Skip to main content
Log in

Linear relaxation times of stochastic processes driven by non-Gaussian noises

  • Articles
  • Published:
Journal of Statistical Physics Aims and scope Submit manuscript

Abstract

The linear relaxation time (LRT) associated with steady-state correlation functions is studied for Langevin equations with non-Gaussian noises: dichotomous Markov noise and Poissonian white shot noise. Exact results for arbitrary models are obtained and compared with results for Gaussian noises. Some general features of LRTs are discussed. The concept of dynamic effective diffusion is introduced and the existence of an optimal effective Fokker-Planck approximation is discussed. Explicit examples for prototype models are presented and briefly compared with the analogs for Gaussian noises.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. N. G. Van Kampen,Stochastic Processes in Physics and Chemistry (North-Holland, Amsterdam, 1983).

    Google Scholar 

  2. C. W. Gardiner,Handbook of Stochastic Methods for Physics, Chemistry and Natural Sciences (Springer-Verlag, Berlin, 1983).

    Google Scholar 

  3. F. Moss and P. V. E. McClintock,Noise in Nonlinear Dynamical Systems (Cambridge University Press, Cambridge, 1989).

    Google Scholar 

  4. W. Horsthemke and R. Lefever,Noise-Induced Transitions (Springer-Verlag, Berlin, 1984).

    Google Scholar 

  5. S. Grossman,Phys. Rev. A 17:1123 (1978).

    Google Scholar 

  6. H. Fujisaka and S. Grossman,Z. Physik B 43:69 (1981).

    Google Scholar 

  7. S. Faetti, P. Grigolini, and F. Marchesoni,Z. Physik B 47:353 (1982).

    Google Scholar 

  8. A. Hernández-Machado, M. San Miguel, and J. M. Sancho,Phys. Rev. A 29:3388 (1984).

    Google Scholar 

  9. H. Risken,The Fokker-Planck Equation (Springer-Verlag, Berlin, 1984).

    Google Scholar 

  10. W. Nadler and K. Schulten,J. Chem. Phys. 82:151 (1985).

    Google Scholar 

  11. W. Nadler and K. Schulten,Z. Physik B 59:53 (1985).

    Google Scholar 

  12. P. Jung and H. Risken,Z. Physik B 59:469 (1985).

    Google Scholar 

  13. K. Binder,Phys. Rev. B 8:3423 (1973).

    Google Scholar 

  14. Z. Racz,Phys. Rev. B 13:2631 (1976).

    Google Scholar 

  15. J. Casademunt, J. I. Jimenez-Aquino, and J. M. Sancho,Physica A 156:628 (1989).

    Google Scholar 

  16. J. Casademunt and J. M. Sancho,Phys. Rev. A 39:4915 (1989).

    Google Scholar 

  17. M. San Miguel, L. Pesquera, M. A. Rodríguez, and A. Hernández-Machado,Phys. Rev. A 35:208 (1987).

    Google Scholar 

  18. J. Casademunt, R. Mannella, P. V. E. McClintock, F. E. Moss, and J. M. Sancho,Phys. Rev. A 35:5183 (1987).

    Google Scholar 

  19. J. Casademunt and A. Hernández-Machado, Correlation functions near instabilities in systems driven by parametric noise,Z. Phys. B (1989), to appear.

  20. J. M. Sancho and M. San Miguel,Prog. Theor. Phys. 69:1085 (1983).

    Google Scholar 

  21. F. Sagués, M. San Miguel, and J. M. Sancho,Z. Physik B 55:269 (1984).

    Google Scholar 

  22. C. Van den Broeck and P. Hanggi,Phys. Rev. A 30:2730 (1984).

    Google Scholar 

  23. C. Van den Broeck,J. Stat. Phys. 31:467 (1983).

    Google Scholar 

  24. M. A. Rodrīguez, L. Pesquera, M. San Miguel, and J. M. Sancho,J. Stat. Phys. 40:669 (1985).

    Google Scholar 

  25. J. M. Sancho, M. San Miguel, S. Katz, and J. D. Gunton,Phys. Rev. A 26:1589 (1982).

    Google Scholar 

  26. J. Casademunt and J. M. Sancho,Phys. Lett. A 123:271 (1987).

    Google Scholar 

  27. M. Suzuki, K. Kaneko, and F. Sasagawa,Prog. Theor. Phys. 65:828 (1981).

    Google Scholar 

  28. J. M. Sancho,J. Math. Phys. 25:354 (1984).

    Google Scholar 

  29. J. Masoliver, B. West, and K. Lindenberg,Phys. Rev. A 35:3086 (1987).

    Google Scholar 

  30. J. Casademunt, Dynamic characterization of relaxation processes in the presence of fluctuations, Ph.D. thesis, University of Barcelona (1988).

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Casademunt, J., Sancho, J.M. Linear relaxation times of stochastic processes driven by non-Gaussian noises. J Stat Phys 56, 911–929 (1989). https://doi.org/10.1007/BF01016785

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01016785

Key words

Navigation