Publication: Origin of the 1/f(alpha) spectral noise in chaotic and regular quantum systems
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2018-10-19
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Amer Physical Soc
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Abstract
Based on the connection between the spectral form factor and the probability to return, the origin of the energy level fluctuation 1/f(alpha) noise in fully chaotic and fully integrable systems is traced to the quantum interference between invariant manifolds of the classical dynamics and the dimensionality of those invariant manifolds. This connection and the order-to-chaos transition are analyzed in terms of the statistics of Floquet's quasienergies of a classically chaotic driving nonlinear system. An immediate prediction of the connection established here is that in the presence of decoherence, the spectral exponent a takes the same value, alpha = 2, for both fully chaotic and fully integrable systems.
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©2018 American Physical Society. Discussions with Thomas Dittrich are acknowledged with pleasure. This work was supported by the Comité para el Desarrollo de la Investigación (CODI) of Universidad de Antioquia, Colombia under the Estrategia de Sostenibilidad and Grant No. 2015-7631, and by Colombian Institute for the Science and Technology Development (COLCIENCIAS) under Grant No. FP44842-119-2016. A.R. is supported by Spanish Grants No. FIS2012-35316 and No. FIS2015-63770-P (MINECO/FEDER).