Quark–hadron phase transition in massive gravity

We study the quark–hadron phase transition in the framework of massive gravity. We show that the modification of the FRW cosmological equations leads to the quark–hadron phase transition in the early massive Universe. Using numerical analysis, we consider that a phase transition based on the chiral symmetry breaking after the electroweak transition, occurred at approximately 10 μs after the Big Bang to convert a plasma of free quarks and gluons into hadrons.     

The Hadron to quark-gluon transition in relativistic heavy-ion collisions

In this paper we construct a scenario for the QCD transition from the hadron phase to the quark/gluon phase using physical models for these phases. The hadron phase is modeled by a spectrum of hadrons with masses which drop (with a common scaling factor) towards zero at chiral symmetry restoration. The number of hadronic effective degrees of freedom is limited by the number of microscopic degrees of freedom in the quark/gluon phase. This limitation can be imposed either by fiat or through the introduction of a temperature-dependent excluded volume. Given that the number of degrees of freedom in hadrons and in quarks and gluons are roughly equal, the QCD phase transition is inhibited by the bag constant. The only phase transition seen in lattice-gauge calculations, once low-mass quarks are included, is the restoration of chiral symmetry which occurs at the relatively low temperature of ˜ 150 MeV. At present, lattice gauge calculations do not have the resolution to determine the properties of the higher hadronic states accurately. They do, however, demonstrate that chiral restoration takes place in the (ρ. a₁), ( +)), ( −)) and (π, σ) systems by yielding “screening masses” for chiral partners which are distinct for T < T _xSR and identical for T>T _xSR. Further, within numerical accuracy, these “screening masses” are consistent with pure thermal energies and show no evidence of remaining bare masses once chiral symmetry is restored. These, and other lattice-gauge results, will be discussed in the light of our scenario. We shall also consider the consequences of our picture for relativistic heavy-ion experiments.     

Effects of Composite Pions on the Chiral Condensate within the PNJL Model at Finite Temperature

We investigate the effect of composite pions on the behaviour of the chiral condensate at finite temperature within the Polyakov-loop improved NJL model. To this end we treat quark-antiquark correlations in the pion channel (bound states and scattering continuum) within a Beth–Uhlenbeck approach that uses medium-dependent phase shifts. A striking medium effect is the Mott transition which occurs when the binding energy vanishes and the discrete pion bound state merges the continuum. This transition is triggered by the lowering of the continuum edge due to the chiral restoration transition. This in turn also entails a modification of the Polyakov-loop so that the SU(3) center symmetry gets broken at finite temperature and dynamical quarks (and gluons) appear in the system, taking over the role of the dominant degrees of freedom from the pions. At low temperatures our model reproduces the chiral perturbation theory result for the chiral condensate while at high temperatures the PNJL model result is recovered. The new aspect of the current work is a consistent treatment of the chiral restoration transition region within the Beth–Uhlenbeck approach on the basis of mesonic phase shifts for the treatment of the correlations.     

Born effective charge reversal and metallic threshold state at a band insulator-Mott insulator transition

We study the quantum phase transition between a band (“ionic”) insulator and a Mott-Hubbard insulator, realized at a critical value in a bipartite Hubbard model with two inequivalent sites, whose on-site energies differ by an offset . The study is carried out both in D=1 and D=2 (square and honeycomb lattices), using exact Lanczos diagonalization, finite-size scaling, and Berry's phase calculations of the polarization. The Born effective charge jump from positive infinity to negative infinity previously discovered in D=1 by Resta and Sorella is confirmed to be directly connected with the transition from the band insulator to the Mott insulating state, in agreement with recent work of Ortiz et al. In addition, symmetry is analysed, and the transition is found to be associated with a reversal of inversion symmetry in the ground state, of magnetic origin. We also study the D=1 excitation spectrum by Lanczos diagonalization and finite-size scaling. Not only the spin gap closes at the transition, consistent with the magnetic nature of the Mott state, but also the charge gap closes, so that the intermediate state between the two insulators appears to be metallic. This finding, rationalized within Hartree-Fock as due to a sign change of the effective on-site energy offset for the minority spin electrons, underlines the profound difference between the two insulators. The band-to-Mott insulator transition is also studied and found in the same model in D=2. There too we find an associated, although weaker, polarization anomaly, with some differences between square and honeycomb lattices. The honeycomb lattice, which does not possess an inversion symmetry, is used to demonstrate the possibility of an inverted piezoelectric effect in this kind of ionic Mott insulator. Received 21 May 1999     

