Influence of a Critical Point on Hydrodynamic Fluctuations in Heavy Ion Collisions

Hydrodynamic fluctuations have been studied in a wide variety of physical, chemical, and biological phenomena in the past decade. In high energy heavy ion collisions, there will be intrinsic fluctuations even if the initial conditions are fixed. Fluctuations will be greatly enhanced if the trajectory in the plane of temperature versus chemical potential passes near a critical point. We construct a model for the thermal conductivity which diverges at the critical point with the correct critical exponents, and use it in a simple illustrative model of a heavy ion collision. The proton correlation function is sensitive to the presence of the critical point. The major reason to study QCD at finite temperature and density and to perform experiments with high energy heavy ion collisions is to map the phase structure of QCD in terms of temper-ature, baryon density, and isospin asymmetry. The results have import for cosmology and for neutron stars, in addition to its intrinsic interest. There are reasons to expect that there is a curve of first-order phase transition in the temperature T versus baryon chemical potential µ plane, terminating at a critical point at Tc> 0 and µc> 0 (with the simplifying condition of isospin symmetric matter). The existence of such a critical point has been found in many effective fiel