Core collapse supernovae in the QCD phase diagram

We compare two classes of hybrid equations of state with a hadron-to-quark matter phase transition in their application to core collapse supernova simulations. The first one uses the quark bag model and describes the transition to three-flavor quark matter at low critical densities. The second one employs a Polyakov-loop extended Nambu-Jona-Lasinio (PNJL) model with parameters describing a phase transition to two-flavor quark matter at higher critical densities. These models possess a distinctly different temperature dependence of their transition densities which turns out to be crucial for the possible appearance of quark matter in supernova cores. During the early post-bounce accretion phase quark matter is found only if the phase transition takes place at sufficiently low densities as in the study based on the bag model. The increase critical density with increasing temperature, as obtained for our PNJL parametrization, prevents the formation of quark matter. The further evolution of the core collapse supernova as obtained applying the quark bag model leads to a structural reconfiguration of the central protoneutron star where, in addition to a massive pure quark matter core, a strong hydrodynamic shock wave forms and a second neutrino burst is released during the shock propagation across the neutrinospheres. We discuss the severe constraints in the freedom of choice of quark matter models and their parametrization due to the recently observed 2M _?? pulsar and their implications for further studies of core collapse supernovae in the QCD phase diagram.     

Phase diagrams in nonlocal Polyakov-Nambu-Jona-Lasinio models constrained by lattice QCD results

Based on lattice QCD-adjusted SU(2)f nonlocal Polyakov-Nambu-Jona-Lasinio (PNJL) models, we investigate how the location of the critical endpoint in the QCD phase diagram depends on the strenght of the vector meson coupling, as well as the Polyakov-loop (PL) potential and the form factors of the covariant model. The latter are constrained by lattice QCD data for the quark propagator. The strength of the vector coupling is adjusted such as to reproduce the slope of the pseudocritical temperature for the chiral phase transition at low chemical potential extracted recently from lattice QCD simulations. Our study supports the existence of a critical endpoint in the QCD phase diagram albeit the constraint for the vector coupling shifts its location to lower temperatures and higher baryochemical potentials than in the case without it.     

改进的PNJL模型下QCD的相图

Polyakov-Nambu-Jona-Lasinio（PNJL）模型是研究强相互作用物质性质的使用最为广泛的有效模型之一。在PNJL模型的基础上考虑了手征凝聚和Polyakov圈之间的纠缠作用,并且引入了化学势修正的Polyakov有效势,由此得到了化学势依赖的entangled PNJL（μEPNJL）模型。在平均场框架下的计算结果表明:相较于原始的PNJL模型,由μEPNJL模型计算得到的临界点（CEP）朝着温度更高、化学势更小处移动,并且手征对称性恢复相变和退禁闭相变在较大的化学势范围内都重合得很好。通过与STAR合作组在相对论重离子对撞机（RHIC）上进行的净质子数分布的测量结果相比,可以发现,通过适当的参数调节,由μEPNJL模型计算得到的CEP更加靠近实验预言的CEP可能存在的区域。Polyakov-Nambu-Jona-Lasinio (PNJL) model is one of the most popular effective quark models to investigate the properties of strongly interacting matter. Based on the PNJL model, we consider the entanglement interactions between the chiral condensate and Polyakov-loop, as well as the chemical potential modification of Polyakov-loop potential simultaneously, which is named μEPNJL model. Compared with the original PNJL model, the calculations in the mean field approximation show that the critical end point (CEP) given in the μEPNJL model moves towards higher temperature and smaller chemical potential in the T-μ phase diagram. Besides, the chiral symmetry restoration and deconfinement phase transition coincide well in a wide range of chemical potential. Comparing our calculations with the measurement of the moments of net-proton multiplicity distributions at Relativistic Heavy-Ion Collider (RHIC) by STAR Collaboration, we find that the CEP given by μEPNJL model can be closer to the range predicted by the experiment through appropriate parameter adjustment.     

