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...
| Authors: | , |
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| 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 |
| 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. |
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