Control of Classical Dynamics in the Morse-Coulomb potential

• Grant number: 23/00690-9
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: May 01, 2023
• End date: April 30, 2026
• Field of knowledge: Physical Sciences and Mathematics - Physics - General Physics
• Principal Investigator: Emanuel Fernandes de Lima
• Grantee: Gabriel Albertin Amici
• Host Institution: Centro de Ciências Exatas e de Tecnologia (CCET). Universidade Federal de São Carlos (UFSCAR). São Carlos , SP, Brazil

Abstract

In this project, we propose the study of the classical dynamics of a particle in the forcedMorse-Coulomb potential. This is a new potential in the literature of Coulombbehavior in the long range linked to a repulsive barrier of the Morse potential type. This potential asymptotically describes the Coulomb potential and is continuous and differentiableup to second order. The potential also has a parameter that makes it possible to adjust thedegree of hardness of the repulsive part along with the depth of the potential well. In thepresence of time-dependent external fields, this model presents chaotic dynamics associatedwith the anharmonicity of the potential and the coupling with the external field. In thisproject, we intend to use the Optimal Control Theory (OCT) to find control fields for thissystem. In the OCT formalism, the external field is considered the control function of thesystem, which must be determined by maximizing a performance criterion. We will seek tofind optimized fields for various performance criteria, numerically solving the Euler-Lagrangeequations associated with the control problem. The central point of the project will be toverify to what extent the control fields of the Morse-Coulomb potential are effective forcontrolling dynamics in the Coulomb potential, thus providing an alternative non-singularpotential for the study of the hydrogen atom. In this way, the research project will allow thedevelopment of theoretical and computational skills of the candidate, as well as providingan investigation of an unprecedented system with the potential for new discoveries.