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 motion, which consist of the Vlasov equation for the density and the gap equation for the mean field, are discussed, and energy and momentum conservation are proven. Numerical solutions of the partial differential equations are obtained by applying finite difference methods. For an expanding fireball of the light quark mass evolves from small values initially to the value of 350 MeV. This leads to a depletion of the high energy part of the quark spectrum and an enhancement at low momenta. When collisions are included one obtains an equation of the Boltzmann type, where the transition amplitudes depend on the properties of the medium. These equations are given for flavor SU(3), i. e. including strangeness. They are solved numerically in the relaxation time approximation and the time evolution of various observables is given. Medium effects in the relaxtion times do not significantly influence the shape of the spectra. The mass of the strange quark changes little during the expansion. The strangeness yield and the slope temperatures of the final spectra are studied as a function of the size of the initial fireball. PACS numbers: 25.75.-q, 12.38.Mh, 12.39.Fe, 52.25.Dg