Abstract
We consider a one-dimensional infinite chain of coupled charged harmonic oscillators in a magnetic field with a small stochastic perturbation of order ϵ. We prove that for a space–time scale of order 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.
| Original language | English |
|---|---|
| Journal | Communications in Mathematical Physics |
| DOIs | |
| Publication status | Published - 2019 Jan 1 |
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ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics
Cite this
5 / 6-Superdiffusion of Energy for Coupled Charged Harmonic Oscillators in a Magnetic Field. / Saitou, Keiji; Sasada, Makiko; Suda, Hayate.
In: Communications in Mathematical Physics, 01.01.2019.Research output: Contribution to journal › Article
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TY - JOUR
T1 - 5 / 6-Superdiffusion of Energy for Coupled Charged Harmonic Oscillators in a Magnetic Field
AU - Saitou, Keiji
AU - Sasada, Makiko
AU - Suda, Hayate
PY - 2019/1/1
Y1 - 2019/1/1
N2 - We consider a one-dimensional infinite chain of coupled charged harmonic oscillators in a magnetic field with a small stochastic perturbation of order ϵ. We prove that for a space–time scale of order 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.
AB - We consider a one-dimensional infinite chain of coupled charged harmonic oscillators in a magnetic field with a small stochastic perturbation of order ϵ. We prove that for a space–time scale of order 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.
UR - http://www.scopus.com/inward/record.url?scp=85068877852&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85068877852&partnerID=8YFLogxK
U2 - 10.1007/s00220-019-03506-4
DO - 10.1007/s00220-019-03506-4
M3 - Article
AN - SCOPUS:85068877852
JO - Communications in Mathematical Physics
JF - Communications in Mathematical Physics
SN - 0010-3616
ER -