Criticality in the Quantum Kicked Rotor with a Smooth Potential

TL;DR

This paper explores the existence of a localization-delocalization transition in the quantum kicked rotor with a smooth potential, revealing critical behavior and symmetry-driven transitions akin to those in disordered metals.

Contribution

It demonstrates the presence of an Anderson-like transition and symmetry-breaking induced transitions in the quantum kicked rotor, expanding understanding of quantum chaos and localization phenomena.

Findings

Identification of multifractal eigenfunctions at criticality

Observation of scale-invariant level statistics at transition

Discovery of symmetry-breaking transitions within chaotic regimes

Abstract

We investigate the possibility of an Anderson type transition in the quantum kicked rotor with a smooth potential due to dynamical localization of the wavefunctions. Our results show the typical characteristics of a critical behavior i.e multifractal eigenfunctions and a scale-invariant level-statistics at a critical kicking strength which classically corresponds to a mixed regime. This indicates the existence of a localization to delocalization transition in the quantum kicked rotor. Our study also reveals the possibility of other type of transitions in the quantum kicked rotor, with a kicking strength well within strongly chaotic regime. These transitions, driven by the breaking of exact symmetries e.g. time-reversal and parity, are similar to weak-localization transitions in disordered metals.