Thermodynamics of quark quasiparticle ensemble

Abstract

The features of the hot and dense gas of quarks, which are considered as the quasiparticles of the model Hamiltonian with a four-fermion interaction, are studied. Being adapted to the Nambu-Jona-Lasinio model, this approach allows us to accommodate a phase transition similar to the nuclear liquid-gas one at the proper scale and to argue the existence of the mixed (inhomogeneous) phase of vacuum and normal baryonic matter as a plausible scenario of chiral symmetry (partial) restoration. Analyzing the transition layer between two phases, we estimate the surface tension coefficient and speculate on the possible existence of a quark droplet.

Surface tension of quark matter in a geometrical approach

“…It is a convenient feature of the method employed that knowledge of the interface profile functions is is not required, because their determination can be quite complicated, as is the case for NJL model [20] (although it is easy for the LSM). In addition to the EoS, the geometrical approach also requires a proper setting of three input parameters, namely the characteristic densities ρ g and E g together with the length scale a.…”

“…The length a as a somewhat adjustable parameter governing the width of the interface region and the magnitude of the tension [12]. For the LSM it is natural to expect that a ≈ 1/m σ ≈ 0.33 fm which, also, is approximately the value found in an application of the Thomas-Fermi approximation to the NJL model [20]. Therefore, we shall adopt the value a = 0.33 fm throughout the present work.…”

“…As in the LSM case, the quantities ρ 1 , ρ 2 , ρ g , E g , and ∆f (ρ) entering the expression (2.3) for the surface tension can be obtained from the equation of state. As already emphasized,the numerical value for the length scale a is chosen to be 1/m σ ≃ 0.33 fm (which is about the value found in a Thomas-Fermi application to the NJL model [20]). The remaining two numerical inputs, ρ g and ǫ g , are automatically fixed once the EoS has been determined.…”

Inhomogeneous chiral condensates

“…Although in both cases, "lasagnetype" density profiles, i.e., alternating parallel plates with high and low density, exist, the mass functions are rather different: In the mixed phase it oscillates between high and low (or vanishing) values, whereas the solitonic mass function oscillates between positive and negative values and vanishes only "in passing". In fact, in contrast to the solitonic phase, mixed phases have a higher free energy than their homogeneous constituents because of the surface tension, which has been estimated to be positive for the NJL model [109,110,111].…”

Quantum liquids resulting from quark systems with four-quark interaction

“…We restrict ourselves by considering the BogolyubovHartree-Fock approximation in which the statistical operator is constructed on the basis of approximating the effective Hamiltonian H app , quadratic in creation and annihilation operators for quasiparticles acting in the corresponding Fock space with a vacuum state |σ . The average specific energy per quark w = E/(V γ ) results in [21][22][23] …”