Spinodal Instabilities of Baryon-Rich Quark-gluon Plasma in the PNJL Model

Using the Polyakov-Nambu-Jona-Lasinia (PNJL) model, we study the spinodal instability of a baryon-rich quark-gluon plasma in the linear response theory. We find that the spinodal unstable region in the temperature and density plane shrinks with increasing wave number of the unstable mode and is also reduced if the effect of Polyakov loop is not included. In the small wave number or long wavelength limit, the spinodal boundaries in both cases of with and without the Polyakov loop coincide with those determined from the isothermal spinodal instability in the thermodynamic approach. Also, the vector interactions among quarks is found to suppress unstable modes of all wave numbers. Moreover, the growth rate of unstable modes initially increases with the wave number but is reduced when the wave number becomes large. Including the collisional effect from quark scattering via the linearized Boltzmann equation, we further find that it decreases the growth rate of unstable modes of all wave numbers. Relevance of these results to relativistic heavy ion collisions is discussed.Comment: 13 pages, 9 figure

Pion flow and antiflow in relativistic heavy-ion collisions

Within the framework of a relativistic transport model (ART) for heavy-ion collisions at AGS energies, we study the transverse flow of pions with respect to that of nucleons using two complementary approaches. It is found that in central collisions pions develop a weak flow as a result of the flow of baryon resonances from which they are produced. On the other hand, they have a weak antiflow in peripheral collisions due to the shadowing of spectators. Furthermore, it is shown that both pion flow and antiflow are dominated by those with large transverse momenta.Comment: Phys. Rev. C, Rapid communication, in press. Figures are available from the authors upon reques

Kaon dispersion relation and flow in relativistic heavy-ion collisions

Within the framework of a relativistic transport model (ART) for heavy-ion collisions at AGS energies, we examine the effects of kaon dispersion relation on the transverse flow of kaons and their transverse momentum and azimuthal angle distributions. We find that the transverse flow is the most sensitive observable for studying the kaon dispersion relation in dense medium.Comment: 7 pages, latex, 3 figures available upon request from the authors, Phys. Rev. C (1996) in pres

Revealing Tripartite Quantum Discord with Tripartite Information Diagram

A new measure based on the tripartite information diagram is proposed for identifying quantum discord in tripartite systems. The proposed measure generalizes the mutual information underlying discord from bipartite to tripartite systems, and utilizes both one-particle and two-particle projective measurements to reveal the characteristics of the tripartite quantum discord. The feasibility of the proposed measure is demonstrated by evaluating the tripartite quantum discord for systems with states close to Greenberger-Horne-Zeilinger, W, and biseparable states. In addition, the connections between tripartite quantum discord and two other quantum correlations---namely genuine tripartite entanglement and genuine tripartite Einstein-Podolsky-Rosen steering---are briefly discussed. The present study considers the case of quantum discord in tripartite systems. However, the proposed framework can be readily extended to general N-partite systems

Convergence to global equilibrium for Fokker-Planck equations on a graph and Talagrand-type inequalities

In recent work, Chow, Huang, Li and Zhou introduced the study of Fokker-Planck equations for a free energy function defined on a finite graph. When $N\ge 2$ is the number of vertices of the graph, they show that the corresponding Fokker-Planck equation is a system of $N$ nonlinear ordinary differential equations defined on a Riemannian manifold of probability distributions. The different choices for inner products on the space of probability distributions result in different Fokker-Planck equations for the same process. Each of these Fokker-Planck equations has a unique global equilibrium, which is a Gibbs distribution. In this paper we study the {\em speed of convergence} towards global equilibrium for the solution of these Fokker-Planck equations on a graph, and prove that the convergence is indeed exponential. The rate as measured by the decay of the $L_2$ norm can be bound in terms of the spectral gap of the Laplacian of the graph, and as measured by the decay of (relative) entropy be bound using the modified logarithmic Sobolev constant of the graph. With the convergence result, we also prove two Talagrand-type inequalities relating relative entropy and Wasserstein metric, based on two different metrics introduced in [CHLZ] The first one is a local inequality, while the second is a global inequality with respect to the "lower bound metric" from [CHLZ]

Mode Regularized Generative Adversarial Networks

Although Generative Adversarial Networks achieve state-of-the-art results on a variety of generative tasks, they are regarded as highly unstable and prone to miss modes. We argue that these bad behaviors of GANs are due to the very particular functional shape of the trained discriminators in high dimensional spaces, which can easily make training stuck or push probability mass in the wrong direction, towards that of higher concentration than that of the data generating distribution. We introduce several ways of regularizing the objective, which can dramatically stabilize the training of GAN models. We also show that our regularizers can help the fair distribution of probability mass across the modes of the data generating distribution, during the early phases of training and thus providing a unified solution to the missing modes problem.Comment: Published as a conference paper at ICLR 201

Effects of momentum-dependent nuclear potential on two-nucleon correlation functions and light cluster production in intermediate energy heavy-ion collisions

Using an isospin- and momentum-dependent transport model, we study the effects due to the momentum dependence of isoscalar nuclear potential as well as that of symmetry potential on two-nucleon correlation functions and light cluster production in intermediate energy heavy-ion collisions induced by neutron-rich nuclei. It is found that both observables are affected significantly by the momentum dependence of nuclear potential, leading to a reduction of their sensitivity to the stiffness of nuclear symmetry energy. However, the t/$^{3}$He ratio remains a sensitive probe of the density dependence of nuclear symmetry energy.Comment: 20 pages, 11 figure