Fluid Dynamical Description of the Chiral Transition

We investigate the dynamics of the chiral transition in an expanding quark-anti-quark plasma. The calculations are made within a linear sigma model with explicit quark and antiquark degrees of freedom. We solve numerically the classical equations of motion for chiral fields coupled to the fluid dynamical equations for the plasma. Fast initial growth and strong oscillations of the chiral field and strong amplification of long wavelength modes of the pion field are observed in the course of the chiral transition.Comment: 9 pages LaTeX, 4 postscript figure

Explosive Decomposition in Ultrarelativistic Heavy Ion Collision

Recent results from Au+Au collisions at BNL-RHIC energy hint at explosive hadron production at the QCD transition rather than soft hydrodynamic evolution. We speculate that this is due to a rapid variation of the effective potential for QCD close to Tc. Performing real-time lattice simulations of an effective theory we show that the fast evolution of the potential leads to ``explosive'' spinodal decomposition rather than bubble nucleation or critical slowing down

Hydrodynamic Models for Heavy-Ion Collisions, and beyond

A generic property of a first-order phase transition in equilibrium, and in the limit of large entropy per unit of conserved charge, is the smallness of the isentropic speed of sound in the ``mixed phase''. A specific prediction is that this should lead to a non-isotropic momentum distribution of nucleons in the reaction plane (for energies around 40 AGeV in our model calculation). On the other hand, we show that from present effective theories for low-energy QCD one does not expect the thermal transition rate between various states of the effective potential to be much larger than the expansion rate, questioning the applicability of the idealized Maxwell/Gibbs construction. Experimental data could soon provide essential information on the dynamics of the phase transition.Comment: 10 Pages, 4 Figures. Presented at 241st WE-Heraeus Seminar: Symposium on Fundamental Issues in Elementary Matter: In Honor and Memory of Michael Danos, Bad Honnef, Germany, 25-29 Sep 200

Dynamical generation of the constituent mass in expanding plasma

We investigate dynamics of the chiral transition in expanding quark-antiquark plasma produced in an ultra-relativistic heavy ion collision. The chiral symmetry break-down and dynamical generation of the constituent quark mass are studied within the linear sigma model and Nambu-Jona-Lasinio model. Time dependence of the quark and antiquark densities is obtained from the scaling solution of the relativistic Vlasov equation. Fast initial growth and strong oscillations of the constituent quark mass are found in the linear sigma model as well as in the NJL model, when derivative terms are taken into account.Comment: 7 pages, Latex. To appear in Physics Letters

Two-point functions for SU(3) Polyakov Loops near T_c

We discuss the behavior of two point functions for Polyakov loops in a SU(3) gauge theory about the critical temperature, T_c. From a Z(3) model, in mean field theory we obtain a prediction for the ratio of masses at T_c, extracted from correlation functions for the imaginary and real parts of the Polyakov loop. This ratio is m_i/m_r = 3 if the potential only includes terms up to quartic order in the Polyakov loop; its value changes as pentic and hexatic interactions become important. The Polyakov Loop Model then predicts how m_i/m_r changes above T_c.Comment: 5 pages, no figures; reference adde

Chiral Phase Transition within Effective Models with Constituent Quarks

We investigate the chiral phase transition at nonzero temperature $T$ and baryon-chemical potential $\mu_B$ within the framework of the linear sigma model and the Nambu-Jona-Lasinio model. For small bare quark masses we find in both models a smooth crossover transition for nonzero $T$ and $\mu_B=0$ and a first order transition for T=0 and nonzero $\mu_B$. We calculate explicitly the first order phase transition line and spinodal lines in the $(T,\mu_B)$ plane. As expected they all end in a critical point. We find that, in the linear sigma model, the sigma mass goes to zero at the critical point. This is in contrast to the NJL model, where the sigma mass, as defined in the random phase approximation, does not vanish. We also compute the adiabatic lines in the $(T,\mu_B)$ plane. Within the models studied here, the critical point does not serve as a ``focusing'' point in the adiabatic expansion.Comment: 22 pages, 18 figure

Non-perturbative effects in a rapidly expanding quark-gluon plasma

Within first-order phase transitions, we investigate the pre-transitional effects due to the nonperturbative, large-amplitude thermal fluctuations which can promote phase mixing before the critical temperature is reached from above. In contrast with the cosmological quark-hadron transition, we find that the rapid cooling typical of the RHIC and LHC experiments and the fact that the quark-gluon plasma is chemically unsaturated suppress the role of non-perturbative effects at current collider energies. Significant supercooling is possible in a (nearly) homogeneous state of quark gluon plasma.Comment: LaTeX, 7 pages with 7 Postscript figures. Figures added, discussions added. Version to appear in Phys. Rev.

P-Wave Morphology, Amplitude, Duration and Dispersion in Atrial Arrhythmias

The detailed analysis of the P-wave duration and dispersion by means of conventional electrocardiography with the 12 standard surface leads in the stratification of patients suffering from AF is a recognized universal approach. P-wave dispersion (PWD) has received increasing attention in the field of non-invasive electrophysiology studying atrial arrhythmias and has been examined in a broad range of clinical settings including cardiovascular and non-cardiovascular diseases. It is well accepted that, not only the P-wave duration, but also the P-wave morphology and dispersion have the potential to give information about the anatomical substrate predisposing to AF. Patients with diseased atrial myocardium with fibrotic changes may develop abnormal electrophysiological alterations. Therefore, these atrial anisotropic characteristics may play an important role in creating reentry circuits by causing inhomogeneous and discontinuous propagation of the impulse in the atrial tissue. The altered atrial myocardium may generate unidirectional block, conduction delay and reentrant atrial rhythms. The P-wave of the electrocardiogram may show alterations that can be associated with atrial arrhythmias and AF. PWD is considered a noninvasive electrocardiographic marker for atrial remodeling and predictor for AF. It has been shown that increased P-wave duration and PWD reflect prolongation of intra-atrial and inter-atrial conduction time. In patients prone to develop atrial arrhythmias and AF, PWD reflects prolonged, inhomogeneous and anisotropic distribution of connections between myocardial fibers resulting in discontinuous anisotropic propagation of sinus impulses and atrial conduction. PWD is considered as a sensitive and specific ECG marker and predictor of atrial arrhythmias and paroxysmal AF

Chiral phase transition in the presence of spinodal decomposition

The thermodynamics of a first order chiral phase transition is considered in the presence of spinodal phase separation within the Nambu-Jona-Lasinio (NJL) model. The properties of the basic thermodynamic observables in the coexistence phase are discussed for zero and non-zero quark masses. We focus on observables that probe the chiral phase transition. In particular, the behavior of the specific heat and entropy as well as charge fluctuations are calculated and analyzed. We show that the specific heat and charge susceptibilities diverge at the isothermal spinodal lines. We determine the scaling behavior and compute the critical exponent $\gamma$ of the net quark number susceptibility at the isothermal spinodal lines within the NJL model and the Ginsburg-Landau theory. We show that in the chiral limit the critical exponent $\gamma=1/2$ at the tricritical point as well as along the isothermal spinodal lines. On the other hand, for finite quark masses the critical exponent at the spinodal lines, $\gamma=1/2$, differs from that at the critical end point, $\gamma=2/3$, indicating a change in the universality class. These results are independent of the particular choice of the chiral Lagrangian and should be common for all mean field approaches.Comment: 12 pages, 11 figure