标题： 硬球在强约束下的动力学和运动论 显示英文标题

标题： Dynamics and kinetic theory of hard spheres under strong confinement

摘要： 低密度硬球或圆盘气体，被限制在两个平行板之间，其距离小于粒子直径的两倍，从系统的Liouville方程出发进行描述。 与约化分布函数相关的BBGKY方程层次按一个参数展开，该参数以适当的无量纲单位衡量系统的密度。 通过仅保留该参数的最低两个阶次，得到玻尔兹曼层次的描述。 特别是，单粒子分布函数遵循一组方程。 与基于启发式方法为同一系统提出的类似玻尔兹曼的动能方程不同，此处制定的动能理论允许与平衡统计力学一致的定态解，无论是否存在外场。 在后一种情况下，由于由限制产生的不均匀性和外场产生的不均匀性之间的耦合，密度剖面相当复杂。 所制定的通用理论为研究强限制稀薄气体的性质提供了坚实的基础。 显示英文摘要

摘要： The kinetic theory description of a low density gas of hard spheres or disks, confined between two parallel plates separated a distance smaller than twice the diameter of the particles, is addressed starting from the Liouville equation of the system. The associated BBGKY hierarchy of equations for the reduced distribution functions is expanded in powers of a parameter measuring the density of the system in the appropriate dimensionless units. The Boltzmann level of description is obtained by keeping only the two lowest orders in the parameter. In particular, the one-particle distribution function obeys a couple of equations. Contrary to what happens with a Boltzmann-like kinetic equation that has been proposed for the same system on a heuristic basis, the kinetic theory formulated here admits stationary solutions that are consistent with equilibrium statistical mechanics, both in absence and presence of external fields. In the latter case, the density profile is rather complex due to the coupling between the inhomogeneities generated by the confinement and by the external fields. The general theory formulated provides a solid basis for the study of the properties of strongly confined dilute gases.