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Combescure, M.

Recurrent versus diffusive dynamics for a kicked quantum oscillator. (English) Zbl 0766.58061

Ann. Inst. Henri Poincaré, Phys. Théor. 57, No. 1, 67-87 (1992).
This work studies the large-time behavior of the kicked quantum oscillator, where the time-dependent kick force is of the form \(F(t)=\sum_ n\varepsilon_ n\delta(t-n)\) with the \(\varepsilon_ n\) alternating randomly in sign. Typically, there is a diffusive energy growth in the system corresponding to the escape to infinity of classical trajectories. But there is also an exceptional ‘resonant’ time evolution with partially recurrent behavior of both the classical and the quantum paths. Though the author believes that the model provides a reasonable scenario for quantum chaos, it would be more fair to say that the stochastic behavior of this model is clearly induced by the external random force.
Reviewer: G.Roepstorff (Aachen)

Cited in 7 Documents

MSC:

58Z05 Applications of global analysis to the sciences
11B85 Automata sequences
81Q50 Quantum chaos

Keywords:

diffusion; quantum oscillator; quantum chaos
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\textit{M. Combescure}, Ann. Inst. Henri Poincaré, Phys. Théor. 57, No. 1, 67--87 (1992; Zbl 0766.58061)
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