Domain growth in chiral phase transitions

Abstract

We study the kinetics of chiral phase transitions in quark matter. We discuss the phase diagram of this system in both a microscopic framework (using the Nambu-Jona-Lasinio model) and a phenomenological framework (using a Landau free energy). Then, we study the far-from-equilibrium coarsening dynamics subsequent to a quench from the chirally-symmetric phase to the massive quark phase. Depending on the nature of the quench, the system evolves via either spinodal decomposition or nucleation and growth. The morphology of the ordering system is characterized using the order-parameter correlation function, structure factor, domain growth laws, etc.

Role of a polymeric component in the phase separation of ternary fluid mixtures: a dissipative particle dynamics study

“…The length ℓ 0 is the average domain size of the transient regime, when the system becomes unstable due to fluctuations at early time 0 since the quench. 52,53 Here, 0 = 4 is the onset time for different composition ratios and their corresponding ℓ 0 values are 1.454 (for A:B:C = 1:1:1), 1.538 (for A:B:C = 2:2:1), 1.576 (for A:B:C = 4:4:1), and 1.621 (for A:B:C = 1:1:0), respectively. 53 We notice that the diffusive regime ( = 1/3) is very short lived on the time scale of our simulation, as DPD simulation is best known for preserving the hydrodynamics behavior of the system.…”

Z(3) metastable states in a Polyakov quark meson model

“…In present investigation, we discuss domain growth for the Polyakov loop and quark condensate order parameter in a quench scenario. The non equilibrium effects have been studied using Langevin equations within different effective models of QCD like PQM model [18] as well as Nambu-Jona-Lasinio (NJL) model [19].…”

Dynamical scaling for underdamped strain order parameters quenched below first-order phase transitions

“…For Y 1, the leading term is Y 4 , yieldingḡ ∼ 1/t 1/4 , while for Y 1 the leading term is Y 3 , yieldingḡ ∼ 1/t 1/3 . For multicomponent 1,10 or 'vector' OP with N OP ≥ 2, the Landau termḡ 2+NOP is comparable to the Ginzburg termḡ 4 for N OP = 2; and smaller than it, for N OP > 2. Hence the long-time exponent is predicted to be α = 1/4 for vector order parameters.…”

“…Interacting systems such as magnets, binary fluids, liquid crystals, and quantum spin models can be probed by the dynamical evolutions of order parameters, after temperature or coupling-constant quenches below transition [1][2][3][4][5][6][7][8][9][10][11][12][13] . Such phase ordering can be quantitatively described by a time-dependent, two-point, orderparameter correlation C( R, t), that can exhibit dynamical scaling, dependent on space and time through a single scaled variable 1,5-13R ≡ | R|/L(t), with consequent data collapse onto a single scaled curve G(R).…”

“…It can increase as L(t) ∼ t α , where the exponent α is independent of material parameter values, but could depend on the nature of the OP dynamics, the number of components of the order parameter N OP , the number of competing low-temperature variants N V , and the spatial dimension d. There can be a sequential appearance of different exponents, during coarsening 1 . In various dynamic models, the exponents α have been estimated by heuristic arguments, energy dissipation matchings, Gaussian fluctuations of domain wall profiles, self-consistent correlation function dynamics, and through numerical simulations 1,[5][6][7][8][9][10][11][12] . The Allen-Cahn relaxation equation 1 for a nonconserved OP and the CahnHilliard equation 1,4 for a locally conserved OP are familiar models, both with a single time derivative, and typically use a double-well Landau free energy describing a second-order transition.…”