Approach to equilibrium for the phonon Boltzmann equation

Jean Bricmont, Antti Kupiainen

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We study the asymptotics of solutions of the Boltzmann equation describing the kinetic limit of a lattice of classical interacting anharmonic oscillators. We prove that, if the initial condition is a small perturbation of an equilibrium state, and vanishes at infinity, the dynamics tends diffusively to equilibrium. The solution is the sum of a local equilibrium state, associated to conserved quantities that diffuse to zero, and fast variables that are slaved to the slow ones. This slaving implies the Fourier law, which relates the induced currents to the gradients of the conserved quantities.
Original languageEnglish
JournalCommunications in Mathematical Physics
Issue number1
Pages (from-to)179-202
Number of pages24
Publication statusPublished - 2008
MoE publication typeA1 Journal article-refereed

Fields of Science

  • 114 Physical sciences
  • 111 Mathematics

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