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 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.

arXiv comment27 pages

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Cited by in corpus (1)

• Non-equilibrium stationary properties of the boundary driven zero-range process with long jumps