Critical point fluctuations: Finite size and global charge conservation effects

Abstract

We investigate simultaneous effects of finite system size and global charge conservation on thermal fluctuations in the vicinity of a critical point. For that we consider a finite interacting system, which exchanges particles with a finite reservoir (thermostat), comprising a statistical ensemble that is distinct from the common canonical and grand canonical ensembles. As a particular example the van der Waals model is used. The global charge conservation effects strongly influence the cumulants of particle number distribution when the system size is comparable to that of the reservoir. If the system size is large enough to capture all the physics associated with the interactions, the global charge conservation effects can be accurately described and corrected for analytically, within a recently developed subensemble acceptance method. The finite size effects start to play a significant role when the correlation length grows large due to proximity of the critical point or when the system is small enough to be comparable to an eigenvolume of an individual particle. We discuss our results in the context of fluctuation measurements in heavy-ion collisions.

Particlization of an interacting hadron resonance gas with global conservation laws for event-by-event fluctuations in heavy-ion collisions

“…Event-by-event fluctuations, especially the high-order cumulants, are strongly affected by global conservation laws [35][36][37], requiring large corrections to the grand-canonical distributions. Other mechanisms include volume fluctuations [38][39][40], finite system size [41], as well as non-equilibrium dynamics such as memory effects [42] or hadronic phase evolution [43]. Proper modeling of these effects is thus required for analyzing the experimental data quantitatively.…”

Effects of centrality fluctuation and deuteron formation on proton number cumulant in Au+Au collisions at $\sqrt{s_\mathrm{NN}}$ = 3 GeV from JAM model

“…ative values up to sixth order at large rapidity acceptance at √ s NN = 3 GeV. Those strong rapidity acceptance dependence are mainly attributed to the effects of baryon number conservations [64][65][66][67]. In addition, we observed that if we randomly drop 7% protons in each event then the cumulants are close to the deuteron formation case.…”

Non-equilibrium cumulants within model A near the QCD critical point

“…In order to quantitatively describe the experimental observed cumulants of net proton multiplicities, more sophisticated and realistic dynamical modeling are required from the theoretical side [56,57]. Besides, a number of effects play their role, including the subject of the proper equation of state [58][59][60], of the unknown parameters of the Ising-to-QCD mapping [61], of the critical transport coefficients [62][63][64][65], of the finite size, finite size scaling and global charge conservation in the vicinity of a CP [66][67][68][69][70], of the non-critical baseline for the cumulants of net-proton number fluctuations [71], and of the nonuniform temperature/chemical potential effects [72]. In addition, further connections between the criticality and the experimental observables have been established through theoretical efforts [73][74][75][76][77][78].…”