Marcelo Losada

A Semiclassical Condition for Chaos Based on Pesin Theorem

A semiclassical method to determine if the classical limit of a quantum system shows a chaotic behavior or not based on Pesin theorem, is presented. The method is applied to a phenomenological Gamow–type model and it is concluded that in the classical limit the dynamics exhibited by its effective Hamiltonian is chaotic.

Quantum histories without contrary inferences

Abstract In the consistent histories formulation of quantum theory it was shown that it is possible to retrodict contrary properties. We show that this problem do not appear in our formalism of generalized contexts for quantum histories.

Quantum histories and correlations in quantum measurements

In this paper, the measurement process is described as an interaction between two quantum systems: the system to be measured and the measuring instrument. The time evolution is determined only by the Schrödinger equation, i.e., there is no collapse postulate. The description of the measurement process is performed using the quantum histories approach, which allows to express the correlation between the properties of the measured system, before the measurement, and the properties of the pointer variable of the instrument, after the measurement. From the point of view of this approach, we explore the possibility of obtaining information of incompatible observables with the same instrument, using different families of histories.

About the Concept of Quantum Chaos

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.