HP Labs Technical Reports
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Orbit Bifurcations and Spectral Statistics
Berry, M.V.; Keating, J.P.; Prado, S.D.
Keyword(s): spectral statistics; semiclassical approximation; orbit bifurcations
Abstract: Systems whose phase space is mixed have been conjectured to exhibit quantum spectral correlations that are, in the semiclassical limit, a combination of Poisson and random-matrix, with relative weightings determined by the corresponding measures of regular and chaotic orbits. We here identify an additional component in long-range spectral statistics, associated with periodic orbit bifurcations, which can be semiclassically large. This is illustrated for a family of perturbed cat maps. PACS 05.45.+b, 3.65.Sq, 05.40.+j
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