Skip to Main content Skip to Navigation
Journal articles

Anharmonic oscillator driven by additive Ornstein-Uhlenbeck noise

Abstract : We present an analytical study of a nonlinear oscillator subject to an additive Ornstein-Uhlenbeck noise. Known results are mainly perturbative and are restricted to the large dissipation limit (obtained by neglecting the inertial term) or to a quasi-white noise (i.e., a noise with vanishingly small correlation time). Here, in contrast, we study the small dissipation case (we retain the inertial term) and consider a noise with finite correlation time. Our analysis is non perturbative and based on a recursive adiabatic elimination scheme: a reduced effective Langevin dynamics for the slow action variable is obtained after averaging out the fast angular variable. In the conservative case, we show that the physical observables grow algebraically with time and calculate the associated anomalous scaling exponents and generalized diffusion constants. In the case of small dissipation, we derive an analytic expression of the stationary Probability Distribution Function (P.D.F.) which differs from the canonical Boltzmann-Gibbs distribution. Our results are in excellent agreement with numerical simulations.
Complete list of metadatas

Cited literature [35 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-00014739
Contributor : Philippe Marcq <>
Submitted on : Monday, August 31, 2020 - 4:14:38 PM
Last modification on : Wednesday, September 2, 2020 - 8:52:03 AM

File

mall3.pdf
Files produced by the author(s)

Identifiers

Collections

Citation

Kirone Mallick, Philippe Marcq. Anharmonic oscillator driven by additive Ornstein-Uhlenbeck noise. Journal of Statistical Physics, Springer Verlag, 2005, 119, pp.1-33. ⟨10.1007/s10955-004-2135-5⟩. ⟨hal-00014739⟩

Share

Metrics

Record views

346

Files downloads

38