fast-Slow Hamiltonian System. Commun. Math. Phys. 308, 201–225 (2011). https://doi.org/10.1007/s00220-011-1317-7

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  • DOI: https://doi.org/10.1007/s00220-011-1317-7

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