### 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 language | English |
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Journal | Communications in Mathematical Physics |

DOIs | |

Publication status | Published - 2019 Jan 1 |

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### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics

### Cite this

**5 / 6-Superdiffusion of Energy for Coupled Charged Harmonic Oscillators in a Magnetic Field.** / Saitou, Keiji; Sasada, Makiko; Suda, Hayate.

Research output: Contribution to journal › Article

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TY - JOUR

T1 - 5 / 6-Superdiffusion of Energy for Coupled Charged Harmonic Oscillators in a Magnetic Field

AU - Saitou, Keiji

AU - Sasada, Makiko

AU - Suda, Hayate

PY - 2019/1/1

Y1 - 2019/1/1

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- 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.

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- 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.

UR - http://www.scopus.com/inward/record.url?scp=85068877852&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85068877852&partnerID=8YFLogxK

U2 - 10.1007/s00220-019-03506-4

DO - 10.1007/s00220-019-03506-4

M3 - Article

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

SN - 0010-3616

ER -