Systematics of thermodynamic quantities in a 3-region phase diagramme from strange particle ratios

Using the strange-hadron mass spectrum, theμ _q/T andμ _s/T values obtained from strange particle ratios, we estimate the temperature of the equilibrated primordial state for several nuclear interactions at AGS and SPS. Fitting the systematics forT,μ _q and transverse flow velocity we predict their values at RHIC. On the basis of lattice calculations and experimental evidence, we propose the existence of an intermediate phase: the Deconfined Quark Matter (DQM) phase with massive and correlated quarks. We define theμ _s = 0 curve as the boundary between the HG and DQM phases for the strange-hadron sector and write an empirical EoS for the latter region. Its distinct characteristic is the negative strange-quark chemical potential. Experimental suggestion forμ _s < 0 may have been seen in S+A interactions at 200A GeV.     

Discussion of thermodynamic features within the PNJL model

We discuss some thermodynamical features of a QCD system within the two-flavor Polyakov loop extended Nambu–Jona-Lasinio(PNJL) model. Several thermodynamical quantities of interest(pressure, energy density,specific heat, speed of sound, etc.) are investigated and discussed in detail with two different forms of Polyakov loop potential. The effective coupling strength G incorporating a quark feedback(quark condensate) through operator product expansion is also discussed, as well as the relationship between color deconfinement and chiral phase crossover.We find that some thermodynamical quantities have quite different behavior for different Polyakov loop potentials.By changing the characteristic temperature T_0 of the pure Yang-Mills field, we find that when T_0 becomes small,color deconfinement might happen earlier than chiral phase crossover, while their relationship can be determined via some thermodynamical quantities. Furthermore, the behavior of the thermodynamical quantities is quite different in the two different forms of Polyakov loop potential studied. Especially, one of the potentials, specific heat, has two peaks, which correspond to color deconfinement and chiral phase crossover respectively. This interesting phenomenon may shed some light on whether the inflection points of the chiral condensate and deconfinement transitions happen at the same temperature or not for lattice QCD and experimental studies.     

Excluded volume,bag constant and hadron-quark phase transition

The model of hadron-quark phase transitions proposed by Cleymans et al. is modified by taking into account the fact that the nuclear repulsive force is operative between a pair of nucleons or a pair of antinucleons but not between a nucleon and an antinucleon. The phase boundary in the temperature (T)-chemical potential (μ) plane is calculated for some values of the bag constantB and the hard core radiusR. Stability of the normal nuclear matter together with the bag picture for the nucleon yields rather stringent bounds forB as functions ofR. The most probable range of values is estimated to beB ^1/4?150～200 MeV being consistent with the estimate from hadron spectroscopy. For this range ofB, it is improbable to realize the broken chiral phase with deconfining constituent quarks and Goldstone pions at someT and μ.     

Phase structure of dynamical triangulation models in three dimensions

The dynamical triangulation model of three-dimensional quantum gravity is shown to have a line of transitions in an expanded phase diagram which includes a coupling μ to the order of the vertices. Monte Carlo renormalization group and finite size scaling techniques are used to locate and characterize this line. Our results indicate that for μ < μ₁ ∼ −1.0 the model is always in a crumpled phase independent of the value of the curvature coupling. For μ < 0 the results are in agreement with an approximate mean field treatment. We find evidence that this line corresponds to first-order transitions extending to positive μ. However, the behavior appears to change for μ > μ₂ ∼ 2.0−4.0. The simplest scenario that is consistent with the data is the existence of a critical end point.     

