Limites dinâmicos para operadores de Schrödinger com potenciais Sturmianos

• Ano de defesa: 2016
• Autor(a) principal: Rocha, Vinícius Lourenço da [UNESP]
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Universidade Estadual Paulista (Unesp)
• Palavras-chave em Português: Schrödinger operators; Sturmian potentials; Dynamical bounds; Operadores de Schrödinger; Potenciais Sturmianos; Limites dinâmicos
• Link de acesso: http://hdl.handle.net/11449/134286

By following recent papers in the literature, the present work aims to study dynamical bounds for one dimensional discrete Schrödinger operators with Sturmian potentials by bounding the rates of propagation of the wavepacket. By a method developed by Damanik and Tcheremchantsev, is obtained a non trivial upper bound for almost all Sturmian Schrödinger operator associated with irrational numbers. Moreover, it presents a global lower bound for the upper box counting dimension of the spectrum of these operators, which is used to obtain a lower dynamical bound for such Sturmian Schrödinger operators associated with bounded density irrational numbers. Will be used results about the traces of transfer matrices and spectral properties of Sturmian Schrödinger operators.