Abstract
We study the mechanism of current rectification in Hamiltonian systems driven by an external periodic force with broken time reversal symmetry. We show that directed transport arises due to breaking the symmetry of fiights near regular islands. In the framework of the continuous time random walk (CTRW) approach we construct a generalized asymmetric fiights model and derive an expression for the current in terms of the characteristics of the relevant islands. The broken-symmetry strategy allows to manipulate the transport properties of both individual particles and statistical ensembles of particles.
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References
P. Reimann: Phys. Rep. 361, 57 (2002)
H. Risken: The Fokker Planck Equation. (Springer, Berlin, 1984)
P. Hänggi and R. Bartussek, in: Nonlinear Physics of Complex Systems, Lecture Notes in Physics, 476, ed. by J. Parisi, S. C. Muller, and W. Zimmermann (Springer, Berlin 1996) p.294; P. Jung, J. G. Kissner, and P. Hänggi: Phys. Rev. Lett. 76, 3436 (1996); J. L. Mateos: Phys. Rev. Lett. 84, 258 (2000)
S. Flach, O. Yevtushenko, and Y. Zolotaryuk: Phys. Rev. Lett. 84, 2358 (2000)
T. Dittrich, R. Ketzmerick, M.-F. Otto and H. Schanz: Ann. Phys. (Leipzig) 9, 755 (2000); H. Schanz, M.-F. Otto, R. Ketzmerick, and T. Dittrich: Phys. Rev. Lett 87 07601 (2001)
R. Z. Sagdeev, D. A. Usikov, and G. M. Zaslavsky: Nonlinear physics: from the pendulum to turbulence and chaos. (Harwood Academic Publ. 1992)
M. F. Shlesinger, G. M. Zaslavsky and J. Klafter: Nature 363, 31 (1993); J. Klafter, M. F. Shlesinger, and G. Zumofen: Physics Today 49, 33 (1996)
J. Klafter and G. Zumofen: Phys. Rev. E 49, 4873 (1994)
S. Wiggins: Chaotic transport in dynamical systems. (Springer, Berlin 1992)
S. Denisov, S. Flach: Phys. Rev. E 64, 056236 (2001)
S. Denisov, J. Klafter, M. Urbakh, and S. Flach, Physica D (in press)
T. Geisel, A. Zacherl, and G. Radons: Phys. Rev. Lett. 59 2503 (1987)
S. Denisov, J. Klafter, M. Urbakh, submitted
G. Zumofen, J. Klafter, and A. Blumen: Phys. Rev. E 47, 2183 (1993)
E. R. Weeks and H. L. Swinney: Phys. Rev. E 57 4915 (1998)
N. Kac: Statistical Independence in Probability, Analysis, and Number Theory. (Mathematical Association of America, Oberlin, OH, 1959)
J.R. Robinson et al: Phys. Rev. Lett. 76, 3304 (1996); F. L. Monte et al: Phys. Rev. Lett. 75, 4598 (1995); B. G. Klappauf, W. H. Oskay, D. A. Steck, and M. G. Raizen, Phys. Rev. Lett. 81, 4044 (1998)
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Denisov, S., Klafter, J., Urbakh, M. (2003). Directed Transport in AC-Driven Hamiltonian Systems. In: Rangarajan, G., Ding, M. (eds) Processes with Long-Range Correlations. Lecture Notes in Physics, vol 621. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44832-2_11
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DOI: https://doi.org/10.1007/3-540-44832-2_11
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