A Study Of KPZ Nonlinear Effects In Low-dimensional Exciton-polariton Systems

Exciton polarons(EPs)in semiconductor microcavity constitute a typical driving dissipation system.Its spatiotemporal coherence is affected by the non-equilibrium phase fluctuation of the system.This is a large-scale nonlinear effect,which belongs to the universal class of Kardar-Parisi-Zhang.Exciton polaron is a kind of quasi particle,which has the characteristics of photon and exciton at the same time.They inherit the good coherence characteristics of photon and a large number of interaction characteristics of exciton.In recent decades,semiconductor microcavity exciton polaritons have been widely studied and attracted the attention of many scholars at home and abroad.The research on EPs has developed to many small systems,including thin films,quantum dots,quantum wires,quantum wells and so on.Many physical problems can be explained by studying EPs,such as Bose Einstein condensation(BEC),KPZ effect,superfluid phenomenon,vortex and so on.The unique properties of exciton polaritons make them our research object.KPZ equation was originally used to simulate the continuous approximation of discrete growth models(such as vapor deposition and Eden model).It describes the non-equilibrium process.Here,we describe the KPZ nonlinear effect in one-dimensional and two-dimensional systems through the scaling characteristics of KPZ,which plays an important role in statistical physics.KPZ universal class is to meet the dynamic scaling law of 3:2:1,The image decays exponentially and e exponentially under Bogoliubov's linear theory.Viscous falling body model,Eden model,ballistic deposition model and EPS all belong to KPZ universal class.Starting from the generalized gross Pitaevskii(GP)equation and adding the influence of random noise,we calculate the one-dimensional and two-dimensional first-order coherence function,density fluctuation and scale function,and discuss the influence of interaction intensity g and pump intensity P0 on the system,that is,the influence of external driving and internal dissipation on the system,The variation of scale index Z value under different conditions is analyzed,and the dimension dependence of nonlinear effect is analyzed and numerically studied.The results show that there are obvious differences in KPZ nonlinear effects in one-dimensional and two-dimensional exciton polarization systems.This paper is arranged as follows:In the first chapter,we introduce the concept of Bose Einstein condensation and exciton polariton,and why exciton polariton can realize Bose Einstein condensation.At the same time,we explain the research status and significance of exciton polariton.In the second chapter,we introduce the theoretical basis and numerical calculation method of this paper.The GP equation is mainly introduced.By solving the generalized gross Pitaevskii equation,we analyze and numerically study the dimension dependence of nonlinear effects.In the third chapter,we focus on the core content of this paper,KPZ equation and the universality of KPZ equation,and how to solve KPZ equation in one dimension.In the fourth chapter,we introduce our work in detail,and compare the differences of first-order coherence function,density fluctuation,scaling function and scaling index in one-dimensional and two-dimensional cases.The contribution of nonlinear effects to the development of long-range coherence in one-dimensional and two-dimensional EP systems is discussed.It is found that for one-dimensional systems,KPZ nonlinearity plays a constructive role in the development of long-range correlation.On the contrary,in a two-dimensional system,it plays a destructive role.In 2D,KPZ dynamic scale invariance is destroyed in a short distance due to algebraic order.In addition,the KPZ region in 2D contains two stages with different scale behavior.In the fifth chapter,we make a brief summary of this thesis and look forward to the follow-up research.