The Analysis Of Evolution Of Elliptic Flow At Rhic Energy

The goal of high energy heavy-ion collisions is to extract information about prop-erties of nuclear matter at high density and high temperature and to obtain the nuclearequation of state. Both the theoretical and experimental results demonstrate that the ellip-tic ?ow is sensitive to the evolution of the collision system and it is a important observableto extract the information of the early stage of the source. In this thesis, using the rela-tivistic quantum molecule dynamics(RQMD) model and relativistic hydrodynamic modelwhich are phenomenological models we study the mechanism of the generation of elliptic?ow and its space-time evolution for Au+Au collisions at RHIC energy.The average transverse velocity of the freeze out particles in the RQMD model iscalculated, and the time and space dependence of the transverse velocity in and out ofreaction plane is analyzed. The average transverse velocity of freeze out particles is com-pared with the expansion speed of the source calculated by the hydrodynamical model,the results show that the correlation between space and momentum exists in the processof interaction. The time and space dependence of transverse velocity demonstrates that atthe early stage, if the transverse radius of freeze-out particles are smaller than the averageradius of initial surface of the source, the transverse velocity is bigger in in-plane than thatin out-of-plane; if the transverse radius of freeze-out particles are more than the averageradius of initial surface of the source, the transverse velocity is bigger in out-of-plane.At lately stage, if the transverse radius is bigger than the initial surface, the transversevelocity of particles are nearly same for in-plane and out-of-plane. HBT is one kind ofspecial correlation and can re?ect the structure of space-time. We calculate the HBT ofprotons using RQMD model.The time and space dependence of the elliptic ?ow is analyzed by using both theRQMD model and the relativistic hydrodynamical model. The results from RQMD showthat the elliptic ?ow of particles which freeze-out decreases with time. The results fromthe hydrodynamical model shows that the elliptic ?ow of the whole source increases withtime. The transverse radius dependence of the elliptic ?ow is analyzed at different stageand the results from RQMD model and hydrodynamical model are similar. The resultsshow that the elliptic ?ow reaches the peak value at the average radius of initial surface in the early stage, the elliptic ?ow reaches the saturation at the average radius of initialsurface in the lately stage. The results are related with the evolution of distribution ofparticles in coordinate space.The effect of first order phase transition on the evolution of the elliptic ?ow is dis-cussed. The analysis demonstrates that when the QGP phase nearly transform to themixed phase completely, the evolution of the source is mainly dominated by the mixedphase, the elliptic ?ow can be seen as the function of the energy density and increase withthe energy density. The decrease of the energy density from the expansion of the sourceespecially the longitudinal expansion maybe the main cause of that the elliptic ?ow de-crease with time. Further, we analyze the contribution of different matter phase to thetotal momentum anisotropy. The results demonstrate that the final elliptic ?ow is mainlygenerated by the QGP phase and mixed phase for semi-central collisions and by hadrongas phase for peripheral collisions.In the hydrodynamical model, if the speed of sound is a constant the eccentricityscaling invariance of elliptic ?ow can be seen. If the EoS contains the first order transitionthe speed of sound varies with the different phase. The transmission of the perturbation inthe source is analyzed, and the difference of the evolutions are distinct for collisions withdifferent impact parameters. The characteristic distance of the transmission of the pertur-bation is introduced and scaled by the initial size of the source. The eccentricity scalinginvariance of the characteristic distance can be seen except for peripheral collisions. Onthis basis, the eccentricity scaled elliptic ?ow is also analyzed. For√sNN =200 GeVAu+Au collisions, the results from the hydrodynamical model show the eccentricity scal-ing invariance of the elliptic ?ow, and the transmission of the perturbation can characterizethe evolution of the elliptic ?ow.