1964
DOI: 10.1016/0031-8914(64)90017-5
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On the statistical mechanical theory of brownian motion

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Cited by 53 publications
(18 citation statements)
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“…In our case, however, the separation of time-scales is a consequence of the fast decorrelation times of the quantity ζ(t) defined by Eq. (12), which is in turn due to the overdamped nature of the original dynamics we are considering. As a consequence, it is sufficient to take ∆t dt, where dt is the time-step of the integration algorithm.…”
Section: Appendix B: Extrapolating Langevin Equations From Datamentioning
confidence: 99%
See 1 more Smart Citation
“…In our case, however, the separation of time-scales is a consequence of the fast decorrelation times of the quantity ζ(t) defined by Eq. (12), which is in turn due to the overdamped nature of the original dynamics we are considering. As a consequence, it is sufficient to take ∆t dt, where dt is the time-step of the integration algorithm.…”
Section: Appendix B: Extrapolating Langevin Equations From Datamentioning
confidence: 99%
“…A remarkable example is the approach dating back to Smoluchowski to obtain, using kinetic theory, the Langevin equation for a heavy particle in a dilute gas of light particles [9]. Another important attempt was suggested by several authors in the 60's [10][11][12][13] and later by Zwanzig [14], which amounts to rigorously deriving Langevin equations for an heavy particle interacting with a chain of light harmonic oscillators.…”
Section: Introductionmentioning
confidence: 99%
“…Further analyses [30] on the frequency spectrum of the normal modes pointed out that the previous approximation was valid only if the ratio M/ √ km continued to be finite when the heavy mass limit was taken. Several generalizations of this simple model have been explored: the linear chain with nearest-neighbours interactions has been shown to be just a particular case of a wider class of harmonic systems with similar properties [31] [32], that can be used as "thermal baths" for the intruder even if the heavy particle is subjected to non-linear forces [14]. Since the properties of this harmonic chain are completely known, checking our method on this model is a quite natural choice.…”
Section: Empirical Procedures To Determine the Parameters Of A Langevimentioning
confidence: 99%
“…where the function P (11) The corresponding averages values are q = x, q = 0, while the variances are mω 2 n (q − x) 2 = m q 2 = β −1 . The functions P (n) β (q n0 − x 0 ,q n0 ) depend parametrically on the initial central particle coordinate x 0 ; this choice of the oscillator equilibrium positions naturally follows from the form of the Lagrangian (3) [14,26]. It is to be noticed that Eq.…”
Section: Classical Modelmentioning
confidence: 99%