Accelerator modes and their effect in the diffusion properties in the kicked rotator

Abstract

We highlight a few recent results on the effect of the diffusion process in deterministic area preserving maps with noncompact phase space, namely the standard map. In more detail, we focus on the anomalous diffusion arising due to the accelerator modes, i.e. resonant-like features of the phase space which are transported in a super-diffusive (ballistic) manner. Their presence affects also the trajectories lying in the immediate neighborhood resulting in anomalous (non-Gaussian) diffusion. We aim to shed some light on these special properties of the phase space by utilizing the diffusion exponent (rate of diffusion) and the momentum distribution in terms of the Lévy stable distributions, with the goal to reach an understanding of the global behaviour. To this end we consider a rather large interval for the kick parameter ($0\le K\le 70$) of the standard map where accelerator modes of different periodicity exist.

arXiv comment5 pages, 3 figures, proceedings of the Conference "New Challenges in Complex Systems Science", Waseda University, Tokyo, Japan, October 2014

References in corpus (5)

• The Lyapunov Characteristic Exponents and their computation
• Geometrical properties of local dynamics in Hamiltonian systems: the Generalized Alignment Index (GALI) method
• Detecting chaos, determining the dimensions of tori and predicting slow diffusion in Fermi--Pasta--Ulam lattices by the Generalized Alignment Index method
• Survey on the role of accelerator modes for anomalous diffusion: The case of the standard map
• Dynamical localization in chaotic systems: spectral statistics and localization measure in the kicked rotator as a paradigm for time-dependent and time-independent systems