振子晶格网络中的能量扩散和超扩散

Superdiffusion of energy in a chain of harmonic oscillators with noise

We consider a one dimensional infinite chain of har- monic oscillators whose dynamics is perturbed by a stochastic term conserving energy and momentum. We prove that in the unpinned case the macroscopic evolution of the energy converges to a fractional diffusion. For a pinned system we prove that energy evolves diffusively, generalizing some of the results of [4].

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

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。

Diffusion and superdiffusion from hydrodynamic projections

Hydrodynamic projections, the projection onto conserved charges representing ballistic propagation of fluid waves, give exact transport results in many-body systems, such as the exact Drude weights. Focussing one one-dimensional systems, I show that this principle can be extended beyond the Euler scale, in particular to the diffusive and superdiffusive scales. By hydrodynamic reduction, Hilbert spaces of observables are constructed that generalise the standard space of conserved densities and describe the finer scales of hydrodynamics. The Green-Kubo formula for the Onsager matrix has a natura…

记忆诱导的反常动力学：从单个随机游走模型中扩散、次扩散和超扩散的出现

Memory-induced anomalous dynamics: emergence of diffusion, subdiffusion, and superdiffusion from a single random walk model

我们提出了一个随机游动模型，表现出渐近亚扩散，扩散，超扩散行为在不同的参数制度。这似乎是通过简单地改变参数值导致所有三种行为形式的单个随机游走模型的第一个实例。此外，该模型提供了很大的优势，分析处理。我们的模型是非马尔可夫的，因为步行者的下一次跳跃（概率）由过去的跳跃历史决定。它也有不连贯的元素，因为每一步的一种可能性是步行者根本不动。这个由单一模型产生的丰富的包含场景提供了对不同类型渐近行为的来源的有用见解。

Lévy-Lorentz气体的大涨落与输运性质

Large fluctuations and transport properties of the Lévy-Lorentz gas

本文研究Lévy-Lorentz气体的大涨落与输运性质，证明退火情形存在超扩散，而淬火典型环境下长时间呈正常扩散。

声子玻尔兹曼方程的超级扩散转变

Superdiffusion transition for a phonon Boltzmann equation

本文研究带电粒子谐波链在磁场和随机噪声下的能量输运，量化了从$3/4$分数扩散到$5/6$分数扩散的磁场强度阈值，并描述了转变机制。