Faculty of Physics, M. V. Lomonosov Moscow State University, Moscow 119991, Russia.
Phys Rev Lett. 2012 Oct 26;109(17):178001. doi: 10.1103/PhysRevLett.109.178001. Epub 2012 Oct 23.
Brownian motion in a granular gas in a homogeneous cooling state is studied theoretically and by means of molecular dynamics. We use the simplest first-principles model for the impact-velocity dependent restitution coefficient, as it follows for the model of viscoelastic spheres. We reveal that for a wide range of initial conditions the ratio of granular temperatures of Brownian and bath particles demonstrates complicated nonmonotonic behavior, which results in a transition between different regimes of Brownian dynamics: It starts from the ballistic motion, switches later to a superballistic one, and turns at still later times into subdiffusion; eventually normal diffusion is achieved. Our theory agrees very well with the molecular dynamics results, although extreme computational costs prevented us from detecting the final diffusion regime. Qualitatively, the reported intermediate diffusion regimes are generic for granular gases with any realistic dependence of the restitution coefficient on the impact velocity.
在均匀冷却状态下的颗粒气体中的布朗运动在理论上和通过分子动力学进行了研究。我们使用最简单的基于冲击速度的恢复系数的第一性原理模型，就像粘弹性球体模型一样。我们揭示出，对于广泛的初始条件，布朗粒子和浴粒子的温度比表现出复杂的非单调行为，这导致了布朗动力学的不同状态之间的转变：它从弹道运动开始，后来切换到超弹道运动，然后在更晚的时候变成亚扩散；最终实现了正常扩散。我们的理论与分子动力学结果非常吻合，尽管极端的计算成本使我们无法检测到最终的扩散状态。从定性的角度来看，报道的中间扩散状态对于任何具有实际的恢复系数与冲击速度相关的颗粒气体都是通用的。
