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Colored noise driven systems with inertia

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Zeitschrift für Physik B Condensed Matter

Abstract

We present a novel approximation scheme, termed unified colored noise approximation (UCNA), for colored Gaussian noise driven nonlinear systems with inertia. This approximation allows one to evaluate static (stationary distributions, moments) as well as dynamical quantities (correlation functions) for small-to-moderate-to-large values of the correlation time. The approximation replaces a three-dimensional Markovian process by a reduced, two-dimensional Markovian dynamics with new drift and diffusion coefficients. For a harmonic potential the stationary moments are reproduced exactly. Most importantly, we present a criterion involving the noise strengthD, the friction strength γ and the noise color τ, which describes the region of validity of UCNA in the parameter space given by (D, τ, γ). At small τ-values we contrast the UCNA with the well-known small τ approximation. In order to have a comparison onanalytical grounds, we test the static and dynamical predictions of UCNA versus the well-known analytical results obtained from a three-dimensional Ornstein-Uhlenbeck process.

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Authors and Affiliations

  1. Institut für Mathematik, Universität Augsburg, Memminger Strasse 6, D-8900, Augsburg, Federal Republic of Germany

    L. H'walisz, P. Jung & P. Hänggi

  2. Institut für Theoretische Physik, Universität Basel, Klingelbergstrasse 82, CH-4056, Basel, Switzerland

    P. Talkner

  3. Sektion Physik, Humboldt-Universität zu Berlin, Invalidenstrasse 42, DDR-1040, Berlin, German Democratic Republic

    L. Schimansky-Geier

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  1. L. H'walisz
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  2. P. Jung
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  3. P. Hänggi
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  4. P. Talkner
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  5. L. Schimansky-Geier
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H'walisz, L., Jung, P., Hänggi, P. et al. Colored noise driven systems with inertia. Z. Physik B - Condensed Matter 77, 471–483 (1989). https://doi.org/10.1007/BF01453798

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  • DOI: https://doi.org/10.1007/BF01453798

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