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Published online by Cambridge University Press: 09 June 2025
For the Brownian motion of a particle in a fluid, the Langevin equation for its momentum is introduced phenomenologically. The strength of the noise is shown to be related to friction, and, in a second step, to the diffusion coefficient. Excellent agreement with experiments on a levitated particle in gas is demonstrated. This phenomenological Langevin equation is then shown to follow from a general projection approach to the underlying Hamiltonian dynamics of the full system in the limit of an infinite mass ratio between Brownian particles and fluid molecules. For Brownian motion in liquids, additional time-scales enter that are discussed phenomenologically and illustrated with experiments.
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