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Motivated by the experimental search for the QCD critical point we perform simulations of a stochastic field theory with purely relaxational dynamics (model A). We verify the expected dynamic scaling of correlation functions. Using a finite size scaling analysis we obtain the dynamic critical exponent $z=2.026(56)$. We investigate time dependent correlation functions of higher moments $M^n(t)$ of the order parameter $M(t)$ for $n=1,2,3,4$. We obtain dynamic scaling with the same critical exponent $z$ for all $n$, but the relaxation constant depends on $n$. We also study the relaxation of $M^n(t)$ after a quench, where the simulation is initialized in the high temperature phase, and the dynamics is studied at the critical temperature $T_c$. We find that the evolution does not follow simple scaling with the dynamic exponent $z$, and that it involves an early time rise followed by late stage relaxation., 13 pages, 7 figures. Minor error corrected; shifts normalization of m^2

© 2016 Elsevier B.V. We review the progress achieved in extracting the properties of hot and dense matter from relativistic heavy ion collisions at the relativistic heavy ion collider (RHIC) at Brookhaven National Laboratory and the large hadron collider (LHC) at CERN. We focus on bulk properties of the medium, in particular the evidence for thermalization, aspects of the equation of state, transport properties, as well as fluctuations and correlations. We also discuss the in-medium properties of hadrons with light and heavy quarks, and measurements of dileptons and quarkonia. This review is dedicated to the memory of Gerald E. Brown.

This review gives an overview of effective field theory (EFT) as applied at finite density, with a focus on nuclear many-body systems. Uniform systems with short-range interactions illustrate the ingredients and virtues of many-body EFT and then the varied frontiers of EFT for finite nuclei and nuclear matter are surveyed., 27 pages, 5 figures

In the two decades since the appearance of the book "Bose-Einstein Condensation" in 1995, there have been a number of developments in our understanding of dense matter. After a brief overview of neutron star structure and the Bose-Einstein condensed phases that have been proposed, we describe selected topics, including neutron and proton pairing gaps, the physics of the inner crust of neutron stars, where a neutron fluid penetrates a lattice of nuclei, meson condensates, and pairing in dense quark matter. Especial emphasis is placed on basic physical effects and on connections to the physics of cold atomic gases., Comment: 22 pages, 2 figures, to appear in "Universal Themes of Bose-Einstein Condensation", edited by D.W. Snoke, N.P. Proukakis and P.B. Littlewood (Cambridge University Press)

We consider the time evolution of a dilute atomic Fermi gas after release from a trapping potential. A common difficulty with using fluid dynamics to study the expansion of the gas is that the theory is not applicable in the dilute corona, and that a naive treatment of the entire cloud using fluid dynamics leads to unphysical results. We propose to remedy this problem by including certain non-hydrodynamic degrees of freedom, in particular anisotropic components of the pressure tensor, in the theoretical description. We show that, using this method, it is possible to describe the crossover from fluid dynamics to ballistic expansion locally. We illustrate the use of anisotropic fluid dynamics by studying the expansion of the dilute Fermi gas at unitarity using different functional forms of the shear viscosity, including a shear viscosity which is solely a function of temperature, $\eta\sim (mT)^{3/2}$, as predicted by kinetic theory in the dilute limit., Comment: 22 pages, 6 figures, to appear in Phys Rev A

We consider the most general four fermion operators in QCD for two and three massless flavors and study their renormalization in the vicinity of the Fermi surface. We show that, asymptotically, the largest coupling corresponds to scalar diquark condensation. Asymptotically the direct and iterated (molecular) instanton interactions become equal. We provide simple arguments for the form of the operators that diagonalize the evolution equations. Some solutions of the flow equations exhibit instabilities arising out of purely repulsive interactions., Comment: 13 pages, 2 figures

I review the current understanding of the chiral phase transition in QCD, with particular emphasis on recent results obtained in the instanton liquid model., Comment: 13 pages, 9 PS figures, to appear in QM96 proceedings (Nucl. Phys. A)

In these lectures we discuss the uses of effective field theory in studying dense hadronic matter. We focus on two regimes in the phase diagram. At low baryon density nucleons can be described as non-relativistic point particles interacting via short range forces. Interesting effects arise because of the large nucleon-nucleon scattering length. At very large density QCD matter can be described in terms of quarks and gluons. Unusual many body effects arise because of long range gluons fields, and because of the way color and flavor get entangled in the superconducting state.

