Communications in Mathematical Physics

, Volume 372, Issue 1, pp 151–182 | Cite as

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

  • Keiji Saito
  • Makiko Sasada
  • Hayate SudaEmail author


We consider a one-dimensional infinite chain of coupled charged harmonic oscillators in a magnetic field with a small stochastic perturbation of order \(\epsilon \). We prove that for a space–time scale of order \(\epsilon ^{-1}\) 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.



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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© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Physics, Faculty of Science and TechnologyKeio UniversityYokohamaJapan
  2. 2.Graduate School of Mathematical SciencesUniversity of TokyoTokyoJapan

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