Kolmogorov stochasticity parameter as a measure of quantum chaos

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We propose the Kolmogorov stochasticity parameter, λ 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 λ. 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 λₙ for n energy levels scales as λₙ n⁻α. Furthermore, with α, the stochastic probability (calculated from PDF) is seen to jump by about an order of magnitude as the systems turn chaotic.