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Thermal Conductivity of the Toda Lattice with Conservative Noise

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Abstract

We study the thermal conductivity of the one dimensional Toda lattice perturbed by a stochastic dynamics preserving energy and momentum. The strength of the stochastic noise is controlled by a parameter γ. We show that heat transport is anomalous, and that the thermal conductivity diverges with the length n of the chain according to κ(n)∼n α, with 0<α≤1/2. In particular, the ballistic heat conduction of the unperturbed Toda chain is destroyed. Besides, the exponent α of the divergence depends on γ.

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Authors and Affiliations

  1. CEREMADE, UMR-CNRS 7534, Université de Paris Dauphine, Place du Maréchal De Lattre De Tassigny, 75775, Paris Cedex 16, France

    Alessandra Iacobucci & Stefano Olla

  2. UR Navier, Projet MICMAC Ecole des Ponts ParisTech—INRIA, Université Paris Est, 6 & 8 Av. Pascal, 77455, Marne-la-Vallée Cedex 2, France

    Frédéric Legoll

  3. CERMICS, Projet MICMAC Ecole des Ponts ParisTech—INRIA, Université Paris Est, 6 & 8 Av. Pascal, 77455, Marne-la-Vallée Cedex 2, France

    Stefano Olla & Gabriel Stoltz

Authors
  1. Alessandra Iacobucci
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  2. Frédéric Legoll
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  3. Stefano Olla
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  4. Gabriel Stoltz
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Correspondence to Stefano Olla.

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Iacobucci, A., Legoll, F., Olla, S. et al. Thermal Conductivity of the Toda Lattice with Conservative Noise. J Stat Phys 140, 336–348 (2010). https://doi.org/10.1007/s10955-010-9996-6

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  • DOI: https://doi.org/10.1007/s10955-010-9996-6

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