Czechoslovak Journal of Physics

, Volume 56, Issue 2, pp 125–139 | Cite as

Diffusion in the time-dependent double-well potential

  • Evzen Subrt
  • Petr Chvosta


We investigate the one-dimensional diffusion of a particle in a piecewise linear W-shaped potential, on which a harmonically modulated discontinuity situated at the central tip is superimposed. The simplified description of the external driving enables an exact analysis of the emerging non-linear dynamics. The response is represented by the occupation difference between the regions of attraction of the right and the left minima of the potential profile. We discuss the time-asymptotic and time-averaged occupational differences as a function of the temperature, the amplitude and the frequency of the driving. We compare the analysis with the corresponding results based on the popular two-state description of the underlying resonance effects. The comparison reveals the fundamental role of the intra-well dynamics within the space-continuous formulation.

Key words

stochastic resonance nonlinear response 


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  1. [1]
    N.G. van Kampen: Stochastic Processes in Physics and Chemistry. North-Holland, Amsterdam, 1992.Google Scholar
  2. [2]
    C.W. Gardiner: Handbook of Stochastic Methods, 2nd ed., Springer, Berlin, 1985.Google Scholar
  3. [3]
    H. Risken: The Fokker-Planck Equation. Springer, Berlin, 1989.Google Scholar
  4. [4]
    V.S. Anishchenko, V.V. Astakhov, A.B. Neiman, T.E. Vadivasova, and L. Shimansky-Geier: Nonlinear Dynamics of Chaotic and Stochastic Systems. Tutorial and Modern Developments. Springer, Heidelberg, 2002.Google Scholar
  5. [5]
    L. Gammaitoni, P. Hanggi, P. Jung, and F. Marchesoni: Rev. Mod. Phys. 70 (1998) 223.CrossRefADSGoogle Scholar
  6. [6]
    P. Reimann: Phys. Rep. 361 (2002) 57–256.CrossRefADSMATHMathSciNetGoogle Scholar
  7. [7]
    J.M.R. Parrondo and B.J. De Cisneros: Appl. Phys. A 75 (2002) 179.CrossRefADSGoogle Scholar
  8. [8]
    F. Wolf: J. Math. Phys. 29 (1988) 305.CrossRefADSMATHMathSciNetGoogle Scholar
  9. [9]
    Hu Gang, G. Nicolis, and C. Nicolis: Phys. Rev. A 42 (1990) 2030.CrossRefADSGoogle Scholar
  10. [10]
    B. McNamara and K. Wiesenfeld: Phys. Rev. A 39 (1989) 4854.CrossRefADSGoogle Scholar
  11. [11]
    R.F. Fox: Phys. Rev. A 39 (1989) 4148.CrossRefADSMathSciNetGoogle Scholar
  12. [12]
    M.C. Mahato, S.R. Shenoy: Phys. Rev. E 50 (1994) 2503.CrossRefADSGoogle Scholar
  13. [13]
    P. Chvosta and P. Reineker: J. Phys. A: Math. Gen. 36 (2003) 8753.CrossRefADSMathSciNetGoogle Scholar
  14. [14]
    P. Chvosta and P. Reineker: Phys. Rev. E 68 (2003) 066109.CrossRefADSMathSciNetGoogle Scholar
  15. [15]
    H.L. Frisch, V. Privman, C. Nicolis, and D. Nicolis: J. Phys. A: Math. Gen. 94 (1990) L1147.ADSMathSciNetGoogle Scholar
  16. [16]
    M. Morsch, H. Risken, and H.D. Vollmer: Z. Physik B 32 (1979) 245.Google Scholar
  17. [17]
    E. Gluskin: Eur. J. Phys. 24 (2003) 591.CrossRefMATHGoogle Scholar
  18. [18]
    A.D. Polyanin and A.V. Manzhirov: Handbook of integral equations, CRC Press LLC, London, 1998.Google Scholar
  19. [19]
    D. Keffer: Advanced analytic techniques for the solution of single-and multi-dimensional integral equations, University of Tennessee, Tennessee, 1999.Google Scholar
  20. [20]
    G. Doetsch: Anleitung zum praktischen Gebrauch der Laplace-Transformation und der Z-Transformation. R. Oldenbourg, Munchen, 1967.Google Scholar
  21. [21]
    V. Berdichevsky and M. Gitterman: Phys. Rev. E 59 (1999) R9.CrossRefADSGoogle Scholar

Copyright information

© Institute of Physics, Academy of Sciences of Czech Republic 2006

Authors and Affiliations

  • Evzen Subrt
    • 1
  • Petr Chvosta
    • 1
  1. 1.Department of Macromolecular Physics, Faculty of Mathematics and PhysicsCharles UniversityPrahaCzech Republic

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