@Journal Article{SummonFETCHLOGICAL126451daaa5e1a8a44b948ad2998ecd0c2a5ac534a11b1ef8ae176f1fd628661e05f13,
title = {5 / 6Superdiffusion of Energy for Coupled Charged Harmonic Oscillators in a Magnetic Field},
author = {Saito, Keiji} and {Sasada, Makiko} and {Suda, Hayate},
journal = {Communications in mathematical physics},
address = {Berlin/Heidelberg},
publisher = {Springer Berlin Heidelberg},
year = {2019},
keywords ={Quantum Physics, Mathematical Physics, Classical and Quantum Gravitation, Relativity Theory, Theoretical, Mathematical and Computational Physics, Complex Systems, Physics, Physical Sciences, Physics, Mathematical, Science & Technology, Mathematical analysis, Energy distribution, Phonons, Boltzmann transport equation, Perturbation, Magnetic fields, Wigner distribution, Harmonic oscillators, THERMALCONDUCTIVITY, SUPERDIFFUSION, LIMITTHEOREMS},
issn ={00103616, 14320916},
abstract = {We consider a onedimensional infinite chain of coupled charged harmonic oscillators in a magnetic field with a small stochastic perturbation of order
$$\epsilon $$
ϵ
. We prove that for a space–time scale of order
$$\epsilon ^{1}$$
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.
},
}