Classical Drift in the Arnold Web Induces Quantum Delocalization Transition

TL;DR

This paper shows that classical drift in the Arnold web causes quantum dynamical localization to break down, leading to increased exploration of the web and a universal delocalization transition in higher-dimensional Hamiltonian systems.

Contribution

It introduces the concept that classical drift induces a quantum delocalization transition in the Arnold web, supported by numerical evidence in a four-dimensional kicked Hamiltonian system.

Findings

Classical drift destroys quantum dynamical localization in the Arnold web.

The delocalization transition is universal and characterized by a single parameter.

Numerical simulations confirm the drift-induced transition in a 4D phase space system.

Abstract

We demonstrate that quantum dynamical localization in the Arnold web of higher-dimensional Hamiltonian systems is destroyed by an intrinsic classical drift. Thus quantum wave packets and eigenstates may explore more of the intricate Arnold web than previously expected. Such a drift typically occurs, as resonance channels widen toward a large chaotic region or toward a junction with other resonance channels. If this drift is strong enough, we find that dynamical localization is destroyed. We establish that this drift-induced delocalization transition is universal and is described by a single transition parameter. Numerical verification is given using a time-periodically kicked Hamiltonian with a four-dimensional phase space.