Classical-quantum localization in one dimensional systems: The kicked rotor

Abstract

This work explores the origin of dynamical localization in one-dimensional systems using the kicked rotor as an example. In particular, we propose the fractal dimension of the phase space as a robust indicator to characterize the onset of classical chaos. As a result, we find that the system crosses the stability border when the fractal dimension ≥1.81, and we obtain a functional form for the fractal dimension as a function of the kick strength. At the same time, dynamical localization is explored in the quantum realm by looking into the energy–localization relationship across the classical stability border, thus finding a correlation between the classical chaos and the presence of dynamical localization.