
The results of present lattice QCD calculations are illustrated in Figure which shows the temperature dependence of the Wilson loop L and the quark condensate along with the corresponding generalised susceptibilities . The quantity L is a measure of the free quark energy and thereby of the color mobility or color deconfinement. The sharp jump from very small values (low quark mobility) to large values occurs at the critical temperature corresponding to the deconfinement phase transition. At exactly the same position the quark condensate, a measure for the quark mass acquired by spontaneous breaking of the chiral symmetry in low temperature QCD, drops steeply. These calculations indicate that quarks and, hence, hadrons loose their mass (except for the small current quark masses) at a critical temperature T_{c}, a process called chiral symmetry restoration, and simultaneously acquire a finite free energy in the medium, resulting in a finite mobility corresponding to deconfinement. This interpretation is supported by a concurrent steep jump in the energy density (not illustrated). The susceptibilities shown as the red curves in Figure are a measure of the fluctuations that characteristically are maximal in the vicinity of a phase transition. To put the critical temperature on an absolute energy scale requires calibration of the lattice results by tying them e.g. to a physical hadron mass. The best calibration to date fixes the critical temperature to 150 MeV. Including systematic errors, the temperature range for T_{c} inferred from lattice QCD is between 150 MeV and at most 200 MeV, as indicated in Figure by the arrow. All lattice QCD results obtained so far are valid for a system of vanishing baryon number density (baryochemical potential = 0). To extend the knowledge of the hadron gas  quarkgluon plasma boundary into the domain of finite baryon number one needs to employ QCD inspired models (blue line in Figure ). Energy densities of about the required magnitude are indeed reached in the initial phase of central Pb+Pb collisions at the SPS together with baryon densities of up to 5 times nuclear matter density. However, the lattice calculations describe a stationary state whereas nuclear collisions are a typical example of a rapidly evolving system. Of equal importance as energy density are therefore lifetime and equilibration times in nuclear collisions. A very intense theoretical discussion is currently devoted to the question if thermal relaxation time scales are sufficiently small compared to the expansion time scale. However, the final answer concerning the creation of an equilibrated strongly interacting medium, of either partonic or a hadronic nature, can only be settled by experiment. To fully explore the highdensity regime simulations of the collision show that beam energies of a few tens of GeV per nucleon are optimal. Maximum densities are reached when the colliding nuclei still barely stop each other. A study of the chiral and deconfinement phase transitions along the density axis is complementary to studies at high energy density i.e. high temperature and is equally important for a full understanding of the nature of these phase transitions.