Exact solution of a Lévy walk model for anomalous heat transport

Abhishek Dhar, Keiji Saito, Bernard Derrida

研究成果: Article査読

46 被引用数 (Scopus)

抄録

The Lévy walk model is studied in the context of the anomalous heat conduction of one-dimensional systems. In this model, the heat carriers execute Lévy walks instead of normal diffusion as expected in systems where Fourier's law holds. Here we calculate exactly the average heat current, the large deviation function of its fluctuations, and the temperature profile of the Lévy walk model maintained in a steady state by contact with two heat baths (the open geometry). We find that the current is nonlocally connected to the temperature gradient. As observed in recent simulations of mechanical models, all the cumulants of the current fluctuations have the same system-size dependence in the open geometry. For the ring geometry, we argue that a size-dependent cutoff time is necessary for the Lévy walk model to behave like mechanical models. This modification does not affect the results on transport in the open geometry for large enough system sizes.

本文言語English
論文番号010103
ジャーナルPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
87
1
DOI
出版ステータスPublished - 2013 1月 25

ASJC Scopus subject areas

  • 統計物理学および非線形物理学
  • 統計学および確率
  • 凝縮系物理学

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