一类确定性一维多粒子洛伦兹气体的超扩散热输运
Superdiffusive Heat Transport in a class of Deterministic One-Dimensional Many-Particle Lorentz gases
摘要：
我们研究热输运在一维链的有限数量的$N$相同的细胞，在其边界耦合到随机粒子水库。在每个细胞的中心，示踪粒子与固定的散射体碰撞，交换动量。在最近的一篇论文中，\cite{CE08}，这个模型的空间连续版本中导出的标度制度的示踪剂的散射概率是$γ\sim1/N$，对应于格拉德限制。得到了描述热输运的Boltzmann型方程。在本文中，我们数值计算表明，在\cite{CE08}得到的玻尔兹曼描述确实是一个真正的粒子模型的限制。此外，我们还研究了散射概率为1时模型的热输运，对应于确定性动力学。在粗粒度的水平上，该模型表现为一个持久的随机步行者与广泛的等待时间分布和强相关的确定性散射。我们表明，尽管缺乏全球守恒量，该模型导致超扩散热传输。
英文摘要：
We study heat transport in a one-dimensional chain of a finite number $N$ of identical cells, coupled at its boundaries to stochastic particle reservoirs. At the center of each cell, tracer particles collide with fixed scatterers, exchanging momentum. In a recent paper, \cite{CE08}, a spatially continuous version of this model was derived in a scaling regime where the scattering probability of the tracers is $γ\sim1/N$, corresponding to the Grad limit. A Boltzmann type equation describing the transport of heat was obtained. In this paper, we show numerically that the Boltzmann description obtained in \cite{CE08} is indeed a bona fide limit of the particle model. Furthermore, we also study the heat transport of the model when the scattering probability is one, corresponding to deterministic dynamics. At a coarse grained level the model behaves as a persistent random walker with a broad waiting time distribution and strong correlations associated to the deterministic scattering. We show, that, in spite of the absence of global conserved quantities, the model leads to a superdiffusive heat transport.
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