Research On Wave Packet Diffusion In Periodic Driven Nonlinear Systems

The research on quantum diffusion is significant in physics.Studying the diffusion of electrons in different systems is of great significance for us to master the transport properties of electrons in this system.It provides necessary theoretical basis for studying new materials.In the field of condensed matter physics,Anderson localization is an old and important issue,and is still the key research now.In 1958,Anderson first proved that the wave packet is localized in disordered systems,where the wave packet dose not diffuse with time.Thus the method of wave packet dynamics we take to study the diffu-sion properties of the system is appropriate.In recent years,the technological progress of Feshbach resonances attracts lots of people to study the effects of nonlinear interaction on the diffusion properties of the system in experiments.The nonlinear system can be described by the Gross-Pitaevskii(GP)equation,which includes a nonlinear term intro-duced at the mean-field level.Therefore the theoretical work on the wave packet dynamics in one-dimensional nonlinear systems have also attracted much attention.On the other hand,dynamical localization was originally observed experimentally in atom-optics-based realization of the kicked quantum rotors,which has inspired a renewed interest in the the-oretical study of the kicked systems.Therefore,in this paper,we study the dynamics of wave packets in periodically kicked nonlinear systems.Firstly,we study the diffusion properties of the wave packet in the system with a kicked nonlinear term using the method of numerical calculation.We put a localized wave packet(delta.function)in the middle of the one-dimensional chain,where the on-site potential is quasiperiodic.We find that the diffusion property is relevant to both the kicking period and the nonlinearity strength.In the high-frequency and weak interaction case,when ? = 0,the periodically kicked nonlinearity suppresses the diffusion.That is,there exists a self-trapping transition point depending on the value of ?/T for ?<2,while in the regime of ?>2,the localization will become more efficient as ?/T increases.We also find that the diffusion property is quite ?-dependent.When ? = ?,there is also a similar self-trapping transition point in the regime of A<2,but the self-trapping is less efficient.Furthermore,in the regime of A>2.the wave packet has a transition from self-trapping to subdiffusion.Furthermore,our theoretical analysis shows that the dynamics of this system can be described by an effective Hamiltonian in the high-frequency and weak interaction regime.However,as the system deviates from the high-frequency and weak interaction regime,the dynamics of the wave packet.will become more complex and cannot be obtained analytically.Then we study the dynamics of the wave packet in the nonlinear AA model with a kicked on-site potential in the high-frequency regime.Here we still put a localized wave packet(delta function)in the middle of the one-dimensional chain.The results show that the wave packet has different diffusion properties at different kicking frequencies and strengths.That is,when ?/T>2.the wave packet is localized no matter how strong the nonlinear strength is.Furthermore,the wave packet is more localized with stronger nonlinear strength.However,when ?/T<2,the wave packet is self-trapped as the nonlinear strength reaches a critical value ?c,and the self-trapping transition point is the same as long as the ratio of the driving strength and period is fixed.Further theoretical analysis shows that the dynamics of this system can be described by the effective Hamiltonian in the high-frequency regime.