About the concept of quantum chaos

LOSADA, MARCELO; GOMEZ, IGNACIO SEBASTIÁN; LOMBARDI, OLIMPIA

ENTROPY

MOLECULAR DIVERSITY PRESERVATION INTERNATIONAL-MDPI

Lugar: Basel; Año: 2017 vol. 19 p. 1 - 30

1099-4300

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. Wealsooutlineageneralizationofthequantummixinglevelofthekickedrotatorinthecontext of the impulsive differential equations.