Abstract
This review deals with the dynamics of quantum systems that are subject to high frequency external perturbations. Though the problem may look hopelessly time-dependent, and poised on the extreme opposite side of adiabaticity, there exists a ‘Kapitza Window’ over which the dynamics can be treated in terms of effective time-independent Hamiltonians. The consequent results are important in the context of atomic traps as well as quantum optic properties of atoms in intense and high-frequency electromagnetic fields.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
P L Kapitza, Zh. Eksp. Teor. Fiz. 21, 588 (1951); Collected Papers of P K Kapitza edited by D Ter Haar (Pergamon Press, Oxford, 1965)
L D Landau and E M Lifshitz, Mechanics (Pergamon, Oxford, 1960) pp. 93–95
A V Gaponov and M A Miller, Zh. Eksp. Teor. Fiz. 34, 242 (1958)
E S Weibel and G L Clark, Plasma Phys. 2, 112 (1960)
I C Percival and D Richards, Introduction to dynamics (Cambridge University Press, London, 1982)
E A Cornell and C E Wieman, Rev. Mod. Phys. 74, 875 (2002)
C Cohen-Tannoudji, J Dupont-Roc and G Grynberg, Atom-photon interactions (Wiley, New York, 1992)
F H M Faisal, Theory of multiphoton processes (Plenum, New York, 1987)
V Milner, J L Hanssen, W C Campbell and M G Raizen, Phys. Rev. Lett. 86, 1514 (2001)
N Friedman, A Kaplan, D Carasso and N Davidson, Phys. Rev. Lett. 86, 1518 (2001)
P Lambropoulous, P Margakis and J Zhang, Phys. Rep. 305, 203 (1998)
M Lein, E K U Gross and V Engel, Phys. Rev. Lett. 85, 4707 (2000)
G L Kamta and A F Starace, Phys. Rev. Lett. 86, 5687 (2001); Phys. Rev. A65, 053418 (2002)
A Scrinizi and B Piraux, Phys. Rev. A58, 1310 (1998)
There are numerous text books on this subject. A ready reference is: L D Landau and E M Lifshitz, Quantum mechanics (nonrelativistic theory) (Pergamon, Oxford, 1989)
See, however a phase-space formulation of classical mechanics, in E C G Sudarshan and N Mukunda, Classical dynamics: A modern perspective (Wiley, New York, 1974)
R J Cook, D G Shankland and A L Wells, Phys. Rev. A31, 564 (1985)
T P Grozdanov and M J Raković, Phys. Rev. A38, 1739 (1988)
I Gillary and N Moiseyev, Phys. Rev. A66, 063415 (2002)
H A Kramers, Collected scientific papers (North-Holland, Amsterdam, 1956)
W C Henneberger, Phys. Rev. Lett. 21, 838 (1968)
S Rahav, I Gillary and S Fishman, Phys. Rev. Lett. 91, 110404 (2003); Phys. Rev. A68, 013820 (2003)
Y B Zeldovich, Sov. Phys. JETP 24, 1006 (1967)
J H Shirley, Phys. Rev. B138, 979 (1965)
H Sambe, Phys. Rev. A7, 2203 (1973)
W R Salzman, Phys. Rev. A10, 461 (1974)
F Gesztesy and H Mitter, J. Phys. A14, L79 (1981)
K Husimi, Progr. Theor. Phys. 9, 381 (1953)
See also F H Kerner, Can. J. Phys. 36, 371 (1958)
P Hänggi, in Quantum transport and dissipation edited by T Dittrich, P Hänggi, G L Ingold, B Kramer, G Schön, W Zwerger (Wiley-VCH Verlag GmbH, Weinheim, Germany, 1998)
See also C Zerbe and P Hänggi, Phys. Rev. E52, 1533 (1995)
I Gilary, N Moiseyev, S Rahav and S Fishman, J. Phys. A: Math. Gen. 36, L409 (2003)
W Paul, Rev. Mod. Phys. 62, 531 (1990)
N Moiseyev, Phys. Rep. 302, 211 (1998)
M Bandyopadhyay and S Dattagupta (in preparation)
E Schrödinger, Naturwissenschaflen 23, 807–812, 823–827, 844–849 (1935)
M Bandyopadhyay and S Dattagupta (in preparation)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Bandyopadhyay, M., Dattagupta, S. Quantum mechanics of rapidly and periodically driven systems. Pramana - J Phys 70, 381–398 (2008). https://doi.org/10.1007/s12043-008-0056-6
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12043-008-0056-6