AI 中文总结
该研究针对含可移动壳层与有限内部粒子的孤立小系统，推导了壳层坐标与动量的精确分布，分析了壳层混沌运动特性，得到了其均方根偏差的通用表达式，可用于推断系统内部结构。
AI 中文摘要
考虑一个由可移动壳层和有限个内部粒子组成的孤立小系统，在系统总能量和动量守恒的条件下，针对不同类型的内部粒子运动，得到了壳层坐标和动量的精确分布。坐标分布由有限个分支构成，可能包含平台区域；动量分布对应系统自由度间能量的非均匀分布。研究表明，坐标分布依赖于内部粒子的数量，且在内部粒子运动维度变化时保持不变，而动量分布则依赖于自由度的数量。因此，对比壳层的坐标与动量分布可推断系统的内部结构。还分析了内部粒子碰撞导致的壳层混沌运动，其与布朗运动不同，即使在无外部介质时也会持续存在。明确得到了壳层均方根偏差的通用表达式，该表达式依赖于内部粒子的数量及其质量。
英文摘要
An isolated small system consisting of a movable shell and a finite number of internal particles is considered. Exact distributions of the shell coordinates and momenta are obtained for various types of internal particle motion under the conditions of conservation of the total energy and momentum of the system. The coordinate distribution consists of a finite number of branches and may contain plateau regions. The momentum distribution corresponds to a non-uniform distribution of energy among the degrees of freedom of the system. It is shown that the coordinate distribution depends on the number of internal particles and remains unchanged when the dimensionality of their motion varies, whereas the momentum distribution depends on the number of degrees of freedom. Consequently, comparison of the coordinate and momentum distributions of the shell makes it possible to draw conclusions about the internal structure of the system. The chaotic motion of the shell caused by impacts from the internal particles is analyzed; unlike Brownian motion, it persists even in the absence of an external medium. A universal expression for the root-mean-square deviation of the shell is obtained explicitly, depending on the number of internal particles and their masses.
Comments13 pages, 8 figures
