A NONLINEAR QUARK-GLUON CASCADE CONVERGES AND TRANSITS TO A CHAOTIC REGIME

Computer simulations of the transition of quarks to hadrons, hadrons to quark-gluon plasma, and plasma to hadrons have been carried out. Nonlinear quark-gluon dynamics is considered a quantum process within the framework of discrete mappings. The dynamic variable is the momentum fraction (x) of the QCD parton, which acts as a one-dimensional Poincare section in the momentum phase space. The probability of finding a certain fraction of the momentum of a parton at a given moment is determined by the momentum distribution of the partons at the previous moment in time. At critical values of the control parameter, bifurcations of phase quark-gluon trajectories occur. As a result of the counteraction of the processes of emission and absorption of gluons, stable attractor quark-gluon structures are formed. The Poisson stability is determined by the Lyapunov exponents. The sequence of bifurcations converges and chaos arises. The change from regular quark-gluon dynamics to irregular chaotic one corresponds to the limit of multiple hadronic processes and the emergence of quark-gluon matter in the deconfinement state. Chaotization of the dynamical system leads to thermalization of the quark-gluon medium.