TY  Journal Article
T1  5 / 6Superdiffusion of Energy for Coupled Charged Harmonic Oscillators in a Magnetic Field
JF  Communications in mathematical physics
VL  372
IS  1
SP  151
EP  182
A1  Saito, Keiji
A2  Sasada, Makiko
A2  Suda, Hayate
CY  Berlin/Heidelberg
PB  Springer Berlin Heidelberg
PY  2019
UR  https://bonnus.ulb.unibonn.de/SummonRecord/FETCHLOGICAL126451daaa5e1a8a44b948ad2998ecd0c2a5ac534a11b1ef8ae176f1fd628661e05f13
N2  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.
KW  Quantum Physics
KW  Mathematical Physics
KW  Classical and Quantum Gravitation, Relativity Theory
KW  Theoretical, Mathematical and Computational Physics
KW  Complex Systems
KW  Physics
KW  Physical Sciences
KW  Physics, Mathematical
KW  Science & Technology
KW  Mathematical analysis
KW  Energy distribution
KW  Phonons
KW  Boltzmann transport equation
KW  Perturbation
KW  Magnetic fields
KW  Wigner distribution
KW  Harmonic oscillators
KW  THERMALCONDUCTIVITY
KW  SUPERDIFFUSION
KW  LIMITTHEOREMS
ER 