Quantum chaos: double resonance model and its physical applications

  • Andrey R. Kolovsky
Part II: Seminars
Part of the Lecture Notes in Physics book series (LNP, volume 457)


We have analyzed the dynamics of DRM and EDRM. The main conclusion from this analysis might sound surprising - there are no analogies with quantum kicked rotor at all. Thus the chaotic systems with bounded chaotic component is really different class of the dynamical system and they require a different approach in the quantum case. We note that the same conclusion have been independently done in Ref. [4].

We also would like to note an interesting chain of the transformations on the way from classics to quanta in DRM. In fact, in the classical approach any system trajectory is random in the chaotic regime. However, when we average over an ensemble of the trajectories, the dynamics of an arbitrary classical average becomes a pure regular process [5]. On the last stage, when we substitute the classical average by the quantum-mechanical average, its dynamics appears to be a quasirandom process. This “quasirandomness” is a sign of the underlaying classical chaos and it is absent when the classical dynamics is regular.


Induce Polarization Quantum Case Nonlinear Resonance Chaotic Regime Regular Regime 
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Copyright information

© Springer-Verlag 1995

Authors and Affiliations

  • Andrey R. Kolovsky
    • 1
  1. 1.L.V. Kirensky Institute of PhysicsKrasnoyarskRussia

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