Publication: Distribution of the ratio of consecutive level spacings for different symmetries and degrees of chaos
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2020-02-28
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American Physical Society
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Abstract
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) P(r; beta), where beta is an element of [0, +infinity) 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 ansatze for different transitions, with a negligible associated error in the limits corresponding to standard random ensembles.
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©2020 American Physical Society. We acknowledge financial support through Spanish Grants No. PGC2018-094180-B-I00 (MCIU/AEI/FEDER, EU) and No. FIS2015-63770-P (MINECO/FEDER, EU).