### 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