Distribution of the Ratio of Consecutive Level Spacings for Different Symmetries and Degrees of Chaos

16 Feb 2020  ·  Corps A. L., Relaño A. ·

Theoretical expressions for the distribution of the ratio of consecutive level spacings for quantum systems with transiting dynamics remain unknown. We propose a family of one-parameter distributions $P(r)\equiv P(r;\beta)$, where $\beta\in[0,+\infty)$ is a generalized Dyson index, that describes the eigenlevel statistics of a quantum system characterized by different symmetries and degrees of chaos... We show that this crossover strongly depends on the specific properties of each model, and thus the reduction of such a family to a universal formula, albeit desirable, is not possible. We use the information entropy as a criterion to suggest particular ansatzs for different transitions, with a negligible associated error in the limits corresponding to standard random ensembles. read more

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Quantum Physics Statistical Mechanics Mathematical Physics Mathematical Physics Chaotic Dynamics