Domain growth and ordering kinetics in dense quark matter
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ELEMENTARY PARTICLES AND FIELDS Theory
Domain Growth and Ordering Kinetics in Dense Quark Matter* A. Singh1) , S. Puri1) , and H. Mishra2)** Received March 31, 2011
Abstract—The kinetics of chiral transitions in quark matter is studied in a two-flavor Nambu–JonaLasinio model. We focus on the phase-ordering dynamics subsequent to a temperature quench from the massless quark phase to the massive quark phase. We study the dynamics by considering a phenomenological model (Ginzburg–Landau free-energy functional). The morphology of the ordering system is characterized by the scaling of the order-parameter correlation function. DOI: 10.1134/S1063778812060282
Heavy-ion collision experiments at high energies produce hot and dense strongly-interacting matter and provide the opportunity to explore the phase diagram of QCD [1]. It is worthwhile to stress that, in a phase transition process, information about which equilibrium phase has lowest free energy is not sufficient to discuss all possible structures that the system can have. One has to understand the kinetics of the process by which the phase ordering or disordering proceeds and the nature of nonequilibrium structures that the system must go through on its way to reach equilibrium [2, 3]. In the present work, we study kinetics of chiral transitions in hot and dense matter [4]. We use the two-flavor Nambu–Jona-Lasinio (NJL) model to study the chiral symmetry breaking in QCD [5]. The expression for the thermodynamic potential is obtained in the mean-field approximation: ˜ Ω(M, β, μ) (1) √ 12 2 2 dk ln 1 + e−β ( k +M −μ) =− 3 (2π) β √ 2 2 + ln 1 + e−β ( k +M +μ) M2 12 2 + M 2 − |k| + . k dk − (2π)3 4G
Here, we have taken vanishing current quark mass, and introduce the constituent mass M = −2gρs with ¯ being the scalar density and g = G[1 + ρs = ψψ 1/(4Nc )]. The details of the mean-field approximation are reported elsewhere [6]. ∗
The text was submitted by the authors in English. School of Physical Sciences, Jawaharlal Nehru University, New Delhi, India. 2) Theory Division, Physical Research Laboratory, Ahmedabad, India. ** E-mail: [email protected] 1)
The phase diagram resulting from Eq. (1) is shown in Fig. 1a. For the parameters of the NJL model, we have taken the three-momentum cutoff Λ = 653.30 MeV and coupling G = 5.0163 × 10−6 MeV−2 [7]. With these parameters, the vacuum mass of quarks is M 312 MeV. At T = 0 a firstorder transition takes place at μ 326.321 MeV. For μ = 0 a second-order transition takes place at T 190 MeV. The first-order line (I) meets the secondorder line (II) at the tricritical point (μtcp , Ttcp ) (282.58, 78) MeV. Close to the phase boundary, the potential in Eq. (1) may be expanded as a Ginzburg–Landau (GL) potential in the order parameter M : ˜ (M ) = Ω ˜ (0) Ω (2) b d a + M 2 + M 4 + M 6 + O(M 8 ), 2 4 6 correct up to logarithmic corrections [8]. In the fol˜ (M ) lowing we consider the expansion of potential Ω 6 up to the M term. The first two coefficients in Eq. (2) can then be exactly obtained by comparison with Eq. (1), whi
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