Scaled variance, skewness, and kurtosis near the critical point of nuclear matter

Abstract

The van der Waals (VDW) equation of state predicts the existence of a first-order liquid-gas phase transition and contains a critical point. The VDW equation with Fermi statistics is applied to a description of the nuclear matter. The nucleon number fluctuations near the critical point of nuclear matter are studied. The scaled variance, skewness, and kurtosis diverge at the critical point. It is found that the crossover region of the phase diagram is characterized by the large values of the scaled variance, the almost zero skewness, and the significantly negative kurtosis. The rich structures of the skewness and kurtosis are observed in the phase diagram in the wide region around the critical point, namely, they both may attain large positive or negative values.

van der Waals hadron resonance gas and QCD phase diagram

“…10 shows that for the values of the constants, a = 329 MeV fm 3 and b = 3.42 fm 3 for ground-state nuclear matter [24,25], the point in between regions of the first-order phase transition and the crossover, in terms of discontinuity in η/s, appears near T = 19.5 MeV and at μ B = 910 MeV (we calculate η/s at intervals of 10 MeV in μ B and 0.3 MeV in T ), while in Refs. [24] and [25], the critical point at the end of nuclear liquid-gas phase transition has been shown to be at T = 19. resides at T = 62.1 MeV and μ B = 720 MeV against the estimated critical point at T = 62.1 MeV and μ B = 708 MeV (where ∂p/∂n equals to zero) in Ref. [27].…”

“…In this article, we present our study in terms of temperaturedependent normalized entropy density, s/T 3 and the ratio of shear viscosity and entropy density, η/s for hadron gas in a HRG model, incorporated with van der Waals (VDW) form of equation of state that was appropriately developed [23][24][25] for grand canonical ensemble of fermions. By fixing the parameters of VDW EoS for fermions with the properties of the nuclear matter ground state, the location of critical point at the end of first-order nuclear liquid-gas phase transition has been predicted [24].…”

“…In the VDWHRG model [25,26], the VDW interactions have been considered between (anti)baryons, only, while the interactions were neglected between pairs of baryonantibaryon, meson-meson, and meson-(anti)baryon. In this study, while following the VDW form of interactions between (anti)baryons, the attractive and the repulsive interactions among meson-pairs get effective through the resonances and excluded volume effect [57,58], introduced with hard-core radius of mesons r M , respectively.…”

Thermodynamics of van der Waals Fluids with Quantum Statistics

“…From the equation of state, one can also calculate fluctuations of the particle number, which are important characteristics of the phase transition [15,[18][19][20][21][22][23][24][25]. These are quantified by the corresponding cumulants χ k of order k > 0, as…”

“…It is a semi-quantitative theory which has many applications to model the observed experimental behaviors of critical phenomena in the liquid-gas phase transition. In particular, under some approximations, it can be used as a phenomenological tool to describe phase structure of nuclear-, or thermodynamical properties of hadronic-matter [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16].…”