Abstract
In 1930 L.S. Ornstein and G.F. Uhlenbeck [1] addressed again the problem of elaborating a suitable model for the Brownian motion, and they refined in more detail the Langevin dynamical equation to investigate the phenomenon at time scales shorter than those considered by Einstein [2] and Smoluchowski [3] in 1905-6.
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Notes
- 1.
The behavior of a Brownian motion under the effect of an elastic restoring force has also been empirically investigated with a few clever experiments by E. Kappler [6] confirming the idea that the Smoluchowski approximation holds well when the drag \(\alpha \) is large.
References
Ornstein, L.S., Uhlenbeck, G.E.: On the theory of Brownian Motion. Phys. Rev. 36, 823 (1930)
Einstein, A.: Über die von der molekularkinetischen Theorie der Wärme geforderte Bewegung von in ruhenden Flüssigkeiten suspendierten Teilchen. Ann. Phys. 17, 549 (1905)
von Smoluchowski, M.: Zur kinetischen Theorie der Brownschen Molekularbewegung und der Suspensionen. Ann. Phys. 21, 757 (1906)
Neckel, T., Rupp, F.: Random differential equations in scientific computing. Versita, London (2013)
Chandrasekhar, S.: Stochastic problems in physics and astronomy. Rev. Mod. Phys. 15, 1 (1943)
Kappler, E.: Versuche zur Messung der Avogadro-Loschmidtschen Zahl aus der Brownschen Bewegung einer Drehwaage. Ann. Phys. 11, 233 (1931)
Nelson, E.: Dynamical Theories of Brownian Motion. Princeton, Princeton UP, (1967)
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Cufaro Petroni, N. (2020). Dynamical Theory of Brownian Motion. In: Probability and Stochastic Processes for Physicists. UNITEXT for Physics. Springer, Cham. https://doi.org/10.1007/978-3-030-48408-8_9
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