Energy dissipation in the Nagel-Schreckenberg model with open boundary condition

In this paper, we numerically investigate energy dissipation caused by traffic in the Nagel-Schreckenberg (NaSch) model with open boundary conditions (OBC). Boundary results in excess energy dissipation. The effects of the stochastic boundary conditions on energy dissipation are discussed. The behaviors of energy dissipation in different traffic phase are distinct. As an order parameter, energy dissipation rate E _d characterizes the phase transition behaviors well. It is shown that there is no true free-flow state in nondeterministic NaSch model with OBC. We refer to this non-true free-flow state as quasi-free-flow (QFF) phase in which there are interactions between vehicles caused by stochastic braking but no backward moving jam exists. In the maximum current phase, E _d is minimal thus the social payoff is maximal. Energy dissipation profiles in QFF, jammed and maximum current phase are presented. Theoretical analyses are in good agreement with numerical results for the case v _max = 1.     

Fermionic van Hemmen spin glass model with a transverse field

In the present work it is studied the fermionic van Hemmen model for the spin glass (SG) with a transverse magnetic field Γ. In this model, the spin operators are written as a bilinear combination of fermionic operators, which allows the analysis of the interplay between charge and spin fluctuations in the presence of a quantum spin flipping mechanism given by Γ. The problem is expressed in the fermionic path integral formalism. As results, magnetic phase diagrams of temperature versus the ferromagnetic interaction are obtained for several values of chemical potential μ and Γ. The Γ field suppresses the magnetic orders. The increase of μ alters the average occupation per site that affects the magnetic phases. For instance, the SG and the mixed SG+ferromagnetic phases are also suppressed by μ. In addition, μ can change the nature of the phase boundaries introducing a first order transition.     

Bulk viscosity of hot dense Quark matter in the PNJL model

Starting from the Kubo formula and the QCD low energy theorem, we study the the bulk viscosity of hot dense quark matter in the PNJL model from the equation of state. We show that the bulk viscosity has a sharp peak near the chiral phase transition, and that the ratio of bulk viscosity over entropy rises dramatically in the vicinity of the phase transition. These results agree with those from the lattice and other model calculations. In addition, we show that the increase of chemical potential raises the bulk viscosity.     

Repetition versus noiseless quantum codes for correlated errors

We study the performance of simple quantum error correcting codes with respect to correlated noise errors characterized by a finite correlation strength μ. Specifically, we consider bit flip (phase flip) noisy quantum memory channels and use repetition and noiseless quantum codes. We characterize the performance of the codes by means of the entanglement fidelity F(μ,p) as function of the error probability p and degree of memory μ. Finally, comparing the entanglement fidelities of repetition and noiseless quantum codes, we find a threshold μ^*(p) for the correlation strength that allows to select the code with better performance.     

A finite element-spherical harmonics radiation transport model for photon migration in turbid media

In this paper, we solve the steady-state form of the Boltzmann transport equation in homogeneous and heterogeneous tissue-like media with a finite element-spherical harmonics (FE-P_N) radiation transport method. We compare FE-transport and diffusion solutions in terms of the ratio of absorption to reduced scattering coefficient, (μ_a/μ_s′) and the anisotropy factor g. Two different scattering phase function formulas are employed to model anisotropic scattering in the slab media with high g-value. Influence of void-like heterogeneities, and of their boundaries with the surrounding medium on the transport of photons are also examined.     

The paramagnetic phase boundary of EuTe at low temperatures

Taking into account the presence of long-range dipolar interactions, we propose a model hamiltonian to calculate the canted—paramagnetic phase boundary of EuTe at low temperatures. By using spin-wave techniques we show that the critical field depends on T² asymptotically. Our calculations are in good agreement with the experimental data.     

Muon hyperfine fields in iron and its dilute alloys

The temperature dependence (240 to 633 K) of the interstitial magnetic field, B_μ, as determined by the rotation of the spin of the μ⁺, has been measured for dilute polycrystalline iron alloys with Mo, Ti and Nb additions. In all cases the behaviours differ from one another and from the Fe(A1) alloys previously studied. B_μ, which is negative with respect to the magnetization, is increased in magnitude by A1 and Mo, and decreased greatly by Ti. The addition of Nb creates a two- phase alloy from which we can assess the role of heterogeneity and/or strain on B_μ in iron. If the temperature dependence of the hyperfine field B_hf extracted from B_μ for Fe(Mo) alloys is interpreted on the model previously used to discuss the Fe(A1) data, we would conclude that the muon is attracted to the Mo atom while repelled by the A1 atoms as the temperature decreases. Measurements giving room temperature values of B_μ for iron alloys with Mn, Cr, V and W taken after annealing above the recrystallization temperature are also reported.     

