Distribution of the ratio of consecutive level spacings for different symmetries and degrees of chaos

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 descr...

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Bibliographic Details
Authors: Corps, Angel L., Relaño Pérez, Armando
Format: article
Publication Date:2020
Country:España
Institution:Universidad Complutense de Madrid (UCM)
Repository:Docta Complutense
Language:English
OAI Identifier:oai:docta.ucm.es:20.500.14352/6193
Online Access:https://hdl.handle.net/20.500.14352/6193
Access Level:Open access
Keyword:536
Gaudin models
Quantum
Statistics
Hermite
Termodinámica
2213 Termodinámica
Description
Summary: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.