Resonance- and chaos-assisted tunneling in mixed regular-chaotic systems

[en] We present evidence that nonlinear resonances govern the tunneling process between symmetry-related islands of regular motion in mixed regular-chaotic systems. In a similar way as for near-integrable tunneling, such resonances induce couplings between regular states within the islands and states that are supported by the chaotic sea. On the basis of this mechanism, we derive a semiclassical expression for the average tunneling rate, which yields good agreement in comparison with the exact quantum tunneling rates calculated for the kicked rotor and the kicked Harper.

Disciplines :

Physics

Author, co-author :

Eltschka, C.

Schlagheck, Peter ; Université de Liège - ULiège > Département de physique > Physique quantique statistique

Language :

English

Title :

Resonance- and chaos-assisted tunneling in mixed regular-chaotic systems

Publication date :

2005

Journal title :

Physical Review Letters

ISSN :

0031-9007

eISSN :

1079-7114

Publisher :

American Physical Society, Ridge, United States - New York

Volume :

Issue :

Pages :

014101

Peer reviewed :

Peer Reviewed verified by ORBi

Available on ORBi :

since 05 November 2010

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Bibliography

M. J. Davis and E. J. Heller, J. Chem. Phys. 75, 246 (1981).
S. Creagh, in Tunneling in Complex Systems, edited by S. Tomsovic (World Scientific, Singapore, 1998), p. 1.
W. A. Lin and L. E. Ballentine, Phys. Rev. Lett. 65, 2927 (1990); F. Grossmann, T. Dittrich, P. Jung, and P. Hänggi, Phys. Rev. Lett. 67, 516 (1991).
W. A. Lin and L. E. Ballentine, Phys. Rev. Lett. 65, 2927 (1990); F. Grossmann, T. Dittrich, P. Jung, and P. Hänggi, Phys. Rev. Lett. 67, 516 (1991).
O. Bohigas, S. Tomsovic, and D. Ullmo, Phys. Rep. 223, 43 (1993); O. Bohigas, D. Boosé, R. Egydio de Carvalho, and V. Marvulle, Nucl. Phys. A560, 197 (1993).
O. Bohigas, S. Tomsovic, and D. Ullmo, Phys. Rep. 223, 43 (1993); O. Bohigas, D. Boosé, R. Egydio de Carvalho, and V. Marvulle, Nucl. Phys. A560, 197 (1993).
S. Tomsovic and D. Ullmo, Phys. Rev. E 50, 145 (1994).
E. Doron and S. D. Frischat, Phys. Rev. Lett. 75, 3661 (1995); S. D. Frischat and E. Doron, Phys. Rev. E 57, 1421 (1998).
E. Doron and S. D. Frischat, Phys. Rev. Lett. 75, 3661 (1995); S. D. Frischat and E. Doron, Phys. Rev. E 57, 1421 (1998).
J. Zakrzewski, D. Delande, and A. Buchleitner, Phys. Rev. E 57, 1458 (1998).
J. U. Nöckel and A. D. Stone, Nature (London) 385, 45 (1997).
C. Dembowski et al., Phys. Rev. Lett. 84, 867 (2000).
A. Mouchet, C. Miniatura, R. Kaiser, B. Grémaud, and D. Delande, Phys. Rev. E 64, 016221 (2001).
W. K. Hensinger et al., Nature (London) 412, 52 (2001); D. A. Steck, W. H. Oskay, and M. G. Raizen, Science 293, 274 (2001).
W. K. Hensinger et al., Nature (London) 412, 52 (2001); D. A. Steck, W. H. Oskay, and M. G. Raizen, Science 293, 274 (2001).
F. Leyvraz and D. Ullmo, J. Phys. A 29, 2529 (1996).
A. Shudo and K. S. Ikeda, Phys. Rev. Lett. 74, 682 (1995); 76, 4151 (1996); T. Onishi, A. Shudo, K. S. Ikeda, and K. Takahashi, Phys. Rev. E 64, 025201(R) (2001).
A. Shudo and K. S. Ikeda, Phys. Rev. Lett. 74, 682 (1995); 76, 4151 (1996); T. Onishi, A. Shudo, K. S. Ikeda, and K. Takahashi, Phys. Rev. E 64, 025201(R) (2001).
A. Shudo and K. S. Ikeda, Phys. Rev. Lett. 74, 682 (1995); 76, 4151 (1996); T. Onishi, A. Shudo, K. S. Ikeda, and K. Takahashi, Phys. Rev. E 64, 025201(R) (2001).
V. A. Podolskiy and E. E. Narimanov, Phys. Rev. Lett. 91, 263601 (2003).
A. M. Ozorio de Almeida, J. Phys. Chem. 88, 6139 (1984).
L. Bonci, A. Farusi, P. Grigolini, and R. Roncaglia, Phys. Rev. E 58, 5689 (1998).
O. Brodier, P. Schlagheck, and D. Ullmo, Phys. Rev. Lett. 87, 064101 (2001); Ann. Phys. (N.Y.) 300, 88 (2002).
O. Brodier, P. Schlagheck, and D. Ullmo, Phys. Rev. Lett. 87, 064101 (2001); Ann. Phys. (N.Y.) 300, 88 (2002).
S. Keshavamurthy, J. Chem. Phys. 119, 161 (2003).
A. J. Lichtenberg and M. A. Lieberman, Regular and Stochastic Motion (Springer-Verlag, New York, 1983).
S. Tomsovic, M. Grinberg, and D. Ullmo, Phys. Rev. Lett. 75, 4346 (1995).
P. Leboeuf, J. Kurchan, M. Feingold, and D. P. Arovas, Phys. Rev. Lett. 65, 3076 (1990).
T. Geisel, G. Radons, and J. Rubner, Phys. Rev. Lett. 57, 2883 (1986); N. T. Maitra and E. J. Heller, Phys. Rev. E 61, 3620 (2000).
T. Geisel, G. Radons, and J. Rubner, Phys. Rev. Lett. 57, 2883 (1986); N. T. Maitra and E. J. Heller, Phys. Rev. E 61, 3620 (2000).
R. Ketzmerick, L. Hufnagel, F. Steinbach, and M. Weiss, Phys. Rev. Lett. 85, 1214 (2000).