From anomalous energy diffusion to levy walks and heat conductivity in one-dimensional systems

P Cipriani, S Denisov, A Politi

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The evolution of infinitesimal, localized perturbations is investigated in a one-dimensional diatomic gas of hard-point particles (HPG) and thereby connected to energy diffusion. As a result, a Levy walk description, which was so far invoked to explain anomalous heat conductivity in the context of noninteracting particles is here shown to extend to the general case of truly many-body systems. Our approach does not only provide firm evidence that energy diffusion is anomalous in the HPG, but proves definitely superior to direct methods for estimating the divergence rate of heat conductivity which turns out to be 0.333 +/- 0.004, in perfect agreement with the dynamical renormalization-group prediction (1/3).

Original languageEnglish
Article number244301
Number of pages4
JournalPhysical Review Letters
Issue number24
Publication statusPublished - 24 Jun 2005


  • Lyapunov exponents
  • propagation
  • flow

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