Abstract
An accurate and fast approach for numerically solving a non-Markovian Langevin equation with a thermal band-passing noise is proposed. The algorithm combines the closed integration for both damping and noise terms with the Runge–Kutta method for nonlinear force in the Markovian Langevin equation transferred from the original equation. The present algorithm is tested through simulating diffusion of a free particle by using different initial distributions, and then a strong superdiffusion is shown. The mean velocity of a particle in a flashing ratchet driven by the band-passing colored noise is calculated numerically. The dependence of the resulting mean velocity on temperature, asymmetry of the ratchet potential, and inertia of the particle is discussed, and some novel behaviors in comparison with the usual model are observed.
Similar content being viewed by others
REFERENCES
For a review, see R. Metzler and J. Klafter, Phys. Rep. 339:1 (2000).
A. Mauger and N. Pottier, Phys. Rev. E 65:056107 (2002).
E. Lutz, Phys. Rev. E 64:051106 (2001); Europhys. Lett. 54:293 (2001).
R. Metzler and I. M. Sokolov, Europhys. Lett. 58:482 (2002); R. Metzler and J. Klafter, Phys. Rev. E 61:6308 (2000).
R. Morgado, F. A. Oliveira, G. G. Batrouni, and A. Hansen, Phys. Rev. Lett. 89:100601 (2002).
H. Scher, M. F. Shlesinger, and J. T. Bendler, Phys. Today 44:26 (1991); M. F. Shlesinger, G. M. Zaslavsky, and J. Klafter, Nature 363:31 (1993); T. Srokowski, Phys. Rev. Lett. 85:2232 (2000).
J. D. Bao and S. J. Liu, Phys. Rev. E 60:7572 (1999).
For a recent review, see P. Reimann, Phys. Rep. 361:57 (2002).
S. A. Guz, I. G. Rusavin, and M. V. Sviridov, Phys. Lett. A 274:104 (2000); S. A. Guz and M. V. Sviridov, Chaos 11:605 (2001).
T. Munakata and T. Kawakatsu, Prog. Theor. Phys. 74:262 (1985).
J. D. Bao and Y. Z. Zhuo, Phys. Lett. A 239:228 (1998).
J. D. Bao, J. Stat. Phys. 99:595 (2000).
R. L. Honeycutt, Phys. Rev. A 45:604 (1992).
R. Mannella and V. Palleschi, Phys. Rev. A 40:3381 (1989).
R. F. Fox, Phys. Rev. A 43:2649 (1991).
L. Schimansky-Geier and Ch. Zülicke, Z. Phys. B 79:41 (1990); M. I. Dykman and R. Mannella, Phys. Rev. E 47:3996 (1993); S. J. B. Einchcomb and A. J. McKane, Phys. Rev. E. 49:259 (1994).
P. Jung, Phys. Rev. E 50:2513 (1994); Phys. Lett. A 207:93 (1995).
L. P. Faucheux, L. S. Bourdieu, P. D. Kaplan, and A. J. Libchaber, Phys. Rev. Lett. 74:1504 (1995).
R. D. Astumian, Science, 276:917 (1997); R. D. Astumian and M. Bier, Phys. Rev. Lett. 72:1766 (1994).
A. Mielke, Ann. Phys. 4:721 (1995).
J.-F. Chauwin, A. Ajdari, and J. Prost, Europhys. Lett. 32:373 (1995); J. D. Bao, Phys. Lett. A 267:122 (2000).
B. Lindner, L. Schimansky-Geier, P. Reimann, P. Hänggi, and M. Nagaoka, Phys. Rev. E 59:1417 (1999).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Bao, JD. Numerical Integration of a Non-Markovian Langevin Equation with a Thermal Band-Passing Noise. Journal of Statistical Physics 114, 503–513 (2004). https://doi.org/10.1023/B:JOSS.0000003118.62044.b7
Issue Date:
DOI: https://doi.org/10.1023/B:JOSS.0000003118.62044.b7