Estimativas de magnitudes da dinâmica quântica envolvendo dimensões de Hausdorff e de empacotamento

Abstract

In this work we approach the nonrelativistic quantum mechanics from the point of view of mathematical physics; we present estimates of some dynamical quantities that are used to describe the return probability to the initial state. Such estimates are related to Hausdorff and packing dimensions of the relevant spectral measures. After defining such dimensions we discuss some tools to characterize the quantum dynamics of a particle in one dimension. Then we summarize some standard facts from the literature and the quantities we are interested in. Finally, as an application, estimates of some dynamical quantities based on concepts from statistical mechanics are presented.