Ideal gas approximation for a two-dimensional rarefied gas under Kawasaki dynamics
Ideal gas approximation for a two-dimensional rarefied gas under Kawasaki dynamics
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川崎动力学下二维稀薄气体的理想气体近似
DOI：
10.1016/j.spa.2008.04.008
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发表时间：
2009
影响因子：
1.4
通讯作者：
E. Scoppola
中科院分区：
文献类型：
--
作者：
A. Gaudilliere;D. Hollander;F. Nardi;F. Nardi;E. Olivieri;E. Scoppola
本文考虑二维格气在川崎动力学下的动力学行为，即，粒子随机跳跃，受到核心排斥和最近邻吸引。我们表明，在固定的温度和粒子密度趋于零的极限，这样的气体演变的方式是接近理想气体，其中粒子没有相互作用。特别是，我们证明了三个定理表明，粒子轨迹是非超扩散的，并有扩散的财产。我们还考虑了温度和粒子密度同时趋于零的情况，并分别关注稳定，亚稳和不稳定气体的三个区域。我们的结果制定在更一般的背景下的系统的“准随机游动”，其中我们表明，低密度晶格气下川崎动力学是一个例子。我们能够处理一个大类的初始条件，没有异常浓度的粒子和时间范围是远远大于典型的粒子碰撞时间。这些结果将被用于两篇即将发表的论文中，涉及低温和低密度下大体积二维晶格气的亚稳行为。
In this paper we consider a two-dimensional lattice gas under Kawasaki dynamics, i.e., particles hop around randomly subject to hard-core repulsion and nearest-neighbor attraction. We show that, at fixed temperature and in the limit as the particle density tends to zero, such a gas evolves in a way that is close to an ideal gas, where particles have no interaction. In particular, we prove three theorems showing that particle trajectories are non-superdiffusive and have a diffusive spread-out property. We also consider the situation where the temperature and the particle density tend to zero simultaneously and focus on three regimes corresponding to the stable, the metastable and the unstable gas, respectively. Our results are formulated in the more general context of systems of “Quasi-Random Walks”, of which we show that the low-density lattice gas under Kawasaki dynamics is an example. We are able to deal with a large class of initial conditions having no anomalous concentration of particles and with time horizons that are much larger than the typical particle collision time. The results will be used in two forthcoming papers, dealing with metastable behavior of the two-dimensional lattice gas in large volumes at low temperature and low density.