Irregular behaviour of a quantum kicked oscillator. (English) Zbl 0972.81539

Summary: The behaviour of the survival amplitudes for high energy levels of a quantum harmonic oscillator driven by periodic, quasiperiodic, and nonperiodic series of delta-kicks is investigated. Being quasiregular for weak kicks, this behaviour becomes rather irregular for sufficiently strong ones (in the quasiperiodic and nonperiodic cases). Two quantitative measures of the irregularity are introduced: the entropy of the Fourier power spectrum, and the average logarithm of the autocorrelation function.


81Q50 Quantum chaos
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[1] Pomeau, Y; Dorizzi, B; Grammaticos, B, Phys. rev. lett., 56, 681, (1986)
[2] Milonni, P.W; Ackerhalt, J.R; Goggin, M.E, Phys. rev. A, 35, 1714, (1987)
[3] Luck, J.M; Orland, H; Smilansky, U, J. stat. phys., 53, 551, (1988)
[4] Geisel, T, Phys. rev. A, 41, 2989, (1990)
[5] Gerry, C.C; Vrscay, E.R, Phys. rev. A, 39, 5717, (1989)
[6] Gerry, C.C; Schneider, T, Phys. rev. A, 42, 1033, (1990)
[7] Feynman, R.P, Phys. rev., 80, 440, (1950)
[8] Schwinger, J, Phys. rev., 91, 728, (1953)
[9] Dodonov, V.V; Man’ko, V.I; Rudenko, V.N; Dodonov, V.V; Man’ko, V.I; Rudenko, V.N, Kvant. elektron., Sov. J. quantum electron., 10, 1232, (1980)
[10] Dodonov, V.V; Man’ko, V.I; Dodonov, V.V; Man’ko, V.I, (), 103, Invariants and the evolution of nonstationary quantum systems
[11] Kerner, E.H, Can. J. phys., 36, 371, (1958)
[12] Badii, R; Meier, P.F, Phys. rev. lett., 58, 1045, (1987)
[13] Hogg, T; Huberman, B.A; Hogg, T; Huberman, B.A, Phys. rev. lett., Phys. rev. A, 28, 22, (1983)
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