Finite-size effects and finite-size scaling in time evolution during a colorless confining phase transition

The time evolution of the expanding colorless partonic matter, created in ultra-relativistic heavy ion collisions and undergoing the confining phase transition, is discussed in the context of our colorless QCD-MIT bag model with the boost invariant Bjorken expansion and using the L-m,L-n-method. The direct extension of this method to the non-colorless case is clearly formulated. The hydrodynamic equation in the case of a longitudinal expansion scenario of a non-ideal relativistic medium in finite volume is solved using certain initial conditions (tau(i), T(tau(i))). The evolution of the temperature T(tau,V) as a function of the proper time and of the volume is then obtained. Different times characterising the whole time evolution, like the time at which the confining phase transition begins tau(P)(V), the hadronic time tau(H) (V) at which the hadronization is completed, the lifetime of the Colorless Partonic Plasma Delta tau(CPP) (V) and the lifetime of the confining phase transition Delta tau(PT) (V) are carefully extracted and their finite-size scaling properties are studied in detail and compared with the derived laws. The effects of the initial conditions (T-i, tau(i)) on different times and lifetimes are investigated in detail. We find that the time evolution of our system is really affected by the colorlessness requirement.