Dynamical bounds for Sturmian Schrödinger operators

Author(s)

Vinícius Lourenço da Rocha

• Document type: Master's Dissertation
• Press: Presidente Prudente. 2016-02-17.
• Institution: Universidade Estadual Paulista (Unesp). Faculdade de Ciências e Tecnologia. Presidente Prudente
• Defense date: 2016-02-10
• Advisor: Roberto de Almeida Prado

Abstract

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. (AU)

• FAPESP's process: 14/04321-9 - Dynamical Bounds for Sturmian Schrodinger Operators
• Grantee: Vinícius Lourenço da Rocha
• Support Opportunities: Scholarships in Brazil - Master