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NATO ASI series. Series B : Physics

Chaotic Behavior in Quantum Systems

Casati, Giulio

Published Jan 1, 1985• 209 citations
Publisher
DOI
10.1007/978-1-4613-2443-0

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The question of the behavior of quantum systems in time-dependent fields whose classical counterparts exhibit chaotic behavior is addressed. For any nondissipative bounded quantum system under the influence of polychromatic (i.e., quasiperiodic) fields, it is proved by means of the many-mode Floquet theory1 that the autocorrelation function will recur infinitely often in the course of time, indicating no strict quantum stochasticity is possible.2 In particular, for an N-level quantum system undergoing multiphoton transitions, its dynamic behavior is described by the quasiperiodic motion of an (N2 – 1)-dimensional coherence vector S in accord with the SU(N) dynamic symmetries. On the other hand, for any dissipative quantum system, SU(N) symmetries are broken, and chaotic behavior is observed as the coherence vector Sevolves from an initially (N2 – 1)-dimensional space to a lower-dimensional space. The recurrence and chaotic phenomena are illustrated for two- and three-level quantum systems driven by intense bichromatic laser fields.2

International Laser Science Conference•Jan 1, 1986•0 citations
The classical-quantum transition for chaotic systems is understood to be accompanied by the suppression of chaotic effects as the relative variant Planck's over 2pi is increased. We show evidence to the contrary in the behavior of the quantum trajectory dynamics of a dissipative quantum chaotic system, the double-well Duffing oscillator. The classical limit in the case considered has regular behavior, but as the effective variant Planck's over 2pi is increased we see chaotic behavior. This chaos then disappears deeper into the quantum regime, which means that the quantum-classical transition in this case is nonmonotonic in variant Planck's over 2pi.
The question of the behavior of quantum systems in time-dependent fields whose classical counterparts exhibit chaotic behavior is addressed. For any nondissipative bounded quantum system under the influence of polychromatic (i.e., quasiperiodic) fields, it is proved by means of the many-mode Floquet theory1 that the autocorrelation function will recur infinitely often in the course of time, indicating no strict quantum stochasticity is possible.2 In particular, for an N-level quantum system undergoing multiphoton transitions, its dynamic behavior is described by the quasiperiodic motion of an (N2 – 1)-dimensional coherence vector S in accord with the SU(N) dynamic symmetries. On the other hand, for any dissipative quantum system, SU(N) symmetries are broken, and chaotic behavior is observed as the coherence vector Sevolves from an initially (N2 – 1)-dimensional space to a lower-dimensional space. The recurrence and chaotic phenomena are illustrated for two- and three-level quantum systems driven by intense bichromatic laser fields.2