Exact solution of a Lévy walk model for anomalous heat transport

Abhishek Dhar, Keiji Saitou, Bernard Derrida

Research output: Contribution to journalArticle

30 Citations (Scopus)

Abstract

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.

Original languageEnglish
Article number010103
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Volume87
Issue number1
DOIs
Publication statusPublished - 2013 Jan 25

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Heat Transport
Walk
Anomalous
Exact Solution
heat
geometry
Heat
Model
Current Fluctuations
Fourier law
Fourier's Law
Heat Bath
One-dimensional System
Temperature Profile
Cumulants
Heat Conduction
Large Deviations
conductive heat transfer
temperature profiles
baths

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Statistical and Nonlinear Physics
  • Statistics and Probability

Cite this

Exact solution of a Lévy walk model for anomalous heat transport. / Dhar, Abhishek; Saitou, Keiji; Derrida, Bernard.

In: Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, Vol. 87, No. 1, 010103, 25.01.2013.

Research output: Contribution to journalArticle

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