Resonance-assisted tunneling

[en] We present evidence that tunneling processes in near-integrable systems are enhanced due to the manifestation of nonlinear resonances and their respective island chains in phase space. A semiclassical description of this "resonance-assisted" mechanism is given, which is based on a local perturbative description of the dynamics in the vicinity of the resonances. As an underlying picture, we obtain that the quantum state is coupled, via a succession of classically forbidden transitions across nonlinear resonances, to high excitations within the well, from where tunneling occurs with a rather large rate. The connection between this description and the complex classical structure of the underlying integrable dynamics is furthermore studied, giving ground to the general coherence of the description as well as guidelines for the identification of the dominant tunneling paths. The validity of this mechanism is demonstrated within the kicked Harper model, where good agreement between quantum and semiclassical (resonance-assisted) tunneling rates is found. (C) 2002 Elsevier Science (USA).

Disciplines :

Physics

Author, co-author :

Brodier, O.

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

Ullmo, D.

Language :

English

Title :

Resonance-assisted tunneling

Publication date :

2002

Journal title :

Annals of Physics

ISSN :

0003-4916

eISSN :

1096-035X

Publisher :

Academic Press, San Diego, United States - California

Volume :

300

Issue :

Pages :

88-136

Peer reviewed :

Peer Reviewed verified by ORBi

Available on ORBi :

since 05 November 2010

Statistics

Number of views

36 (2 by ULiège)

Number of downloads

0 (0 by ULiège)

More statistics

Scopus citations^®

Scopus citations^®
without self-citations

OpenCitations

OpenAlex citations

Bibliography

M. J. Davis and E. J. Heller, J. Chem. Phys. 75 (1981), 246.
J. Barnas and A. Fert, Phys. Rev. Lett. 80 (1998), 1058.
S. C. Creagh and N. D. Whelan, Phys. Rev. Lett. 77 (1996), 4975; 82 (1999), 5237.
W. A. Lin and L. E. Ballentine, Phys. Rev. Lett. 65 (1990), 2927.
O. Bohigas, S. Tomsovic, and D. Ullmo, Phys. Rep. 223 (1993), 43;
O. Bohigas, D. Boosé, R. Egydio de Carvalho, and V. Marvulle, Nucl. Phys. A 560 (1993), 197.
S. Tomsovic and D. Ullmo, Phys. Rev. E 50 (1994), 145.
E. Doron and S. D. Frischat, Phys. Rev. Lett. 75 (1995), 3661;
S. D. Frischat and E. Doron, Phys. Rev. E 57 (1998), 1421.
F. Leyvraz and D. Ullmo, J. Phys. A 29 (1996), 2529.
J. Zakrzewski, D. Delande, and A. Buchleitner, Phys. Rev. E 57 (1998), 1458.
W. K. Hensinger et al., Nature 412 (2001), 52.
D. A. Steck, W. H. Oskay, and M. G. Raizen, Science 293 (2001), 274; Phys. Rev. Lett. 88 (2002), 120406.
A. Mouchet, C. Miniatura, R. Kaiser, B. Grémaud, and D. Delande, Phys. Rev. E 64 (2001), 016221.
C. Dembowski et al., Phys. Rev. Lett. 84 (2000), 867.
J. U. Nöckel and A. D. Stone, Nature 385 (1997), 45.
J. M. Greene and I. C. Percival, Physica D 3 (1981), 530.
S. Creagh, in "Tunneling in Complex Systems" (S. Tomsovic, Ed.), p. 35, World Scientific, Singapore, 1998.
A. Shudo and K. S. Ikeda, Phys. Rev. Lett. 74 (1995), 682; Phys. Rev. Lett. 76 (1996), 4151;
T. Onishi, A. Shudo, K. S. Ikeda, and K. Takahashi, Phys. Rev. E 64 (2001), 025201;
A. Shudo, Y. Ishii, and K. S. Ikeda, J. Phys. A 35 (2002), L1-L7.
L. Bonci, F. Farusi, P. Grigolini, and R. Roncaglia, Phys. Rev. E 58 (1998), 5689.
T. Uzer, D. W. Noid, and R. A. Marcus, J. Chem. Phys. 79 (1983), 4412.
A. M. Ozorio de Almeida, J. Phys. Chem. 88 (1984), 6139.
D. Farrely and T. Uzer, J. Chem. Phys. 85 (1986), 308.
H. P. Breuer and M. Holthaus, Ann. Phys. (N.Y.) 211 (1991), 249.
O. Brodier, P. Schlagheck, and D. Ullmo, Phys. Rev. Lett. 87 (2001), 064101.
P. Leboeuf, J. Kurchan, M. Feingold, and D. P. Arovas, Phys. Rev. Lett. 65 (1990), 3076.
R. Lima and D. Shepelyansky, Phys. Rev. Lett. 67 (1991), 1377.
T. Geisel, R. Ketzmerick, and G. Petschel, Phys. Rev. Lett. 67 (1991), 3635.
R. Roncaglia, L. Bonci, F. Izrailev, B. J. West, and P. Grigolini, Phys. Rev. Lett. 73 (1994), 802.
V. V. Sokolov, Sov. J. Theor. Math. Phys. 67 (1986), 223;
V. V. Sokolov, O. V. Zhirov, D. Alonso, and G. Casati, Phys. Rev. Lett. 84 (2000), 3566.
A. J. Lichtenberg and M. A. Lieberman, "Regular and Stochastic Motion," Springer-Verlag, New York, 1983.
F. Grossmann, T. Dittrich, P. Jung, and P. Hänggi, Phys. Rev. Lett. 67 (1991), 516.
J. Moser, Mem. Amer. Math. Soc. 81 (1981).
V. P. Maslov and M. V. Fedoriuk, "Semiclassical Approximation in Quantum Mechanics," Reidel, Dordrecht, 1981; original Russian edition, 1965.
See, e.g., V. I. Arnold, "Mathematical Methods of Classical Mechanics," Appendices 10 and 11, Springer-Verlag, New York/Berlin, 1978.
L. Landau and E. Lifchitz, "Mécanique Quantique," Mir, Moscow, 1966.
S. C. Creagh, J. Phys. A 27 (1994), 4969.
B. V. Chirikov, Phys. Rep. 52 (1979), 265.
M. Wilkinson, Physica D 21 (1986), 341; J. Phys. A 20 (1987), 635.
R. E. Langer, Phys. Rev. 51 (1937), 669.
We should note that we cannot rigorously show Eq. (46) to hold in the extreme perturbative regime. The matching between the semiclassical and the quantum transition amplitudes is therefore not necessarily expected.
E. B. Bogomolny, Physica D 13 (1984), 281.