六分之五超扩散的能量分布：磁场所耦合带电谐振子系统
5/6-Superdiffusion of energy for coupled charged harmonic oscillators in a magnetic field
AI总结：
研究磁场所耦合带电谐振子在小随机扰动下的能量分布演化，证明其遵循线性声波玻尔兹曼方程，并证明其分数扩散方程解的极限。
摘要：
我们考虑一个一维无限链的耦合带电谐振子系统，在磁场中存在小随机扰动，扰动阶为ε。我们证明在空间-时间尺度为ε^{-1}的尺度下，能量分布密度（威格纳分布）遵循线性声波玻尔兹曼方程。我们还证明线性声波玻尔兹曼方程解的适当缩放极限是分数扩散方程指数为5/6的解。
英文摘要：
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.
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