<Article>Resonance and its Stochastic Behavior in Quantum Kicked Rotator

概要

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A modified standard map incorporating quantum correction is derived on the basis of the semiclassical approximation of Zaslavsky as part of our study to investigate the behaviors of the classical and quantum chaoses including a relationship therebetween, more particularly at present to investigate what kind of information can be obtained from the modified standard map concerning the classical resonance and the quantum resonance. We have obtained a behavior corresponding to the quantum resonance found by Izlairev, in which as a periodicity parameter is increased, the state becomes stochastic. This is a quantum version of the Chirikov's overlap of resonances (criterion of stochasticity). It has been further found that also when random noise is applied, the state becomes stochastic. Further, as nonlinear coupling strength with other degrees of freedom in the present map is increased, the state becomes also stochastic. Demonstration of the stochastic behavior of the quantum resonance with such a modified standard map including quantum correction as in the present study is first so far as we know.
日本医科大学の論文
1997-06-30