Abstract
The behavior of nonequilibrium systems under the influence of an external noise is the subject of active research. The theoretical and experimental aspects of this problem have been reviewed in a recent monograph by HORSTHEMKE and LEFEVER [l] (see also the papers by other authors in this volume). Most of the studies made so far concern the properties of time-independent stationary quantities, as for example the changes of the stationary distribution of the relevant variable of the system as a function of noise parameters. A different and less studied aspect of the problem concerns the effect of external noise on dynamical properties like the steady state correlation function and its associated relaxation time. A complete description of a system with random control parameters requires the understanding of these dynamical aspects. In this paper we discuss a mathematical framework in which these dynamical problems can be analyzed for a nonwhite external noise. In the white noise limit there exist well-known techniques to calculate time-dependent properties [2]. For a nonwhite noise, the formalism presented here gives a general basis to study dynamical properties of a non-Markovian process. Our discussion is made under the assumption of negligible internal fluctuations. This is a standard assumption in the study of external noise problems. A joint description of internal and external fluctuations and their coupling effects has been discussed elsewhere [3].
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
W. Horsthemke and R. Lefever: Noise-Induced Transitions. Springer Series in Synergetics. Vol. 15. Springer Verlag, 1983.
Η. Risken: The Fokker-Planck equation. Methods of Solution and Aplications. Springer Verlag, in press.
J.M. Sancho and M. San Miguel: Phys. Lett. A90,455(1982); Preprint (1984).
R. Short, L. Mandel and R. Roy: Phys. Rev. Lett. 49,647(1982).
S. Dixit and P. Sahni: Phys. Rev. Lett. 50,1273(1983).
See the paper by R. Lefever in this volume.
J.M. Sancho and M. San Miguel: Z. Physik B36,357(1980).
J.M. Sancho, M. San Miguel, S. Katz and J.D. Gunton: Phys. Rev. A26,1589(1982).
A. Hernández-Machado, M. San Miguel and J.M. Sancho: Phys. Rev. A29 (1984).
F. Haake and M. Lewenstein: Phys. Rev. A28,3606(1983).
E.A. Novikov: Sov. Phys. JETP 20,1290(1965).
A. Hernández-Machado, J.M. Sancho, M. San Miguel and L. Pesquera: Ζ. Physik B52,3351(1983).
A. Hernández-Machado and M. San Miguel: J. Math. Phys. (to appear 1984).
R.F. Fox: J. Stat. Phys. 16,259(1977).
R.F. Fox: J. Math. Phys. 18,2331(1977).
V.S. Volkov and V.N. Pedrovsky: J. Math. Phys. 24,267(1983).
A. Hernández-Machado and F. Sagúes: Phys. Lett. A98,98(1983).
M. San Miguel and J.M. Sancho: J. Stat. Phys. 22,605(1980).
R. Kitahara, W. Horsthemke, R. Lefever and Y. Inaba: Progr. Theor. Phys. 64,1233(1980).
F. Sagúes, M. San Miguel and J.M. Sancho: Ζ. Physik В (to appear, 1984).
J.M. Sancho and M. San Miguel: Progr. Theor. Phys. 69,1085(1983).
J.M. Sancho: J. Math. Phys. 25,354(1984).
M. San Miguel and J.M. Sancho: Ζ. Physik B43,361(1981).
K. Wodckiewicz: J. Math. Phys. 23,11(1982).
S. Kai, T. Kai, M. Takata and K. Mirakawa: J. Phys. Soc. Jpn. 47,1379(1979).
T. Kawakubo, A. Yanagita and S. Kabashima: J. Phys. Soc. Jpn. 50,145(1981).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1984 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Sancho, J.M., San Miguel, M. (1984). Dynamical Aspects of External Nonwhite Noise. In: Horsthemke, W., Kondepudi, D.K. (eds) Fluctuations and Sensitivity in Nonequilibrium Systems. Springer Proceedings in Physics, vol 1. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-46508-6_12
Download citation
DOI: https://doi.org/10.1007/978-3-642-46508-6_12
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-46510-9
Online ISBN: 978-3-642-46508-6
eBook Packages: Springer Book Archive