Lattice Boltzmann Method For Bose-Einstein Condensation Dynamics And Its Application

As a new state of matter,Bose-Einstein Condensation(Bose Einstein Condensate,BEC)provides a unique medium for experimental physics.Its discovery further promotes the development of many disciplines such as materials science,atomic physics,and nanotechnology.The use of BEC to develop high-precision atomic interferometers,manufacture atomic lasers,and realize phase printing technology is of great significance and potential value.However,for complex nonlinear systems such as BEC,many parameters and physical phenomena make theoretical analysis very difficult.At the same time,due to the high cost,long period and low repeatability of experimental research,the experimental methods also have great limitations.With the rapid development of computer science,numerical methods have become the main means to study the dynamic behaviors of BEC.Although traditional numerical methods have made a lot of contributions to the study of such problems,they still face the problems of computational coupling problems and low efficiency.As a mesoscopic numerical method,lattice Boltzmann(Lattice Boltzmann,LB)method has the characteristics of good locality,high computational efficiency,and is suitable for parallel computation,which shows great advantages in solving nonlinear partial differential equations.In this paper,the LB method is used to carry out a series of problems research on the nonlinear Schrodinger(Nonlinear Schr?dinger,NLS)equation,which is a mathematical model describing the dynamic properties of BEC.It mainly includes the following aspects:Firstly,based on the LB model of nonlinear diffusion equation,the evolution process of NLS equation is decomposed into two evolution equations in which the real part and the imaginary part are coupled to each other,and then the LB model is established to solve the problem.Finally,we validate the validity of the model for solving the NLS equation through three examples,one-dimensional,two-dimensional and three-dimensional,from both qualitative and quantitative aspects.Secondly,based on the above-developed LB model,the numerical study of the bright soliton solution in BEC is carried out without considering the external potential.The influence of shape factor,velocity factor and nonlinear coefficient on the evolution of bright soliton is considered.The numerical result provides a theoretical basis for the regulation of bright solitons in practical applications.Finally,numerical simulation of the strange wave of BEC in one-dimensional periodic potential shows that the position of the strange wave can be adjusted by changing the driving intensity and driving frequency of the external periodic potential,and the peak value of the strange wave can be adjusted by changing the scattering length of S-wave,so as to achieve the effect of prevention and control.