A Model Study of the Chiral Phase Diagram of QCD

In this paper we study the chiral phase transition of QCD at finite temperature and density by using the rank-2 confining separable gluon propagator model in the framework of Dyson–Schwinger Equations. The critical end point is located at (T _CEP , μ _CEP ) = (69, 270.3 MeV). It is also found that the first order phase transition might not end at one point, but experiences a two-phase coexisting meta-stable state. A comparison with the results in the previous literature is given.     

On Dynamical Systems and Phase Transitions for q + 1-state p-adic Potts Model on the Cayley Tree

In the present paper, we study a new kind of p-adic measures for q?+?1-state Potts model, called p-adic quasi Gibbs measure. For such a model, we derive a recursive relations with respect to boundary conditions. Note that we consider two mode of interactions: ferromagnetic and antiferromagnetic. In both cases, we investigate a phase transition phenomena from the associated dynamical system point of view. Namely, using the derived recursive relations we define a fractional p-adic dynamical system. In ferromagnetic case, we establish that if q is divisible by p, then such a dynamical system has two repelling and one attractive fixed points. We find basin of attraction of the fixed point. This allows us to describe all solutions of the nonlinear recursive equations. Moreover, in that case there exists the strong phase transition. If q is not divisible by p, then the fixed points are neutral, and this yields that the existence of the quasi phase transition. In antiferromagnetic case, there are two attractive fixed points, and we find basins of attraction of both fixed points, and describe solutions of the nonlinear recursive equation. In this case, we prove the existence of a quasi phase transition.     

N=2 boundary supersymmetry in integrable models and perturbed boundary conformal field theory

Boundary integrable models with N=2 supersymmetry are considered. For the simplest boundary N=2 superconformal minimal model with a Chebyshev bulk perturbation we show explicitly how fermionic boundary degrees of freedom arise naturally in the boundary perturbation in order to maintain integrability and N=2 supersymmetry. A new boundary reflection matrix is obtained for this model and N=2 boundary superalgebra is studied. A factorized scattering theory is proposed for a N=2 supersymmetric extension of the boundary sine-Gordon model with either (i) fermionic or (ii) bosonic and fermionic boundary degrees of freedom. Exact results are obtained for some quantum impurity problems: the boundary scaling Lee–Yang model, a massive deformation of the anisotropic Kondo model at the filling values g=2/(2n+3) and the boundary Ashkin–Teller model.     

QCD at a Finite isospin density: From the pion to quark-antiquark condensation

QCD at a finite isospin chemical potential μ _I is studied. This theory has no fermion-sign problem and can be simulated on a lattice by using present-day techniques. We solve this theory analytically in two limits: low μ _I, where chiral perturbation theory is applicable, and asymptotically high μ _I, where perturbative QCD is at work. At a low isospin density, the ground state is a superfluid pion condensate. At a very high density, it is a Fermi liquid with Cooper pairing. The pairs carry the same quantum numbers as the pions. Motivated by this observation, we put forward a conjecture that the transition from hadron to quark matter is smooth. The conjecture passes several nontrivial tests. Our results imply a nontrivial phase diagram in the space of the temperature and chemical potentials of isospin and baryon number. At asymptotically large values of μ _I and small values of the baryon chemical potential, the ground state is in a phase similar to the Fulde-Ferrell-Larkin-Ovchinnikov phase. It is characterized by a spatially modulated superfluid order parameter 〈ūγ ₅ d〉 and may be the asymptotic limit of the inhomogeneous pion-condensation phase advocated by Migdal and others.