Chaotic scattering in the presence of time-dependente external fields

• Grant number: 15/26120-8
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: July 01, 2016
• End date: December 31, 2016
• Field of knowledge: Physical Sciences and Mathematics - Physics - General Physics
• Principal Investigator: Emanuel Fernandes de Lima
• Grantee: Igor César de Almeida
• Host Institution: Centro de Ciências Exatas e de Tecnologia (CCET). Universidade Federal de São Carlos (UFSCAR). São Carlos , SP, Brazil

Abstract

In this work, we intent to investigate the scattering dynamics based on the Hénon-Heiles model. The Hénon-Heiles potential is a 2D potential, which varies from an approximately harmonic shape for small displacements around the origin to three equipotential lines forming a triangle, which separates bound and unbound motion. If the energy of the particle is below a threshold value, called the escape energy, the particle is trapped inside the well; otherwise, the particle undergoes unbound motion. A particle coming from infinity with an energy greater than the escape energy may enter the region where the potential is approximately harmonic, called the scattering region, and, after some period, the particle escapes again to infinity. The final conditions of speed and direction depend on the initial conditions in an extremely sensible way, which is a characteristic of chaotic scattering. The focus of the present project is in the Hénon-Heiles potential under the action of time-dependent external fields. The presence of external perturbations alters the phase space structure and consequently the scattering dynamics. We consider bichromatic external fields, consisting of two commensurate frequencies with a fixed phase difference between the frequencies. We will investigate the effects of changing these frequencies, as well of changing the relative phase, on the system dynamics. The system dynamics will be investigated through the analysis of the phase space, the escape basin, and the decaying law from the scattering region. We aim with this study to extend the results of the literature, exploring the possibility of controlling the escape dynamics, and consequently the scattering, through the manipulation of the field parameters.