Forced dichotomic diffusion in a viscous media

  • Hector Calisto
  • Mauro Bologna
  • Kristopher J. Chandía
Regular Article

Abstract

In this paper, we study the dynamical properties of a linear system driven by a superposition of a Gaussian white noise and a symmetric Markovian dichotomic noise operating simultaneously on the system. We find exact analytical solutions for the moment generating function and for the probability distribution function. We show analytically that the system presents characteristics belonging to the nonlinear cases, such as a nonequilibrium bimodal distribution. We infer that the white Gaussian noise smooths the two characteristics Diracs delta peaks, generated by a purely dichotomic diffusion, transforming them in two smooth maxima.

Keywords

Statistical and Nonlinear Physics 

References

  1. 1.
    G.I. Taylor, Proc. R. Soc. London 219, 186 (1953)ADSCrossRefGoogle Scholar
  2. 2.
    J.C. Giddings, H. Eyring, J. Phys. Chem. 59, 416 (1955)CrossRefGoogle Scholar
  3. 3.
    J.C. Giddings, J. Chem. Phys. 26, 169 (1957)ADSCrossRefGoogle Scholar
  4. 4.
    N.G. van Kampen, Physica A 96, 435 (1979)ADSMathSciNetCrossRefGoogle Scholar
  5. 5.
    C. van den Broeck, Physica A 168, 677 (1990)ADSMathSciNetCrossRefGoogle Scholar
  6. 6.
    M. Vlad, J. Ross, M. Mackey, Physica A 243, 319 (1997)ADSCrossRefGoogle Scholar
  7. 7.
    M. Vlad, J. Ross, M. Mackey, Physica A 243, 340 (1997)ADSCrossRefGoogle Scholar
  8. 8.
    M. Vlad, F. Morán, J. Ross, M.C. Mackey, J. Phys. Chem. B 105, 11710 (2001)CrossRefGoogle Scholar
  9. 9.
    G. Drazer, D.H. Zanette, Phys. Rev. E 60, 5858 (1999)ADSCrossRefGoogle Scholar
  10. 10.
    H. Calisto, M. Bologna, Rapid Commun. Phys. Rev. E 75, 050103(R) (2007)ADSCrossRefGoogle Scholar
  11. 11.
    G. Aquino, M. Bologna, H. Calisto, Europhys. Lett. 89, 50012 (2010)ADSCrossRefGoogle Scholar
  12. 12.
    N.G. van Kampen, Phys. Rep. 24, 171 (1976)ADSMathSciNetCrossRefGoogle Scholar
  13. 13.
    C.W. Gardiner, Handbook of Stochastic Methods: For Physics, Chemistry and Natural Sciences (Springer, Berlin, 2004)Google Scholar
  14. 14.
    R. Pawula, S.O. Rice, IEEE Trans. Inf. Theor. 32, 63 (1986)CrossRefGoogle Scholar
  15. 15.
    M. Bologna, K.J. Chandía, B. Tellini, J. Stat. Mech. 2013, P07006 (2013)CrossRefGoogle Scholar
  16. 16.
    H. Friedman, A. Ben-Naim, J. Chem. Phys. 48, 120 (1968)ADSCrossRefGoogle Scholar
  17. 17.
    G.H. Weiss, J. Stat. Phys. 8, 221 (1973)ADSCrossRefGoogle Scholar
  18. 18.
    V. Balakrishnan, C. Van den Broeck, P. Hänggi, Phys. Rev. A 38, 4213 (1988)ADSMathSciNetCrossRefGoogle Scholar
  19. 19.
    B. Spagnolo, A.A. Dubkov, N.V. Agudov, Eur. Phys. J. B 40, 273 (2004)ADSCrossRefGoogle Scholar
  20. 20.
    B. Spagnolo, A. Dubkov, Eur. Phys. J. B 50, 299 (2006)ADSCrossRefGoogle Scholar
  21. 21.
    B. Dybiec, L. Schimansky-Geierb, Eur. Phys. J. B 57, 313 (2007)ADSCrossRefGoogle Scholar
  22. 22.
    M. Bologna, G. Aquino, Eur. Phys. J. B 87, 15 (2014)ADSCrossRefGoogle Scholar
  23. 23.
    N.G. van Kampen, Stochastic Processes in Physics and Chemistry (North-Holland, Amsterdam, 1992)Google Scholar
  24. 24.
    R. Kubo, M. Toda, N. Hashitsume, Statistical Physics II Nonequilibrium Statistical Mechanics (Springer-Verlag, Berlin, 1991)Google Scholar
  25. 25.
    V. Balakrishnan, Pramana J. Phys. 40, 259 (1993)ADSCrossRefGoogle Scholar
  26. 26.
    V.E. Shapiro, V.M. Loginov, Physica A 91, 563 (1978)ADSMathSciNetCrossRefGoogle Scholar
  27. 27.
    Handbook of Mathematical Functions, edited by M. Abramowitz, I.A. Stegun (Dover, New York, 1972)Google Scholar
  28. 28.
    G.N. Watson, Theory of Bessel Functions (Cambridge University Press, London, 1922)Google Scholar
  29. 29.
    M. Sancho, J. Math. Phys. 25, 354 (1984)ADSMathSciNetCrossRefGoogle Scholar
  30. 30.
    M. Bologna, G. Ascolani, P. Grigolini, J. Math. Phys. 51, 043303 (2010)ADSMathSciNetCrossRefGoogle Scholar
  31. 31.
    J. Masoliver, K. Lindenberg, G.H. Weiss, Physica A 157, 891 (1989)ADSMathSciNetCrossRefGoogle Scholar
  32. 32.
    J. Masoliver, G.H. Weiss, Sep. Sci. Tech. 26, 279 (1991)CrossRefGoogle Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  • Hector Calisto
    • 1
  • Mauro Bologna
    • 2
  • Kristopher J. Chandía
    • 3
  1. 1.Sistema de Bibliotecas, Universidad de TarapacáAricaChile
  2. 2.Instituto de Alta Investigación, Universidad de TarapacáAricaChile
  3. 3.Escuela Universitaria de Ingeniería Eléctrica-Electrónica, Universidad de TarapacáAricaChile

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