A Theoretical Study Of Dynamic Localization Regulation In Quantum Many-body Systems

The behavior of quantum many-body system has been widely concerned in recent years.The research on the dynamics and the nonequilibrium state involved in it is worth of discussing.However,the research on this aspect is still in the initial stage.Some researches show that the non-thermal phenomenon will appear in the evolution of many-body system,which is called dynamic localization.The discovery of this phenomenon is helpful to understand quantum effect.It plays an important role and provides guidance for the related experiments and applications of cold atoms.However,there is no deep understanding of the causes of dynamic localization in quantum many-body systems.The influence of various parameters on dynamic localization is unclear.When dynamic localization behavior is required,which parameters can be controlled to achieve,and when the system is needed to be heated,which parameters can be controlled are all the problems to be solved.The previous work shows that the weaker the driving is in the process of system evolution,the easier the dynamic localization behavior is to occur,and the stronger the disturbance,the more likely the system will be heated.In this paper,it is found that in addition to the disturbance of the system in the evolution process,the dynamic localization and heating of the evolution will be affected by the disturbance of the system,and other parameters will affect the dynamic localization effect.Based on the one-dimensional Heisenberg spin chain as a model,the research on the dynamic evolution of quantum multibody systems is carried out.The range of random potential field,the size of coupling parameters,the time of pulse opening and closing in the process of evolution are regulated in order to observe the influence of various parameters on dynamic localization and to conduct relevant phenomena.In addition,it is found that the system is different from the ideal thermalization when it tends to be in the equilibrium of heating up.The heat up is a state between ideal thermalization and ideal localization.The main results are as follows:1.The first coupling coefficient J is set by using one-dimensional Heisenberg spin chain as the main system model Jx=Jy=2,Jz=1,random potential range W=1,and weak evolution pulse ton=1.0,toff=100.0,hz=1.0.The evolution behavior of these parameters presents dynamic localization,and the strength and coupling coefficient of random potential are gradually increased.The constraints of dynamic localization will be destroyed in a certain range(W/J=3.0±0.5).The spin chain thermal ability of these parameters is the strongest.With the increase of these two parameters,the dynamic localization will appear again,it is judged that the dynamic localization phenomenon of evolution will be caused by the many-body localization effect of spin chain.When the many-body localization effect of spin chain is destroyed,the pulse of the system is not weak enough,the dynamic thermalization will appear in the evolution process.The relationship between many-body localization and localization is revealed.2.The parameters W/J=3.0 with strong heating capablity of the previous section are adopted,and other parameters are unchanged.By adjusting the time duration of the system to turn on and off the pulse and the intensity of the pulse,it is found that although the spin chain is in a more heated state,the dynamic localization will still occur with the decrease of the pulse strength and the shortening of the pulse opening time.When the pulse intensity is large and the pulse is on,the dynamic localization will still occur in the system When the time is longer,the system is more thermal.This is because the effect of the system pulse determines the spectral density of the eigenstate resonant transition.When the spectral density width is narrow,the system tends to be localized regardless of the state of the system.When the pulse is strong,the width of spectral density increases,and the range of the occupied number energy transition is wider.The occupation number transition in the process of periodic dynamic evolution is explained theoretically.3.Using the previous parameters,the time of opening the pulse is set to the parameter ton=1.0,which will make the spin chain with strong thermal ability exhibit dynamic localization.We add weak noise to the time length of each off pulse,and get a set of aperiodic pulses.The spin chain evolves in such pulses.It is found that the same parameters can realize dynamic localization in periodic pulses,while in aperiodic pulses,the localization is destroyed and the distribution of heat is present.This phenomenon is explained from the three-dimensional image of real energy quasi energy spectral density.The phenomenon of breaking localization in aperiodic dynamic evolution is theoretically explained.4.In the process of calculation,we find the problems related to the equilibrium state of heat,and discuss the distribution characteristics of the state in the process of heat.