Spectral spacing correlations for chaotic and disordered systems
New aspects of spectral fluctuations of (quantum) chaotic and diffusive systems are considered, namely autocorrelations of the spacing between consecutive levels or spacing autocovariances. They can be viewed as a discretized two point correlation function. Their behavior results from two different...
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todo:paper_00159018_v31_n3_p489_Bohigas2023-10-03T14:13:50Z Spectral spacing correlations for chaotic and disordered systems Bohigas, O. Lebœuf, P. Sánchez, M.J. New aspects of spectral fluctuations of (quantum) chaotic and diffusive systems are considered, namely autocorrelations of the spacing between consecutive levels or spacing autocovariances. They can be viewed as a discretized two point correlation function. Their behavior results from two different contributions. One corresponds to (universal) random matrix eigenvalue fluctuations, the other to diffusive or chaotic characteristics of the corresponding classical motion. A closed formula expressing spacing autocovariances in terms of classical dynamical zeta functions, including the Perron-Frobenius operator, is derived. It leads to a simple interpretation in terms of classical resonances. The theory is applied to zeros of the Riemann zeta function. A striking correspondence between the associated classical dynamical zeta functions and the Riemann zeta itself is found. This induces a resurgence phenomenon where the lowest Riemann zeros appear replicated an infinite number of times as resonances and sub-resonances in the spacing autocovariances. The theoretical results are confirmed by existing "data." The present work further extends the already well known semiclassical interpretation of properties of Riemann zeros. Fil:Sánchez, M.J. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_00159018_v31_n3_p489_Bohigas |
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Universidad de Buenos Aires |
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I-28 |
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R-134 |
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
| description |
New aspects of spectral fluctuations of (quantum) chaotic and diffusive systems are considered, namely autocorrelations of the spacing between consecutive levels or spacing autocovariances. They can be viewed as a discretized two point correlation function. Their behavior results from two different contributions. One corresponds to (universal) random matrix eigenvalue fluctuations, the other to diffusive or chaotic characteristics of the corresponding classical motion. A closed formula expressing spacing autocovariances in terms of classical dynamical zeta functions, including the Perron-Frobenius operator, is derived. It leads to a simple interpretation in terms of classical resonances. The theory is applied to zeros of the Riemann zeta function. A striking correspondence between the associated classical dynamical zeta functions and the Riemann zeta itself is found. This induces a resurgence phenomenon where the lowest Riemann zeros appear replicated an infinite number of times as resonances and sub-resonances in the spacing autocovariances. The theoretical results are confirmed by existing "data." The present work further extends the already well known semiclassical interpretation of properties of Riemann zeros. |
| format |
JOUR |
| author |
Bohigas, O. Lebœuf, P. Sánchez, M.J. |
| spellingShingle |
Bohigas, O. Lebœuf, P. Sánchez, M.J. Spectral spacing correlations for chaotic and disordered systems |
| author_facet |
Bohigas, O. Lebœuf, P. Sánchez, M.J. |
| author_sort |
Bohigas, O. |
| title |
Spectral spacing correlations for chaotic and disordered systems |
| title_short |
Spectral spacing correlations for chaotic and disordered systems |
| title_full |
Spectral spacing correlations for chaotic and disordered systems |
| title_fullStr |
Spectral spacing correlations for chaotic and disordered systems |
| title_full_unstemmed |
Spectral spacing correlations for chaotic and disordered systems |
| title_sort |
spectral spacing correlations for chaotic and disordered systems |
| url |
http://hdl.handle.net/20.500.12110/paper_00159018_v31_n3_p489_Bohigas |
| work_keys_str_mv |
AT bohigaso spectralspacingcorrelationsforchaoticanddisorderedsystems AT lebœufp spectralspacingcorrelationsforchaoticanddisorderedsystems AT sanchezmj spectralspacingcorrelationsforchaoticanddisorderedsystems |
| _version_ |
1782028417607139328 |