Scaling Properties of Out-of-equilibrium Hydrodynamic Fluctuations near the QCD Critical Point

Abstract

In a heavy ion experiment the system travels along trajectories of constant n/s in absence of dissipation. Ideally one can tune the beam energy so that the system goes exactly through the QCD critical point (CP), in which case the equilibrium two point correlator 〈δ(n/s)δ(n/s)〉eq [5] of the thermal fluctuations δ(n/s) diverges at the CP while the actual value of this correlator 〈δ(n/s)δ(n/s)〉 falls out of equilibrium and consequently remains finite. In this paper we first show that this out-of-equilibrium dynamics exhibits universal scaling properties known as Kibble-Zurek scaling. The relevant physical scale is called Kibble-Zurek scale and it is a function of a small dimensionless parameter ϵ≡τo/τQ, where τo is the microscopic mean-free-time and τQ is the macroscopic total expansion time. Realistically the trajectory always misses the CP, the equilibrium correlator is then cut off by a new scale which we call the crossing scale. The crossing scale is a function of another small dimensionless parameter Δs≡(nc/sc)(s/n−sc/nc) that's controlled by the beam energy. We then show from the scaling properties of Ising EOS that the equilibrium correlator scales universally with the crossing scale. The paper is concluded by a quantitative analysis on how the out-of-equilibrium KZ dynamics competes with missing the CP since they both limit the growth of the correlator 〈δ(n/s)δ(n/s)〉 near the CP.