Assinaturas de dinâmica clássica em densidades locais de bilhares quânticos

• Main Author: Santos, Tatiane Pereira dos
• Other Authors: La Torre, Gustavo Michel Mendoza
• Format: Others
• Language: Portuguese
• Published: 2014
• Subjects: BILHARES QUÂNTICOS; DENSIDADE LOCAL DE ESTADOS; DINÂMICAS INTERMEDIÁRIAS; QUANTUM BILLIARDS; LOCAL DENSITY OF STATES; INTERMEDIATE DYNAMICS; PROGRAMA DE PÓS-GRADUAÇÃO EM FÍSICA - UFABC
• Online Access: http://www.biblioteca.ufabc.edu.brhttp://biblioteca.ufabc.edu.br/index.php?codigo_sophia=77189

Orientador: Prof. Dr Gustavo Michel Mendoza La Torre === Dissertação (mestrado) - Universidade Federal do ABC, Programa de Pós-Graduação em Física, 2014. === Classical billiards are versatile models for detecting efects of the billiard table over dynamical properties of Hamiltonian systems. Similarly, quantum billiards are ultra-small versions of the same table but now their properties are re ected on eigenvalues of the stationary Schrodinger equation for certain boundary conditions. Integrable and chaotic signatures must distinguish systems at any scale in order to ensure quantum-classical correspondence in the limit ~ ! 0. We demonstrate the classical properties that characterize system dynamics. Also, two intermediate cases are added to debate - mixed and pseudointegrable - for the understanding of possible transitions between dierent dynamics. To do so, the role of action-angle variables in Hamiltonian maps must be discussed. In the quantum context, we seek for ngerprints of classical properties through a systematic study on Local Density of States (LDOS) generated by Green's function numerical methods applied to a lattice representing a Tight-Binding Hamiltonian. We analyze scatisticically the distributions of LDOS from ground state to suciently high levels of energy, trying to identify new characteristics of these systems. This study aims to stimulate experimental measures on LDOS capable to map these signatures through an AFM tip (Atomic Force Microscopy).