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Entropy 2017, 19(5), 205; doi:10.3390/e19050205

About the Concept of Quantum Chaos

1
National Scientific and Technical Research Council (CONICET), Facultad de Ciencias Exactas, Instituto de Física La Plata (IFLP), Universidad Nacional de La Plata (UNLP), Calle 115 y 49, 1900 La Plata, Argentina
2
National Scientific and Technical Research Council (CONICET), University of Buenos Aires, 1420 Buenos Aires, Argentina
3
National Scientific and Technical Research Council (CONICET), University of Buenos Aires, Larralde 3440, 1430 Ciudad Autónoma de Buenos Aires, Argentina
*
Author to whom correspondence should be addressed.
Academic Editors: Mariela Portesi, Alejandro Hnilo and Federico Holik
Received: 5 February 2017 / Revised: 22 April 2017 / Accepted: 23 April 2017 / Published: 3 May 2017
(This article belongs to the Special Issue Foundations of Quantum Mechanics)
View Full-Text   |   Download PDF [364 KB, uploaded 3 May 2017]   |  

Abstract

The research on quantum chaos finds its roots in the study of the spectrum of complex nuclei in the 1950s and the pioneering experiments in microwave billiards in the 1970s. Since then, a large number of new results was produced. Nevertheless, the work on the subject is, even at present, a superposition of several approaches expressed in different mathematical formalisms and weakly linked to each other. The purpose of this paper is to supply a unified framework for describing quantum chaos using the quantum ergodic hierarchy. Using the factorization property of this framework, we characterize the dynamical aspects of quantum chaos by obtaining the Ehrenfest time. We also outline a generalization of the quantum mixing level of the kicked rotator in the context of the impulsive differential equations. View Full-Text
Keywords: quantum chaos; ergodic hierarchy; quantum ergodic hierarchy; classical limit quantum chaos; ergodic hierarchy; quantum ergodic hierarchy; classical limit
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Gomez, I.S.; Losada, M.; Lombardi, O. About the Concept of Quantum Chaos. Entropy 2017, 19, 205.

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