The Influence Of Time Disorder In A One-dimensional Drive System

In the study of condensed matter physics,the study of electron transport properties has always been an important topic.The law of electron diffusion plays an important role in the research and the development of new materials.The disorder regulation in Anderson system can lead to the transition between metal and insulator,making the localization of Anderson has always been an important research direction.In 1958,Anderson predicted the localization of electron wave functions in disordered lattices,and confirmed by numerical calculations that the wave function will not diffuse with time and is in a localized state.In addition to disordered system,quasi-periodic systems also have an effect on the localization of wave functions.This phenomenon has been fully studied in the Aubry-André(AA)model.At the same time,in the study of periodically kicked quantum rotors,the concept of localization of dynamics in the momentum space was proposed,so Shu Chen's research team proposed a periodically kicked AA model,which was a great breakthrough,the study found that under the double influence of on-site potential energy ? and kicked period T,the localization of dynamics in space can be achieved.On the other hand,under the revelation of the spontaneous symmetry breaking based on the quantum state destroying the symmetry implied by its original Hamiltonian quantity,Wilczek proposed the concept of time crystal to study the existence of time translation symmetry breaking.After further research,it was proposed that a many-body Floquet system,with periodic driving,can form a stable time crystal.In this paper,we studied the periodically kicked AA model with temporal disorder or quasi-periodicity,to study the effect on the wave packet dynamics along a one-dimensional chain.And the effect of temporal disorder on the formation of time crystal.Firstly,we investigate the effect of temporal disorder or quasi-periodicity in onedimensional kicked lattices with pulsed on-site potential.We found that,unlike the spatial disorder or quasi-periodicity which usually leads to localization,the effect of the temporal one is more complex and depends on the spatial configuration.If the kicked on-site potential is periodic in real space,then the wave packet will stay diffusive in the presence of temporal disorder or quasi-periodicity.On the other hand,if the kicked on-site potential is spatially quasi-periodic,then the temporal disorder or quasi-periodicity may lead to a shift of the transition point of the dynamical localization and destroy the dynamical localization in a certain parameter range.The results we obtained can be readily tested by experiments and may help us better understand the dynamical localization.Then we studied the effect of temporal disorder on the formation of time crystal,when we added the temporal disorder pairs in the many-body Floquet system can form a stable discrete time crystal,using numerical calculation.We found that the disorder of time also have affects to the formation of time crystal.We get a summary that the temporal disorder has a similar effect to perturbation.All of them hinder the formation of time crystal.Adding the nearest interaction between two spins can resist the effects of a certain range of perturbations or temporal disorder on the formation of the discrete time crystal.