Anomalous diffusion in the resonant quantum kicked rotor

TL;DR

This paper investigates how deterministic time-dependent excitations affect the long-term spreading behavior of the quantum kicked rotor, revealing diverse diffusion regimes and analytical relations for primary resonances.

Contribution

It provides analytical and numerical insights into the long-time dynamics of the quantum kicked rotor under various resonant conditions with time-dependent excitation.

Findings

Different asymptotic spreading behaviors observed: super-ballistic, ballistic, sub-ballistic, diffusive, sub-diffusive, localized.

Analytical relation established between long-time standard deviation and kick strength for primary resonances.

Numerical results extend findings to secondary resonances, showing similar behavior.

Abstract

We study the resonances of the quantum kicked rotor subjected to an excitation that follows a deterministic time-dependent prescription. For the primary resonances we find an analytical relation between the long-time behavior of the standard deviation and the external kick strength. For the secondary resonances we obtain essentially the same result numerically. Selecting the time sequence of the kick allows to obtain a variety of asymptotic wave-function spreadings: super-ballistic, ballistic, sub-ballistic, diffusive, sub-diffusive and localized.