| At present,the exciton-polariton Bose-Einstein condensation has become a good platform to study nonlinear excitation.The exciton-polariton formed by strong coupling between exciton in semiconductor material and photon in microcavity is a new quasi-particle,One of its advantages over ordinary particles with bose propertiesis that the effective mass is very small and has a strong interaction,and another advantage is that the temperature requirements are relatively low,so it’s easier to form Bose-Einstein condensates.In nonlinear phenomena,soliton as a nonlinear excitation has aroused the interest of many scholars at home and abroad.In recent years,the research on solitons in the exciton-polariton Bose-Einstein condensation has been developed rapidly,and the research results have been widely applied in other fields.In this paper,starting from the open-dissipative Gross-Pitaevskii equation,we use analytical and numerical simulation methods to study the dissipative solitons in the exciton-polariton Bose-Einstein condensates and the dark solitons dynamics in the case of Parity-Time symmetry.The thesis is mainly divided into the following parts:Part i: we briefly introduce the research background of soliton,exciton-polariton,dissipative system and parity-time symmetry.Part ii: we introduce the Gross-Pitaevskii equation used to describe the condensates,in which we focus on the equation describing exciton excited exciton condensates,namely,open dissipated Gross-Pitaevskii equation,and dimensionless processing is carried out to obtain its standard form.Based on our research model,we briefly introduce the method to solve the model numerically and the method to analyze the dynamic evolution of the key physical variables in the equation: Fast Fourier transform and Hamiltonian variational method.Part iii: using the two methods introduced in part ii,we prove the existence of a vector dissipative soliton based on a bose-einstein condensate of spin polaron,and call this new vector dissipative soliton as a dissipative magnetic soliton.Itis an isolated spin polarized wave excited in the background of a linearly polarized polarizon condensate,which can keep the energy unchanged when propagating in a dissipative system.More importantly,the dissipative magnetic soliton is an exact solution to the dissipative Gross-Pitaevskii equation driven by two components.Unlike most previously discovered dissipative solitons,which are caused by double equilibria in a single excitation channel,dissipative magnetic polaron solitons rely on a new physical mechanism,that is,a double equilibrium mechanism in which multiple excitation channels work together.Part iv: in this part,based on PT symmetry,we study the dynamics of dark solitons in spatially pumped exciton-polariton condensates,and analytically derive the evolution equation of dark solitons velocity.Within the framework of the Hamiltonian method,our results show how the combination of open dissipation and PT symmetry affects the physical nature of the dark soliton lifetime,and solve the modified Gross-Pitaevskii equation of open dissipation in a mathematically precise manner. |
