Quantum Dynamics of Chaotic Systems

M. S. Santhanam

Jincheng Zhang

This paper investigates the analysis of chaotic system dynamics using quantum simulation, aiming to construct a robust quantum simulation framework for enhanced understanding. The core of this research lies in leveraging the unique quantum properties of simulation to reveal intricate dynamics within complex systems. We present a novel approach that utilizes quantum mechanics to model and analyze chaotic behavior, resulting in a framework capable of probing fundamental aspects of these phenomena. The investigation focuses on building a quantum simulation framework to provide a deeper insight into the underlying mechanisms driving chaotic behavior. This work represents a significant advance in the field of chaotic system dynamics, potentially offering a more accurate and insightful approach compared to traditional simulation methods.

Boris V. Chirikov

Lylyane S. Yonya Tchapda, Martin Tchoffo, M. Vubangsi +2 more

Studying quantum properties of a system has been quite popular in quantum mechanics. One of the most important systems that are very crucial to the framework of quantum mechanics is the system of harmonic oscillator a system whose classical evolution is known to exhibit peculiar chaotic dynamics. We are motivated to investigate the behavior of quantum properties for a system with position and time dependent perturbed. Starting with Hamiltonian, we determined the equation of motion and obtained the wave function. The energy of the whole system using the operator ordering method was found. We show that the quantum mechanical picture alludes to a chaotic dynamics as expected. This is evidenced through the appearance of energy level crossings. An additional signature to this chaotic dynamics is observed in the transition of Eigen values from real to imaginary. We also show numerically that one can give the behavior of the system is Poincare section. By so doing we confirmed that increasing and decreasing the perturbation amplitude of the system becomes chaotic.

Giulio Casati, Boris V. Chirikov

The nature of classically chaotic quantum dynamics is studied by menas of a numerical time reversal experiment. It turns out that there is a fundamental quantum scale below which the system cannot exhibit classical irreversibility to external perturbations. On the other hand, a paradoxical phenomenon manifesting that quantum irreversibility may exceed its classical counterpart is discovered. These features are explained in terms of semicalssical dynamical theory. Introduction Classically chaotic quantum systems in general can exhibit intrinsinc chaotic behaviour on a quite restricted time scale [1], In particular localization phenomena provide direct evidence exhibiting the suppression of quantum ergodicity [2]. On the other hand, recent studies reveal that a many-dimensional system can mimic some aspects peculiar to chaotic dynamics quite well on an unexpectedly long time scale [3]. A remarkable feature that distinguishes chaotic motion from integrable motion is the sensitive dependence of dynamics on external perturbations. For classical dynamical systems such a sensitivity can be well defined by measuring how two nearby trajectories in the phase space separate in time. However, there has been proposed no systematic way to examine the sensitivity of quantum dynamics to external perturbation. In quantum dynamics, it is not possible to trace a well defined trajectory in phase space, because both quantum uncertainty and chaotic instability make a localized wavepacket spread suddenly over the phase space [4]. There is, however, a simple way in which we may test the quantum sensitivity quantitively. This is the time reversal experiment described below. In this chapter I describe several remarkable characteristics of quantal instability which have been clarified by the time reversal experiment.

A. G. Lazerson, Alexey Alexeevich Boikov