Das, Ashok K. ; Panda, Sudhakar ; Santos, J. R. L. (2015) A path integral approach to the Langevin equation International Journal of Modern Physics A, 30 (07). p. 1550028. ISSN 0217-751X
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Official URL: http://doi.org/10.1142/S0217751X15500281
Related URL: http://dx.doi.org/10.1142/S0217751X15500281
Abstract
We study the Langevin equation with both a white noise and a colored noise. We construct the Lagrangian as well as the Hamiltonian for the generalized Langevin equation which leads naturally to a path integral description from first principles. This derivation clarifies the meaning of the additional fields introduced by Martin, Siggia and Rose in their functional formalism. We show that the transition amplitude, in this case, is the generating functional for correlation functions. We work out explicitly the correlation functions for the Markovian process of the Brownian motion of a free particle as well as for that of the non-Markovian process of the Brownian motion of a harmonic oscillator (Uhlenbeck–Ornstein model). The path integral description also leads to a simple derivation of the Fokker–Planck equation for the generalized Langevin equation.
Item Type: | Article |
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Source: | Copyright of this article belongs to World Scientific Publishing Co Pte Ltd. |
ID Code: | 124201 |
Deposited On: | 08 Nov 2021 10:16 |
Last Modified: | 08 Nov 2021 10:16 |
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