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).
| Identifer | oai:union.ndltd.org:IBICT/oai:BDTD:77189 |
| Date | January 2014 |
| Creators | Santos, Tatiane Pereira dos |
| Contributors | La Torre, Gustavo Michel Mendoza, Nascimento, Roberto Venegeroles, Aguiar, Marcus Aloizio Martinez de |
| Source Sets | IBICT Brazilian ETDs |
| Language | Portuguese |
| Detected Language | English |
| Type | info:eu-repo/semantics/publishedVersion, info:eu-repo/semantics/masterThesis |
| Format | application/pdf, 139 f. : il. |
| Source | reponame:Repositório Institucional da UFABC, instname:Universidade Federal do ABC, instacron:UFABC |
| Rights | info:eu-repo/semantics/openAccess |
| Relation | http://biblioteca.ufabc.edu.br/index.php?codigo_sophia=77189&midiaext=70563, http://biblioteca.ufabc.edu.br/index.php?codigo_sophia=77189&midiaext=70564, Cover: http://biblioteca.ufabc.edu.brphp/capa.php?obra=77189 |
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