Anomalous energy transport in FPU-$\beta$ chain

Abstract

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-$\beta$ 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

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Cited by in corpus (7)

• Anomalous heat transport in one dimensional systems: a description using non-local fractional-type diffusion equation
• 3/4 Fractional superdiffusion of energy in a system of harmonic oscillators perturbed by a conservative noise
• Wave Turbulence and thermalization in one-dimensional chains
• The fractional diffusion limit of a kinetic model with biochemical pathway
• Kinetic theory of phonons in weakly anharmonic particle chains
• Nonlinear Perturbation of a Noisy Hamiltonian Lattice Field Model: Universality Persistence
• Structural localization in the Classical and Quantum Fermi-Pasta-Ulam Model