Quantum transport in a combined kicked rotor and quantum walk system

TL;DR

This paper investigates the interplay between ballistic transport and localization in a quantum system combining a kicked rotor and quantum walks, revealing complex effects on transport properties and localization lengths.

Contribution

It introduces a novel combined model of a quantum kicked rotor with quantum walks and analyzes the resulting transport and localization phenomena.

Findings

Localization occurs at larger times and lengths than predicted.

Combining with diffusive walks results in pure diffusion.

Localization persists with increased localization length when combined with localizing walks.

Abstract

We present a theoretical and numerical study of the competition between two opposite interference effects, namely interference-induced ballistic transport on one hand, and strong (Anderson) localization on the other. While the former effect allows for resistance free transport, the latter brings the transport to a complete halt. As a model system, we consider the quantum kicked rotor, where strong localization is observed in the discrete momentum coordinate. In this model, we introduce the ballistic transport in the form of a Hadamard quantum walk in that momentum coordinate. The two transport mechanisms are combined by alternating the corresponding Floquet operators. Extending the corresponding calculation for the kicked rotor, we estimate the classical diffusion coefficient for thecombined dynamics. Another argument, based on the introduction of an effective Heisenberg time should then allow to estimate the localization time and the localization length. While this is known to work reasonably well in the kicked rotor case, we find that it fails in our case. While the combined dynamics still shows localization, it takes place at much larger times and shows much larger localization lengths than predicted. Finally, we combine the kicked rotor with other types of quantum walks, namely diffusive and localizing quantum walks. In the diffusive case, the localizing dynamics of the kicked rotor is completely canceled and we get pure diffusion. In the case of the localizing quantum walk, the combined system remains localized, but with a larger localization length.