Lattice Simulations of the Thermodynamics of Strongly Interacting Elementary Particles and the Exploration of New Phases of Matter in Relativistic Heavy Ion Collisions

At high temperatures or densities matter formed by strongly interacting elementary particles (hadronic matter) is expected to undergo a transition to a new form of matter the quark gluon plasma in which elementary particles (quarks and gluons) are no longer confined inside hadrons but are free to propagate in a thermal medium much larger in extent than the typical size of a hadron. The transition to this new form of matter as well as properties of the plasma phase are studied in large scale numerical calculations based on the theory of strong interactions Quantum Chromo Dynamics (QCD). Experimentally properties of hot and dense elementary particle matter are studied in relativistic heavy ion collisions such as those currently performed at the relativistic heavy ion collider (RHIC) at BNL. We review here recent results from studies of thermodynamic properties of strongly interacting elementary particle matter performed on Teraflops-Computer. We present results on the QCD equation of state and discuss the status of studies of the phase diagram at non-vanishing baryon number density. BNL-NT-06/26 August 2006