Chiral crossover characterized by Mott transition at finite temperature

We discuss the proper definition for the chiral crossover at finite temperature,based on Goldstone's theorem.Different from the commonly used maximum change in chiral condensate,we propose defining the crossover temperature using the Mott transition of pseudo-Goldstone bosons,which,by definition,guarantees Goldstone's theorem.We analytically and numerically demonstrate this property in the frame of a Pauli-Villars regularized NJL model.In an external magnetic field,we find that the Mott transition temperature shows an inverse magnetic catalysis effect.     

Recent developments on the UrQMD hybrid model

We present recent results from the UrQMD hybrid approach investigating the influence of a deconfinement phase transition on the dynamics of hot and dense nuclear matter. In the hydrodynamic stage an equation of state that incorporates a critical end-point (CEP) in line with lattice data is used. The equation of state describes chiral restoration as well as the deconfinement phase transition. We compare the results from this new equation of state to results obtained by applying a hadron resonance gas equation of state, focusing on bulk observables. Furthermore we will discuss future improvements of the hydrodynamic model. This includes the formulation of chiral fluid dynamics to be able to study the effects of a chiral critical point as well as considerable improvements in terms of computational time which would open up possibilities for observables that require high statistics.     

Violation of chiral symmetry in curved spacetime with a magnetic field

The phase structure of a four-fermion (4F) model in curved spacetime with a magnetic field is investigated (in the framework of a 1/N expansion and an approximation linear in the curvature). The effective potential for the combined fields is calculated for the following situations: a) nonzero curvature and b) nonzero curvature and nonzero magnetic field. It is shown that the gravitational field may offset the magnetic-field effect, with restoration of chiral symmetry as the result. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 43–47, July, 1997.     

Chiral Lagrangians and the Transition Amplitude for Radiative Muon Capture

 The transition operator for the radiative capture of mesons by protons is constructed starting from a chiral Lagrangian of the system obtained within the approach of hidden local symmetries. The transition operator is gauge invariant and its hadron radiative part satisfies exactly two relevant continuity equations. Received October 16, 1998; accepted for publication February 23, 1999     

Quark potential in a quark–meson plasma

We investigate the effect of the restoration of chiral symmetry on the quark potential in a quark–meson plasma by considering meson exchanges in the two flavor Nambu–Jona-Lasinio model at finite temperature and density. There are two possible oscillations in the chiral restoration phase; one is the Friedel oscillation due to the sharp quark Fermi surface at high density, and the other is the Yukawa oscillation driven by the complex meson poles at high temperature. The quark–meson plasma is strongly coupled in the temperature region 1≤T/T _c≤3, with T _c being the critical temperature of the chiral phase transition. The maximum coupling in this region is located at the phase transition point.     

洪德耦合的调控与轨道选择Mott相变

洪德耦合相互作用是导致多轨道体系发生轨道选择Mott相变的重要因素之一. 通过调控洪德耦合相互作用来研究其不同组成部分对轨道选择Mott相变的作用. 利用基于Lanczos 求解器的动力学平均场理论, 对比了双轨道的J模型和Jz模型的金属-绝缘体相变, 并重点讨论洪德耦合中的自旋翻转项和电子对跃迁项以及轨道宽度比值W₂/W₁如何影响轨道选择Mott 相变. 在J模型的相图中, Mott选择相占有较大的区域, 而Jz模型的轨道选择Mott 相只存在于一个很狭窄的区域内, 这说明自旋翻转项及电子对跳跃项是有利于轨道选择Mott相变发生的关键因素. 此外当轨道宽度之比大于W₂/W₁=0.7时, Jz 模型的轨道选择Mott 相会完全消失, 而J模型中只要轨道宽度不同都存在轨道选择Mott相. 因而, 简化后的Jz 模型只是在特定条件下才适合于研究轨道选择Mott相变.     

