Classical dynamical localization

TL;DR

This paper explores classical models of the kicked rotor that exhibit momentum localization and energy growth behaviors similar to quantum dynamical localization, challenging the notion that such phenomena are purely quantum effects.

Contribution

It introduces classical models with specific kicking potentials that mimic quantum dynamical localization and resonances, providing a classical explanation for these phenomena.

Findings

Classical models show momentum quasi-localization and energy growth.

Classical phase space analysis maps to a disordered tight-binding model.

Results suggest classical origins for phenomena previously attributed to quantum coherence.

Abstract

We consider classical models of the kicked rotor type, with piecewise linear kicking potentials designed so that momentum changes only by multiples of a given constant. Their dynamics display quasi-localization of momentum, or quadratic growth of energy, depending on the arithmetic nature of the constant. Such purely classical features mimic paradigmatic features of the {\it quantum} kicked rotor, notably dynamical localization in momentum, or quantum resonances. We present a heuristic explanation, based on a classical phase space generalization of a well known argument, that maps the quantum kicked rotor on a tight-binding model with disorder. Such results suggest reconsideration of generally accepted views, that dynamical localization and quantum resonances are a pure result of quantum coherence.