Superdiffusion transition for a noisy harmonic chain subject to a magnetic field

Gaëtan Cane

Published 2022-01-10, updated 2022-07-11Version 2

We consider an infinite harmonic chain of charged particles submitted to the action of a magnetic field of intensity $B$ and subject to the action of a stochastic noise conserving the energy. In arXiv:0809.0177 and arXiv:1402.2988 it has been proved that if $B=0$ the transport of energy is described by a $3/4$-fractional diffusion while it has been proved in arXiv:1808.01040 that if $B\ne 0$ it is described by a $5/6$-fractional diffusion. In this paper we quantify the intensity of the magnetic field necessary to pass from one regime to the other one. We also describe the transition mechanism to cross the two different phases.