Dynamical Localization of Coupled Relativistic Kicked Rotors

TL;DR

This paper investigates dynamical localization in nonintegrable quantum relativistic kicked rotors, demonstrating its persistence in few-body systems and exploring the interplay between Anderson localization and integrability, with implications for many-body localization.

Contribution

It extends the study of dynamical localization to nonintegrable QRKRs, bridging the gap between quadratic and linear models, and suggests many-body localization can occur in generic systems.

Findings

Dynamical localization persists in few-body QRKR systems.

Interactions relax resonance conditions, leading to superballistic regimes.

Proposes experimental realizations in cold atom systems.

Abstract

A periodically driven rotor is a prototypical model that exhibits a transition to chaos in the classical regime and dynamical localization (related to Anderson localization) in the quantum regime. In a recent work [Phys. Rev. B 94, 085120 (2016)], A. C. Keser et al. considered a many-body generalization of coupled quantum kicked rotors, and showed that in the special integrable linear case, dynamical localization survives interactions. By analogy with many-body localization, the phenomenon was dubbed dynamical many-body localization. In the present work, we study nonintegrable models of single and coupled quantum relativistic kicked rotors (QRKRs) that bridge the gap between the conventional quadratic rotors and the integrable linear models. For a single QRKR, we supplement the recent analysis of the angular-momentum-space dynamics with a study of the spin dynamics. Our analysis of two and three coupled QRKRs along with the proved localization in the many-body linear model indicate that dynamical localization exists in few-body systems. Moreover, the relation between QRKR and linear rotor models implies that dynamical many-body localization can exist in generic, nonintegrable many-body systems. And localization can generally result from a complicated interplay between Anderson mechanism and limiting integrability, since the many-body linear model is a high-angular-momentum limit of many-body QRKRs. We also analyze the dynamics of two coupled QRKRs in the highly unusual superballistic regime and find that the resonance conditions are relaxed due to interactions. Finally, we propose experimental realizations of the QRKR model in cold atoms in optical lattices.