Spectral spacing correlations for chaotic and disordered systems

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dc.creatorBohigas, O.
dc.creatorLeboeuf, P.
dc.creatorSanchez, M. -J.
dc.date2000-12-22
dc.date.accessioned2026-07-07T05:33:14Z
dc.date.available2026-07-07T05:33:14Z
dc.descriptionNew 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.
dc.description28 pages, 6 figures, 1 table, To appear in the Gutzwiller Festschrift, a special Issue of Foundations of Physics
dc.identifierhttps://arxiv.org/abs/nlin/0012049
dc.identifierhttp://arxiv.org/abs/nlin/0012049
dc.identifierFound. Phys. 31 (2001) 489-517
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/79927
dc.subjectChaotic Dynamics
dc.subjectMesoscale and Nanoscale Physics
dc.titleSpectral spacing correlations for chaotic and disordered systems
dc.typetext

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