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

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.

12 pages, 10 figures

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• Super-exponential diffusion in nonlinear non-Hermitian systems
• Quantum and Classical Superballistic Transport in a Relativistic Kicked-Rotor System
• Superballistic wavepacket spreading in double kicked rotors
• Designing nontrivial one-dimensional Floquet topological phases using a spin-1/2 double-kicked rotor
• A pseudoclassical theory for the wavepacket dynamics of the kicked rotor model
• Quantum Properties of Double Kicked Systems with Classical Translational Invariance in Momentum