A new slant on hadron structure

Rather than regarding the restriction of current lattice QCD simulations to quark masses that are 5–10 times larger than those observed as a problem, we note that this presents a wonderful opportunity to deepen our understanding of QCD. Just as it has been possible to learn a great deal about QCD by treating N _c as a variable, so the study of hadron properties as a function of quark mass is leading us to a deeper appreciation of hadron structure. As examples we cite progress in using the chiral properties of QCD to connect hadron masses, magnetic moments, charge radii and structure functions calculated at large quark masses within lattice QCD with the values observed physically.     

Mott transition from a spin liquid to a Fermi liquid in the spin-frustrated organic conductor kappa-(ET)2Cu2(CN)3

The pressure-temperature phase diagram of the organic Mott insulator kappa-(ET)2Cu2(CN)3, a model system of the spin liquid on triangular lattice, has been investigated by 1H NMR and resistivity measurements. The spin-liquid phase is persistent before the Mott transition to the metal or superconducting phase under pressure. At the Mott transition, the spin fluctuations are rapidly suppressed and the Fermi-liquid features are observed in the temperature dependence of the spin-lattice relaxation rate and resistivity. The characteristic curvature of the Mott boundary in the phase diagram highlights a crucial effect of the spin frustration on the Mott transition.     

On the chiral phase transition in hadronic matter

A qualitative analysis of the chiral phase transition in QCD with two massless quarks and nonzero baryon density is performed. It is assumed that, at zero baryonic density, ρ=0, the temperature phase transition is of the second order. Due to a specific power dependence of baryon masses on the chiral condensate, the phase transition becomes of the first order at the temperature T=T_ph(ρ) for ρ>0. At temperatures T_cont(ρ)> _T>_Tph(ρ), there is a mixed phase consisting of the quark phase (stable) and the hadron phase (unstable). At the temperature T=T_cont(ρ), the system experiences a continuous transition to the pure chirally symmetric phase.     

Search for signatures of phase transition and critical point in heavy-ion collisions

The general concepts in the critical phenomena related with the notions of “scaling” and “universality” are considered. Behavior of various systems near a phase transition is displayed. Search for clear signatures of the phase transition of the nuclear matter and location of the critical point in heavy-ion collisions (HIC) is discussed. The experimental data on inclusive spectra measured in HIC at RHIC and SPS over a wide range of energies s _{N N} ^1/2 = 9–200 GeV are analyzed in the framework of z-scaling. A microscopic scenario of the constituent interactions is presented. Dependence of the energy loss on the momentum of the produced hadron, energy and centrality of the collision is studied. Self-similarity of the constituent interactions described in terms of momentum fractions is used to characterize the nuclear medium by “specific heat” and colliding nuclei by fractal dimensions. Preferable kinematical regions to search for signatures of the phase transition of the nuclear matter produced in HIC are discussed. Discontinuity of the “specific heat” is assumed to be a signature of the phase transition and the critical point.     

The limitimg behaviour of the well width of a quantum two-dimensional metal–insulator transition

Metal–Insulator transition using an exact two-dimensional (2D) dielectric function is investigated for a shallow donor in an isolated well of a GaAs/Ga_1−xAl_sAs superlattice system within the effective mass approximation. Vanishing of the donor ionization energy as a function of well width and the donor concentration suggests that a phase transition is not possible even below a well width of 10 Å, supporting the scaling theory of localization. The effects of Anderson localization, exchange and correlation in the Hubbard model are included in a simple way. The relationship between the present model and the Mott criterion in terms of Hubbard model is also brought out. The critical concentration appears to be enhanced when a random distribution of impurities is considered. The limiting behaviour of the well width for a quantum 2D well is brought out. A simple expression is derived for a Mott constant in 2D, a*N_c^1/2 exp (9.86 exp (−L/a*))=0.123, where N_c is the critical concentration per area. Results are compared with the existing data available and discussed in the light of existing literature.