TITLE:
Revival of Order in the Chaotic Dynamics with Position and Time Dependent Perturbed System
AUTHORS:
Lylyane S. Yonya Tchapda, Martin Tchoffo, Mercel Vubangsi, Faustin B. Migueu, Lukong C. Fai
KEYWORDS:
Schrödinger Equation, Crossing, Chaotic Dynamics, Perturbed System, Harmonic Oscillator
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.8 No.11,
November
30,
2020
ABSTRACT: 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.