Chaotic diffusion in time dependent billiards

• Grant number: 20/07219-1
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Effective date (Start): September 01, 2020
• Effective date (End): August 31, 2021
• Field of knowledge: Physical Sciences and Mathematics - Physics - General Physics
• Principal Investigator: Edson Denis Leonel
• Grantee: Anne Kétri Pasquinelli da Fonseca
• Host Institution: Instituto de Geociências e Ciências Exatas (IGCE). Universidade Estadual Paulista (UNESP). Campus de Rio Claro. Rio Claro , SP, Brazil

Abstract

The thematic line of this project is the investigation of the dynamical properties of a classical billiard with time dependent boundary. The Loskutov-Ryabov-Akhinshin (LRA) conjecture claims that if a billiard exhibits chaotic components in the dynamics with the fixed boundary, such a component is a sufficient condition to produce Fermi acceleration (unlimited energy growth) when a time perturbation to the boundary is introduced. It is known that the introduction of inelastic collision of the particle with the boundary creates attractors in the phase space violating the Liouville's theorem hence suppressing the Fermi acceleration. In such a transition of limited to unlimited energy growth, a set of particle shows that the mean squared velocity is described by an homogeneous and generalized function exhibiting a set of critical exponent that describes the dynamics near the criticality. Recent results in the literature (J. Stat. Phys. {\bf 170}, 69 (2018)) allow one to describe the chaotic dynamics of the particles from the probability to observe a particle with a given velocity at a certain time. Such a probability is obtained from the solution of the diffusion equation imposing specific boundary and initial conditions. In this project our aim is to obtain the expression of the probability from the diffusion equation and from it obtain all the observables of the dynamics recovering the critical exponents known from the literature. This procedure is original for such a type of system and allows an immediate extension of the formalism published in J. Stat. Phys. {\bf 170}, 69 (2018) for the billiard systems.

Scientific publications

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

MIRANDA, LUCAS K. A.; KUWANA, CELIA M.; HUGGLER, YONA H.; DA FONSECA, ANNE K. P.; YOSHIDA, MAKOTO; DE OLIVEIRA, JULIANO A.; LEONEL, EDSON D.. A short review of phase transition in a chaotic system. European Physical Journal-Special Topics, DEC 2021. (20/10602-1, 18/14685-9, 19/14038-6, 20/07219-1)