Escaping particles from a stadium billiard: comparison of static and time-dependent boundaries

• Grant number: 12/17945-5
• Support Opportunities: Scholarships abroad - Research Internship - Scientific Initiation
• Start date: January 05, 2014
• End date: March 04, 2014
• Field of knowledge: Physical Sciences and Mathematics - Physics - General Physics
• Principal Investigator: Edson Denis Leonel
• Grantee: Matheus Palmero Silva
• Supervisor: Carl Dettmann
• Host Institution: Instituto de Geociências e Ciências Exatas (IGCE). Universidade Estadual Paulista (UNESP). Campus de Rio Claro. Rio Claro , SP, Brazil
• Institution abroad: University of Bristol, England
• Associated to the scholarship: 12/00556-6 - Studying the decay of energy in a time-dependent stadium bilhar: the conservative case, BP.IC

Abstract

Dynamical systems described by the so called billiard formalism are fundamental and relevant for the understanding of numerous phenomena, particularly those observed in statistical mechanics, Hamiltonian dynamics, nonlinear physics and many others. Such an approach has yielded many insights into fundamental ideas like the Boltzmann ergodic hypothesis and hence the foundations of statistical physics, deterministic diffusion, scaling laws, and phase transitions. Moreover, very important and realistic results can be obtained if billiard systems are considered under the effect of a time-dependent boundary perturbation. Such systems constitute anatural generalization of mathematical billiards and therefore successfully explain observed physical phenomena like diffusion, Fermi acceleration, transport of particles etc. When a hole is introduced in the boundary, the particle is allowed to escape the billiard region. It is known that, for fully chaotic dynamics, the recurrence time distribution, i.e. the time the particle stays confined in the billiard domain, is characterized by an exponential decay. On the other hand, for intermittent including mixed phase space dynamics where there is stickiness, generated from a finite time (but arbitrarily long) trapping near periodic/elliptic regions, a power law and/or stretched exponential decay is observed. In this project, our goal is to study and describe theescape from the stadium billiard using both static and time-dependent boundaries. Many results are known in the literature for the static case due to the group of Prof. Dettmann. On the other hand, our project deals with the description on the time-dependent stadium billiard. We intend to joint efforts to understandand describe some properties for the escape dynamics considering the time-dependent perturbation. (AU)