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

Keiji Saito; Makiko Sasada; Hayate Suda

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

Keiji Saito, Makiko Sasada, Hayate Suda

Department of Physics

Research output: Contribution to journal › Article › peer-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 language	English
Journal	Unknown Journal
Publication status	Published - 2018 Aug 2

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

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.",

author = "Keiji Saito and Makiko Sasada and Hayate Suda",

year = "2018",

month = aug,

day = "2",

language = "English",

journal = "Mathematical Social Sciences",

issn = "0165-4896",

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AU - Saito, Keiji

AU - Sasada, Makiko

AU - Suda, Hayate

PY - 2018/8/2

Y1 - 2018/8/2

N2 - 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.

AB - 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.

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M3 - Article

AN - SCOPUS:85094521811

JO - Mathematical Social Sciences

JF - Mathematical Social Sciences

SN - 0165-4896

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