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Anomalous energy transport in FPU-ß chain

journal contribution
posted on 2023-06-20, 14:17 authored by Antoine Mellet, Sara Merino-Aceituno
This paper is devoted to the derivation of a macroscopic fractional diffusion equation describing heat transport in an anharmonic chain. More precisely, we study here the so-called FPU-ß chain, which is a very simple model for a one-dimensional crystal in which atoms are coupled to their nearest neighbors by a harmonic potential, weakly perturbed by a quartic potential. The starting point of our mathematical analysis is a kinetic equation: Lattice vibrations, responsible for heat transport, are modeled by an interacting gas of phonons whose evolution is described by the Boltzmann phonon equation. Our main result is the rigorous derivation of an anomalous diffusion equation starting from the linearized Boltzmann phonon equation.

History

Publication status

  • Published

File Version

  • Published version

Journal

Journal of Statistical Physics

ISSN

0022-4715

Publisher

Springer Verlag

Issue

3

Volume

160

Page range

583-621

Department affiliated with

  • Mathematics Publications

Full text available

  • No

Peer reviewed?

  • Yes

Legacy Posted Date

2018-02-19

First Compliant Deposit (FCD) Date

2018-02-19

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