BROWNIAN MOTION, DYNAMICAL FRICTION, AND STELLAR DYNAMICS
BROWNIAN MOTION, DYNAMICAL FRICTION, AND STELLAR DYNAMICS
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DOI：
10.1103/revmodphys.21.383
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发表时间：
1949-01-01
影响因子：
44.1
通讯作者：
CHANDRASEKHAR, S
中科院分区：
文献类型：
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作者：
CHANDRASEKHAR, S
众所周知，经典物理学的胜利之一是爱因斯坦和冯·斯莫洛霍夫斯基对布朗运动现象的解释。在爱因斯坦和冯·斯莫卢霍夫斯基的这些早期研究中，关于概率和随机变量理论的大量文献不断涌现。在本文中，我们不会试图总结这些不同的发展；相反，我们将限制自己对理论的物理（不同于数学）基础的分析，并从恒星动力学中说明爱因斯坦的思想如何在非常不同的Geld中找到富有成效的应用。对于A（t）部分，做出以下主要假设：（i）A（t）独立于u，并且（ii）A（t）与u相比变化非常快。这些假设中的第二个简单地表明时间间隔 At 存在，使得在 ht 期间 u 的预期变化非常小，而在同一时间间隔 A (t) 可能会经历非常大量的波动。或者，我们可以通过这样的陈述来表达这一假设：尽管预计 u (t) 和 u (t+At) 之间的差异可以忽略不计，但预计 A (t) 和 A (t+Dt) 之间没有相关性。考虑到速度的净增量，
S is well known, one of the triumphs of classical physics was the unraveling of the phenomenon of Brownian motion by Einstein and von Smoluchowski. Out of these early investigations of Einstein and von Smoluchowski an extensive literature on the theory of probability and random variables has grown. In this paper we shall not attempt to summarize these varied developments; we shall limit ourselves, rather, to an analysis of the physical (as distinct from the mathematical) foundations of the theory and to an illustration from stellar dynamics how Einstein's ideas have found fruitful applications in a very diferent Geld.As for the part A (t) the following principal assumptions are made:(i) A (t) is independent of u,'and (ii) A (t) varies extremely rapidly compared with u. The second of these assumptionsimplies that time intervals At exist such that during ht the changes in u to be expected are very small, while during the same interval A (t) may undergo a very large number of Quctuations. Alternatively, we may express this assumption by the state-ment that though u (t) and u (t+ At) areexpected to differ by a negligible amount, no correlation between A (t) and A (t+ Dt) is expected. Considering then the net increment in velocity,