Abstract
A classical Fermi accelerator model (FAM) is known to show chaotic behavior. The FAM is defined by a free particle bouncing elastically from two rigid walls, one fixed and the other oscillating periodically in time. The central aim of this paper is to connect the quantum and the classical solutions to the FAM in the semiclassical limit. This goal is accomplished using a finite inverted parametric oscillator (FIPO), confined to a box withfixed walls, as an alternative representation of the FAM. In the FIPO representation, an explicit correspondence between classical and quantum limits is accomplished using a Husimi representation of the quasienergy eigenfunctions.
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References
T. H. Seligman and H. Nishioka, eds.,II International Conference on Quantum Chaos (Springer-Verlag, 1986).
O. Bohigas, M. J. Giannoni, and C. Schmit,Phys. Rev. Lett. 52:1 (1984).
M. Mehta, ed.,Random Matrices: An Enlarged and Revised Second Edition (Academic Press, 1991).
J. V. José and R. Cordery,Phys. Rev. Lett. 56:290 (1986).
F. M. Izrailev,Phys. Rev. Lett. 56:541 (1986).
S. J. Chang and K. J. Shi,Phys. Rev. A 34:7 (1986); G. Radons and R. E. Prange,Phys. Rev. Lett. 61:1691 (1988).
R. V. Jensen, M. M. Sanders, M. Saraceno, and B. Sundaram,Phys. Rev. Lett. 63:2771 (1989); W. A. Lin and L. E. Ballentine,Phys. Rev. Lett. 65:2927 (1990).
M. A. Lieberman and A. J. Lichtenberg,Phys. Rev. A 5:1852 (1971).
W. M. Visscher,Phys. Rev. A 36:5031 (1987).
E. Fermi,Phys. Rev. 75:1169 (1949).
R. Bellman,Perturbation Techniques in Mathematics Engineering & Physics (Dover, New York).
L. S. Schulman,Techniques and Applications of Path Integration (Wiley, 1981).
A. Munier, J. R. Burgan, M. Feix, and E. Fijalkow,J. Math. Phys. 22:1219 (1981).
M. V. Berry and G. Klein,J. Phys. A: Math. Gen. 17:1805 (1984).
L. Chetouani, L. Guechi, and T. F. Hammann,Phys. Rev. A 40:1157 (1989).
S. Takagi,Prog. Theor. Phys. 84:1019 (1990).
P. Seba,Phys. Rev. A 41:2306 (1990).
M. Abramowitz and I. A. Stegun,Handbook of Mathematical Functions (Dover, 1972).
Ya. B. Zel'dovich,Sov. Phys.-JETP 24:1006 (1967).
E. J. Heller,Phys. Rev. Lett. 53:1515 (1984).
R. L. Waterland, J. M. Yuan, C. C. Martens, R. E. Grillian, and W. P. Reinhardt,Phys. Rev. Lett. 61:2733 (1988).
R. Geisel, G. Radons, and J. Rubner,Phys. Rev. Lett. 57:2883 (1986).
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Chu, G., José, J.V. The semiclassical limit of a quantum Fermi accelerator. J Stat Phys 68, 153–174 (1992). https://doi.org/10.1007/BF01048840
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DOI: https://doi.org/10.1007/BF01048840