[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
scite shows how a scientific paper has been cited by providing the context of the citation, a classification describing whether it supports, mentions, or contrasts the cited claim, and a label indicating in which section the citation was made.
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.
Similar publications
Sorry the service is unavailable at the moment. Please try again later.
This website uses cookies to improve user experience. Read more
Save & Close
Accept all
Decline all
Show detailsHide details
Cookie declaration
About cookies
Strictly necessary
Performance
Strictly necessary cookies allow core website functionality such as user login and account management. The website cannot be used properly without strictly necessary cookies.
This cookie is used by Cookie-Script.com service to remember visitor cookie consent preferences. It is necessary for Cookie-Script.com cookie banner to work properly.
Performance cookies are used to see how visitors use the website, eg. analytics cookies. Those cookies cannot be used to directly identify a certain visitor.
Used to store the attribution information, the referrer initially used to visit the website
Cookies are small text files that are placed on your computer by websites that you visit. Websites use cookies to help users navigate efficiently and perform certain functions. Cookies that are required for the website to operate properly are allowed to be set without your permission. All other cookies need to be approved before they can be set in the browser.
You can change your consent to cookie usage at any time on our Privacy Policy page.
