Kolmogorov stochasticity parameter as a measure of quantum chaos

Details Kolmogorov stochasticity parameter as a measure of quantum chaos Kolmogorov stochasticity parameter as a measure of quantum chaos

2011-01-28

arxiv.org/abs/1101.5465v1

Nonlinear Sciences

Chaotic Dynamics

Scientific paper

We propose the Kolmogorov stochasticity parameter, $\lambda$ for energy level spectra to classify quantum systems with corresponding classical dynamics ranging from integrable to chaotic. We also study the probability distribution function (PDF) of $\lambda$. Remarkably, the PDF of all the integrable systems studied here is the same and is found to be completely different from the PDF of chaotic systems. We also note that $\lambda_n$ for $n$ energy levels scales as $\lambda_n \sim n^{-\alpha}$. Furthermore, with $\alpha$, the stochastic probability (calculated from PDF) is seen to jump by about an order of magnitude as the systems turn chaotic.

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