Effects of friction on the chiral symmetry restoration in high energy heavy-ion collisions

We study the effects of friction on the chiral symmetry restoration which may take place temporarily in high energy heavy ion collisions. The equations of motion with friction are introduced to describe the time evolution of the chiral condensates within the framework of the linear sigma model. Four types of friction are used to study how the result is sensitive to the choice of the friction. For the thermalization stage, the time dependent temperature is parametrized so as to simulate the result of the parton-cascade model. It is parametrized according to the one-dimensional scaling hydrodynamics for the subsequent cooling stage. The time development of the condensates and the entropy production due to friction are calculated numerically. The time interval in which the chiral symmetry is restored approximately is investigated in detail for four types of friction. It is found that (i) the maximum temperature must be high enough (not lower than 230 MeV) and the friction must be strong enough in order that the chiral symmetry restoration lasts for a long time (not shorter than 3fm/c), (ii) the ratio of time interval in which chiral symmetry is restored, to the time interval in which the temperature is higher than the critical temperature is typically 0.5 when the friction is strong enough, and (iii) the entropy due to the friction is mainly produced in the early stage of the cooling. The effect of freeze-out is discussed briefly.