5/6-superdiffusion of energy for coupled charged harmonic oscillators in a magnetic field

Keiji Saito, Makiko Sasada, Hayate Suda

Research output: Contribution to journalArticlepeer-review

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-1the 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
JournalUnknown Journal
Publication statusPublished - 2018 Aug 2

ASJC Scopus subject areas

  • General

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