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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-AceitunoThis 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 PhysicsISSN
0022-4715Publisher
Springer VerlagExternal DOI
Issue
3Volume
160Page range
583-621Department affiliated with
- Mathematics Publications
Full text available
- No
Peer reviewed?
- Yes