Abstract
The breaking time, known also as the Ehrenfest time, of the quantum—classical crossover scales logarithmically with respect to the Planck constant in chaotic systems. A typical dynamical system is not ergodic and not uniformly hyperbolic. Deviations from the logarithmic scale have been observed for systems with phase space structures, even in the case of strong chaos, when the homogeneous hyperbolicity of phase space does not hold. In this case the breaking time depends on scaling properties of phase space structures. Two examples of chaotic motion with di erent kind of phase space structures are presented here. The first example is quantum flights studied in the kicked rotor in the presence of the accelerator mode island structure. The second example is a model of periodically kicked harmonic oscillator with dissipation.KeywordsSemiclassical approximationquantum—classical breaking timeEhren-fest timesuperdiusionchaotic attractor
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