5 / 6-Superdiffusion of Energy for Coupled Charged Harmonic Oscillators in a Magnetic Field

Keiji Saitou, Makiko Sasada, Hayate Suda

Research output: Contribution to journalArticle

Abstract

We consider a one-dimensional infinite chain of coupled charged harmonic oscillators in a magnetic field with a small stochastic perturbation of order ϵ. We prove that for a space–time scale of order ϵ- 1 the density of energy distribution (Wigner distribution) evolves according to a linear phonon Boltzmann equation. We also prove that an appropriately scaled limit of solutions of the linear phonon Boltzmann equation is a solution of the fractional diffusion equation with exponent 5 / 6.

Original languageEnglish
JournalCommunications in Mathematical Physics
DOIs
Publication statusPublished - 2019 Jan 1

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ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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