Dynamics of the quark-gluon plasma and high density hadronic matter

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1 We have constructed the spectral functions at finite temperature for the vector (J/ψ) and axial-vector (η_c) channels made of a charm and anti-charm quark pair from their correlation functions measured on the Euclidean lattices with the maximum entropy method, which was applied systematically to lattice gauge theory for the first time by our group. It was shown that both states continue to exist up to a temperature that is much higher than the QCD phase transition temperature, that is, about 1.6T_c and that they both disappears in a very narrow temperature region, between about 1.6T_c and 1.7T_c This suggests that the quark-gluon plasma is not a state where quarks and gluons are almost freely moving as usually believed, but that it is a strongly coupled system where also hadronic excitations coexists.2 It has been argued that there is possibly a critical end point on the QCD phase diagram, where the order of the phase transition changes from first to crossover We have derived general equations of states with a critical end point on the basis of the universality hypothesis in phase transition theory and found that it acts as an attractor in the course of the time evolution of the system. Furthermore, we discussed for the first time the time evolution of fluctuations and correlation lengths when the system created in high energy heavy ion collisions pass the proximity of the critical end point in the course of its time evolution and their effects on observables in a unified framework.