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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2018
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/1808.01040 |
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| _version_ | 1866911589323505664 |
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| author | Saito, Keiji Sasada, Makiko Suda, Hayate |
| author_facet | Saito, Keiji Sasada, Makiko Suda, Hayate |
| contents | We consider a one-dimensional infinite chain of coupled charged har- monic 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 lin- ear phonon Boltzmann equation is a solution of the fractional diffusion equation with exponent 5/6. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1808_01040 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | 5/6-Superdiffusion of energy for coupled charged harmonic oscillators in a magnetic field Saito, Keiji Sasada, Makiko Suda, Hayate Probability Mathematical Physics We consider a one-dimensional infinite chain of coupled charged har- monic 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 lin- ear phonon Boltzmann equation is a solution of the fractional diffusion equation with exponent 5/6. |
| title | 5/6-Superdiffusion of energy for coupled charged harmonic oscillators in a magnetic field |
| topic | Probability Mathematical Physics |
| url | https://arxiv.org/abs/1808.01040 |