title: Exponential quantum spreading in a class of kicked rotor systems near high-order resonances.
abstract: Long-lasting exponential quantum 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 exponential quantum 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 toward a better understanding of high-order resonance behavior in δ-kicked quantum systems.
authors: Department of Physics and Centre for Computational Science and Engineering, National University of Singapore, Singapore 117546, Republic of Singapore.
authors: Hailong
authors: H
authors: Wang
authors: Department of Physics and Institute of Theoretical Physics and Astrophysics, Xiamen University, Xiamen 361005, China.
authors: Jiao
authors: J
authors: Wang
authors: Center for Nonlinear and Complex Systems, Università degli Studi dell' Insubria, Via Valleggio 11, 22100 Como, Italy.
authors: Italo
authors: I
authors: Guarneri
authors: Center for Nonlinear and Complex Systems, Università degli Studi dell' Insubria, Via Valleggio 11, 22100 Como, Italy.
authors: Giulio
authors: G
authors: Casati
authors: Department of Physics and Centre for Computational Science and Engineering, National University of Singapore, Singapore 117546, Republic of Singapore and NUS Graduate School for Integrative Science and Engineering, Singapore 117597, Republic of Singapore.
authors: Jiangbin
authors: J
authors: Gong