A mechanical model of Brownian motion for one massive particle including slow light particles
A mechanical model of Brownian motion for one massive particle including slow light particles
复制标题
包括慢光粒子在内的一个大质量粒子的布朗运动力学模型
DOI：
10.1007/s10955-017-1934-4
复制
发表时间：
2018
影响因子：
1.6
通讯作者：
Song Liang
中科院分区：
文献类型：
--
作者：
F. Hiai;R. Konig and M. Tomamichel;Song Liang
我们提供了布朗运动和经典力学系统之间的联系。准确地说，我们考虑一个系统的一个大质量粒子与理想气体相互作用，根据非随机力学原理，通过相互作用势，没有任何假设要求的环境粒子的初始速度应被限制为“足够快”。证明了在一定的标度极限下，有质量粒子的（位置，速度）过程的收敛性，使得环境粒子的质量收敛于0，而密度和速度趋于无穷大，并给出了这一极限过程的精确表达式，即扩散过程.
We provide a connection between Brownian motion and a classical mechanical system. Precisely, we consider a system of one massive particle interacting with an ideal gas, evolved according to non-random mechanical principles, via interaction potentials, without any assumption requiring that the initial velocities of the environmental particles should be restricted to be “fast enough”. We prove the convergence of the (position, velocity)-process of the massive particle under a certain scaling limit, such that the mass of the environmental particles converges to 0 while the density and the velocities of them go to infinity, and give the precise expression of the limiting process, a diffusion process.