Barrier induced chaos in kicked rotor : classical sub-diffusion and quantum localization

TL;DR

This paper investigates how a discontinuous potential barrier in a kicked rotor system induces classical chaos and sub-diffusion, and how these features influence quantum localization, revealing a link between classical and quantum chaotic behaviors.

Contribution

It demonstrates that a discontinuous barrier causes multiple sub-diffusive regimes and affects quantum localization through non-KAM classical dynamics, a novel insight into quantum-classical chaos relations.

Findings

Discontinuous barriers induce classical chaos and multiple sub-diffusive regimes.

Quantum localization reflects non-KAM classical dynamics via quantum break time.

Sub-diffusion exponents influence quantum localization properties.

Abstract

The relation between classically chaotic dynamics and quantum localization is studied in a system that violates the assumptions of Kolmogorov-Arnold-Moser (KAM) theorem, namely, kicked rotor in a discontinuous potential barrier. We show that the discontinuous barrier induces chaos and more than two distinct sub-diffusive energy growth regimes, the latter being an unusual feature for Hamiltonian chaos. We show that the dynamical localization in the quantized version of this system carries the imprint of non-KAM classical dynamics through the dependence of quantum break time on sub-diffusion exponents. We briefly comment on the experimental feasibility of this system.