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arXiv · 1808.01040

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

Keiji Saito·Makiko Sasada·Hayate Suda
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Abstract

We consider a one-dimensional infinite chain of coupled charged har- monic oscillators in a magnetic field with a small stochastic perturbation of order $\epsilon$. We prove that for a space-time scale of order $\epsilon$^{-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 lin- ear phonon Boltzmann equation is a solution of the fractional diffusion equation with exponent 5/6.

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Keiji Saito, Makiko Sasada, Hayate Suda. 2018-08-02. 5/6-Superdiffusion of energy for coupled charged harmonic oscillators in a magnetic field. https://doi.org/10.1007/s00220-019-03506-4

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