5 / 6-Superdiffusion of Energy for Coupled Charged Harmonic Oscillators in a Magnetic Field

Keiji Saito; Makiko Sasada; Hayate Suda

doi:10.1007/s00220-019-03506-4

5 / 6-Superdiffusion of Energy for Coupled Charged Harmonic Oscillators in a Magnetic Field

Keiji Saito, Makiko Sasada, Hayate Suda

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

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
Pages (from-to)	151-182
Number of pages	32
Journal	Communications in Mathematical Physics
Volume	372
Issue number	1
DOIs	https://doi.org/10.1007/s00220-019-03506-4
Publication status	Published - 2019 Nov 1

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics

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title = "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 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.",

author = "Keiji Saito and Makiko Sasada and Hayate Suda",

note = "Funding Information: KS was supported by JSPS Grants-in-Aid for Scientific Research Nos. JP17K05587 and JP16H02211. MS was supported by JSPS Grants-in-Aid for Scientific Research No. JP16KT0021. Funding Information: KS was supported by JSPS Grants-in-Aid for Scientific Research Nos. JP17K05587 and JP16H02211. MS was supported by JSPS Grants-in-Aid for Scientific Research No. JP16KT0021.",

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doi = "10.1007/s00220-019-03506-4",

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T1 - 5 / 6-Superdiffusion of Energy for Coupled Charged Harmonic Oscillators in a Magnetic Field

AU - Saito, Keiji

AU - Sasada, Makiko

AU - Suda, Hayate

N1 - Funding Information: KS was supported by JSPS Grants-in-Aid for Scientific Research Nos. JP17K05587 and JP16H02211. MS was supported by JSPS Grants-in-Aid for Scientific Research No. JP16KT0021. Funding Information: KS was supported by JSPS Grants-in-Aid for Scientific Research Nos. JP17K05587 and JP16H02211. MS was supported by JSPS Grants-in-Aid for Scientific Research No. JP16KT0021.

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Y1 - 2019/11/1

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.

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