Abstract
We calculate stationary state correlation functions of the anharmonic overdamped oscillator driven by multiplicative (white Gaussian) noise of strengthQ together with additive noise of relative strengthq. (i) We donot observe a particular slowing down at the so-called noise induced transition. But there is a region of the oscillator's stiffness parametera neara≈0 in which the decay time is typically enhanced. (ii) If the phase transition point is defined by the minimum of the decay rate, it lies within the ordered phasea>0 forq⋟1 and shifts down toa=0 forq→0. In our approximation it is even in the disordered regiona<0 for very smallq. (iii) As a function of the multiplicative noiseQ the decay ratedecreases with increasingQ if the system is well above or well below threshold. There seem to be experimental indications of this behavior. But within the proper threshold regime of smalla increasing noiseQ increases the decay rate. The valuesa c where the cross-over occurs depend on the fluctuating variable and onq.
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Schenzle, A., Brand, H.: Phys. Rev.A 20, 1628 (1979)
Kabashima, S., Kogure, S., Kawakubo, T., Okada, T.: J. Appl. Phys.50, 6296 (1979)
Kepper, P. De, Horsthemke, W.: C.R. Acad. Sci. (Paris), 287, C-251, 1978
Horsthemke, W., Malek-Mansour, M.: Z. Phys. B-Condensed Matter24, 307 (1976)
Arnold, L., Horsthemke, W., Lefever, R.: Z. Phys. B-Condensed Matter29, 367 (1978)
Kitahara, K., Horsthemke, W., Lefever, R., Inaba, Y.: Prog. Theor. Phys.64, 1233 (1980)
Stochastic Nonlinear Systems in Physics, Chemistry and Biology, Eds. L. Arnold, R. Lefever, Synergetics Series, Springer, Berlin etc., 1981. Proc. Workshop in Bielefeld, October 5–11, 1980
Brenig, L., Banai, N.: Nonlinear Dynamics of Fluctuations: Some Exact Results, Preprint 1981
Mori, H.: Prog. Theor. Phys.33, 423 (1965);34, 399 (1965)
Zwanzig, R.: In: Lectures in Theoretical Physics. Brittin, W., Dunham, L. (eds.), Vol. 3, p. 135. New York: Wiley 1961
Grossmann, S.: Phys. Rev.A17, 1123 (1978)
Bixon, M., Zwanzig, R.: J. Stat. Phys.3, 245 (1971)
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Fujisaka, H., Grossmann, S. External noise effects on the fluctuation line width. Z. Physik B - Condensed Matter 43, 69–75 (1981). https://doi.org/10.1007/BF01295477
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DOI: https://doi.org/10.1007/BF01295477