Dynamic Properties Of Classical Excited Rotors Under Phase Modulation

Diffusion phenomenon exists widely in physics,chemistry,biology,finance and oth-er fields.The study of the diffusion behavior of particles in different systems,helps to grasp the transport properties of the system and to provide important theoretical basis for the research,development and preparation of new materials.The diffusion properties of linear system have been widely studied,but most systems in nature are disordered and nonlinear.Therefore,the study of the diffusion properties of nonlinear systems is more important.Most nonlinear systems cannot be solved accurately,but with the pop-ularization of computer and the development of modern computing technology,people can gradually use numerical methods to study nonlinear systems.The kicked rotor is a paradigm for the study of the diffusion behavior of classical nonlinear systems.The model is not only simple,but also can show rich dynamical phenomena.It is found that the kinetic energy of the kicked rotor undergos a transition in the classical standard kicked rotor system.When the kicking intensity K is relatively small(such as K=0.01),the kinetic energy does not increase with time,but tends to saturate.When the kicking in-tensity K is large(such as K=3),the kinetic energy increases with time.In this paper,based on the classical standard kicked rotor model,we systematically study the effect of phase modulation on the particle dynamics properties,and present the numerical results and figures.At first,we study the dynamical properties of the standard kicked rotor,and calculate the energy growth from four different initial conditions.It is found that there are reso-nance and anti-resonance phenomena in the standard kicked rotor system,and the forms of energy diffusion are localization,normal diffusion and anomalous diffusion.Secondly,we study the dynamical properties of the first and the second kind of the periodically shift-ed kicked rotor.It is found that the resonance and anti-resonance phenomena also occur in the first type of periodically shifted kicked rotor system.There are also three kinds of energy diffusion:localization,normal diffusion and anomalous diffusion.In the second type of periodically shifted kicked rotor system,only resonance phenomenon occurs and the energy shows only ballistic diffusion.Then,the dynamical properties of the randomly kicked rotor are studied.It is found that the energy variation of the classical randomly kicked rotor always shows normal diffusion.Finally,the dynamical properties of the cosine quasi-periodically kicked rotor and two generalized Fibonacci quasi-periodically kicked rotors are studied.Although the phase a_nseems to form a pseudo-random sequence in the quasi-periodically kicked rotor system,its dynamical behavior is different from that of the randomly kicked rotor.Specifically,the expected value of the rotor’s energy growth?L_n~2?is localized even at a relatively large number of kicks at a relatively small kicking intensity,such as K=0.01.When the kicking intensity is relatively large,such as K=6.7,the dynamical behavior of the cosine quasi-periodically kicked rotor is the similar to that of the randomly kicked rotor,which shows normal diffusion.In the first type of generalized Fibonacci quasi-periodically kicked rotor,the energy will undergo the transformation from subdiffusion to normal diffusion with the change of kicking intensity K.In the second type of generalized Fibonacci quasi-periodically kicked rotor,the energy is normally diffused,and there is no subdiffusion to normal diffusion transition similar to that in the first type of generalized Fibonacci quasi-periodically kicked rotor.