Relativistic quantum chaos

Author(s)

Rafael Soares Pinto

• Document type: Master's Dissertation
• Press: Campinas, SP.
• Institution: Universidade Estadual de Campinas (UNICAMP). Instituto de Física Gleb Wataghin
• Defense date: 2011-05-05

Examining board members

Patricio Anibal Letelier Sotomayor; Alberto Vazquez Saa; Márcio José Menon

• Advisor: Patricio Anibal Letelier Sotomayor; Marcus Aloizio Martinez de Aguiar

Abstract

In this dissertation we analyze billiards using the theory of special relativity, both in the classical and quantum versions. First we review classical billiards, with emphasis in its time evolution. Then we study the existence (or lack of) Fermi acceleration in driven billiards, billiards where the walls are moving and, when the particle collides, it can gain or lose energy. We studied some examples, regular and chaotic ones, in the relativistic dynamics, and analyzed the necessary conditions for the existence of relativistic Fermi acceleration. We focus then on quantum billiards. After a brief review of basic concepts, we study the boundary integral method for numerical evaluation of the billiard spectra and analyze its statistical properties, for the non-relativistic case (the Schroedinger equation) and the relativistic, the Dirac billiards introduced by Berry and Mondragon (AU)

• FAPESP's process: 09/02978-2 - Relativistic Quantum Chaos
• Grantee: Rafael Soares Pinto
• Support Opportunities: Scholarships in Brazil - Master