Static and dynamical properties of a one-dimensional model with long-range couplings

Quantum systems can be characterized by studying its static and dynamical properties. Some of these properties are related, for example, correlations between energy levels are manifested as a “hole” in the dynamics of the survival probability (SP), also the saturation value of SP coincides with the inverse participation ratio of the initial state. These facts let us infer some results of the dynamics by studying the static properties and vice versa. We will present our studies about the one-dimensional Anderson model with long range couplings. Specifically, we explore how the properties of the system depend on the range of the couplings, disorder strength and system size. In particular, by means of the survival probability and the imbalance, we present an analysis of two relevant time scales, the Thouless time and the saturation time.