Chaotic Behavior in Quantum Systems: Theory and Applications

Casati, Giulio

Jincheng Zhang

This paper investigates the application of quantum coherence to the analysis of chaotic systems. The core claim is that leveraging the inherent properties of quantum coherence can reveal hidden patterns within chaotic systems. This work models chaotic systems as quantum systems and utilizes quantum coherence to identify critical parameters and potential control methods. The novelty lies in exploring the intersection of quantum mechanics and chaos theory, presenting a new approach to analyzing complex, nonlinear dynamics. We present a theoretical framework, focusing on the impact of quantum coherence on the behavior of specific chaotic systems, without experimental validation. The analysis provides insights into the potential for quantum-inspired control strategies and a deeper understanding of the underlying mechanisms driving chaotic dynamics. The central mathematical framework involves Hamiltonian operators, wave functions, and coherence measures, emphasizing the shift from classical deterministic descriptions to a quantum probabilistic one.

M. S. Santhanam

Joanna K. Kalaga, M.W. Jarosik, Radosław Szczȩśniak +1 more

We consider a model of quantum nonlinear oscillator which is excited by a series of ultrashort coherent pulses.For such a system, we analyze the potential application of the normally ordered variances as a witness of quantum chaotic behavior.We concentrate on the relations between the generation of the squeezing effects and the appearance of the quantum chaotic behavior of the system.

A. G. Lazerson, Alexey Alexeevich Boikov

Ph. Blanchard, Arkadiusz Jadczyk, R. Olkiewicz

Departing from classical concepts of ergodic theory, formulated in terms of probability densities, measures describing the mixing behavior and the loss of information in quantum open systems are proposed. As application we discuss the chaotic outcomes of continuous measurement processes in the EEQT framework. Simultaneous measurement of four noncommuting spin components is shown to lead to a chaotic jumps on the quantum spin sphere and to generate specific fractal images of a nonlinear iterated function system. (C) 2001 Published by Elsevier Science B.V.