论文标题
声子Boltzmann方程的超延伸过渡
Superdiffusion transition for a phonon Boltzmann equation
论文作者
论文摘要
我们考虑一个无限的带电颗粒的谐波链，该粒子的磁场$ b $的作用，并受到节省能量的随机噪声的作用。在ARXIV：0809.0177和ARXIV：1402.2988中，已经证明，如果$ b = 0 $，能源的运输描述了$ 3/4 $ - 级分扩散，而在Arxiv：1808.01040证明，则如果$ 5/6 $ 5/6 $ -6 $-6 $-6 $-6 $-6 $-6 $-6 $-6 $-6 $ fraction diffffffffffife y Ne $ ne $。在Arxiv：0809.0177和Arxiv：1808.01040中，作者使用了两个步骤的参数，即，他们首先证明了Wigner分布的动力学极限是声子Boltzmann方程的解决方案，然后证明了与Expectional Exportiation $ 3/4 $ B = 0 $ b = 0 $ b = 0的解决方案的解决方案， arxiv：0809.0177）和指数$ 5/6 $如果$ b \ ne 0 $（请参阅Arxiv：1808.01040）。在本文中，我们量化了从一个宏观旋转方程式从一个宏观方程式切换到另一个宏观方程的磁场的强度。我们还描述了跨越两个不同阶段的过渡机制。
We consider an infinite harmonic chain of charged particles submitted to the action of a magnetic field of intensity $B$ and subject to the action of a stochastic noise conserving the energy. In arXiv:0809.0177 and arXiv:1402.2988 it has been proved that if $B=0$ the transport of energy is described by a $3/4$-fractional diffusion while it has been proved in arXiv:1808.01040 that if $B\ne 0$ it is described by a $5/6$-fractional diffusion. In arXiv:0809.0177 and in arXiv:1808.01040 the authors used a two step argument, i.e. they first proved that the kinetic limit of the Wigner distribution is the solution of a phonon Boltzmann equation and then proved that this solution converges to the solution of a fractional diffusion equation with exponent $3/4$ if $B = 0$ (see arXiv:0809.0177) and exponent $5/6$ if $B\ne 0$ (see arXiv:1808.01040). In this paper we quantify the intensity of the magnetic field required to switch from one macroscopic regime to the other one from the phonon Boltzmann equation. We also describe the transition mechanism to cross the two different phases.
