Exponential Quantum Spreading in a Class of Kicked Rotor Systems near High-Order Resonances

TL;DR

This paper investigates the mechanisms behind long-lasting quantum exponential spreading in high-order resonance kicked rotor systems, revealing the role of flat-band structures and providing a framework for understanding this phenomenon.

Contribution

It introduces a comprehensive framework using spinor representation and Born-Oppenheimer approximation to explain quantum exponential spreading near high-order resonances.

Findings

Existence of flat-band structures facilitates exponential spreading.

Quantitative predictions based on pseudoclassical maps may be inaccurate.

The framework applies to a broader class of high-order resonance conditions.

Abstract

Long-lasting quantum exponential spreading was recently found in a simple but very rich dynamical model, namely, an on-resonance double-kicked rotor model [J. Wang, I. Guarneri, G. Casati, and J. B. Gong, Phys. Rev. Lett. 107, 234104 (2011)]. The underlying mechanism, unrelated to the chaotic motion in the classical limit but resting on quasi-integrable motion in a pseudoclassical limit, is identified for one special case. By presenting a detailed study of the same model, this work offers a framework to explain long-lasting quantum exponential spreading under much more general conditions. In particular, we adopt the so-called "spinor" representation to treat the kicked-rotor dynamics under high-order resonance conditions and then exploit the Born-Oppenheimer approximation to understand the dynamical evolution. It is found that the existence of a flat-band (or an effectively flat-band) is one important feature behind why and how the exponential dynamics emerges. It is also found that a quantitative prediction of the exponential spreading rate based on an interesting and simple pseudoclassical map may be inaccurate. In addition to general interests regarding the question of how exponential behavior in quantum systems may persist for a long time scale, our results should motivate further studies towards a better understanding of high-order resonance behavior in delta-kicked quantum systems.