A NUMERICAL STUDY OF AN EXPANDING PLASMA OF QUARKS IN A CHIRAL MODEL

We numerically solve the transport equations for a quark gas described by the the Nambu-Jona-Lasinio model. The mean field equations of moti on, which consist of the Vlasov equation for the density and the gap e quation for the mean field, are discussed, and energy acid momentum co nservation are proven. Numerical solutions of the partial differential equations are obtained by applying finite difference methods. For an expanding fireball the light quark mass evolves from small values init ially to the value of 350 MeV. This leads to a depletion of the high e nergy part of the quark spectrum and an enhancement at low momenta. Wh en collisions are included one obtains an equation of the Boltzmann ty pe, where the transition amplitudes depend on the properties of the me dium. These equations are given for flavor SU(3), i.e. including stran geness. They are solved numerically in the relaxation time approximati on and the time evolution of various observables is given. Medium effe cts in the relaxation times do not significantly influence the shape o f the spectra. The mass of the strange quark changes little during the expansion. The strangeness yield and the slope temperatures of the fi nal spectra are studied as a function of the size of the initial fireb all. (C) 1998 Elsevier Science B.V.