In this contribution we summarize recent results on the transport properties of strongly correlated dilute Fermi gases. We discuss the hydrodynamic equations in the normal phase and present new results on the structure of second order terms in the gradient expansion. We also discuss predictions from kinetic theory, and show how these predictions can be tested using experimental data on elliptic flow. We summarize current constraints on the shear viscosity to entropy density ratio $\eta/s$., Comment: 5 pages, to appear in the Proceedings of the 19th Particles and Nuclei International Conference, PANIC 2011, MIT, Cambridge, MA July 2011

In this contribution we summarize recent progress in understanding the shear viscosity of strongly correlated dilute Fermi gases. We discuss predictions from kinetic theory, and show how these predictions can be tested using recent experimental data on elliptic flow. We find agreement between theory and experiments in the high temperature regime $T\gg T_F$, where $T_F$ is the the temperature where quantum degeneracy effects become important. In the low temperature regime, $T\sim T_F$, the strongest constraints on the shear viscosity come from experimental studies of the damping of collective modes. These experiments indicate that $\eta/s\lsim 0.5\hbar/k_B$, where $\eta$ is the shear viscosity and $s$ is the entropy density., Comment: 6 pages, to appear in the proceedings of "Quark Confinement and the Hadron Spectrum IX", August 30 - September 3, 2010, Madrid, Spain

Shear viscosity is a measure of the amount of dissipation in a simple fluid. In kinetic theory shear viscosity is related to the rate of momentum transport by quasi-particles, and the uncertainty relation suggests that the ratio of shear viscosity eta to entropy density s in units of hbar/k_B is bounded by a constant. Here, hbar is Planck's constant and k_B is Boltzmann's constant. A specific bound has been proposed on the basis of string theory where, for a large class of theories, one can show that eta/s is greater or equal to hbar/(4 pi k_B). We will refer to a fluid that saturates the string theory bound as a perfect fluid. In this review we summarize theoretical and experimental information on the properties of the three main classes of quantum fluids that are known to have values of eta/s that are smaller than hbar/k_B. These fluids are strongly coupled Bose fluids, in particular liquid helium, strongly correlated ultracold Fermi gases, and the quark gluon plasma. We discuss the main theoretical approaches to transport properties of these fluids: kinetic theory, numerical simulations based on linear response theory, and holographic dualities. We also summarize the experimental situation, in particular with regard to the observation of hydrodynamic behavior in ultracold Fermi gases and the quark gluon plasma., Comment: 76 pages, 11 figures, review article, extensive revisions

Experimental results obtained at the Relativistic Heavy Ion Collider (RHIC) have been interpreted in terms of a strongly interacting quark gluon plasma. The strongly interacting plasma is characterized by ``perfect fluidity'', i.e. a ratio of shear viscosity to entropy density that saturates a proposed lower bound. In this contribution we explore the possibility that a similar phenomenon takes place in a strongly coupled non-relativistic Fermi liquid in which the scattering length between the Fermions is infinitely large., Comment: Talk given at 23rd Winter Workshop on Nuclear Dynamics, Big Sky, Montana, 11-18 Feb 2007, Acta Physica Hungarica, in press

We review many body calculations of the equation of state of dilute neutron matter in the context of effective field theories of the nucleon-nucleon interaction., Comment: To appear in the proceedings of 4th International Conference On Quarks And Nuclear Physics (QNP06), 5-10 June 2006, Madrid, Spain. European Physical Journal A, in press

We study nuclear and neutron matter by combining chiral effective field theory with non-perturbative lattice methods. In our approach nucleons and pions are treated as point particles on a lattice. This allows us to probe larger volumes, lower temperatures, and greater nuclear densities than in lattice QCD. The low energy interactions of these particles are governed by chiral effective theory and operator coefficients are determined by fitting to zero temperature few-body scattering data. Any dependence on the lattice spacing can be understood from the renormalization group and absorbed by renormalizing operator coefficients. In this way we have a realistic simulation of many-body nuclear phenomena with no free parameters, a systematic expansion, and a clear theoretical connection to QCD. We present results for hot neutron matter at temperatures 20 to 40 MeV and densities below twice nuclear matter density., 41 pages, 23 figures

We explain how an effective theory of the CFL phase can be used to study the effect of the strange quark mass on the ground state and the excitation spectrum. We also apply the effective theory to the problem of neutrino emission from a CFL quark core inside a neutron star., Comment: 4 pages, to appear in the proceedings of Quark Matter 2002

Inspired by a recent proposal for a Higgs description of QCD we study the possible formation of a color-octet/flavor-octet quark-anti-quark condensate in the instanton liquid model. For this purpose we calculate two-point correlation functions of color-singlet and octet quark-anti-quark operators. We find long range order in the standard $$ channel, but not in the color-octet channel. We emphasize that similar calculations in lattice QCD can check whether or not a color-flavor locked Higgs phase is realized in QCD at zero temperature and baryon density., Comment: 10 pages, 2 figures, (revised) added discussion of flavor symmetry breaking source terms

We consider QCD at a nonzero chemical potential for strangeness. At a critical value of the chemical potential equal to the kaon mass, kaon condensation occurs through a continuous phase transition. We show that, when the isospin symmetry is exact in the Lagrangian, a Goldstone boson with a dispersion relation $E \sim p^2$ appears in the kaon condensed phase. At the same time, the number of the Goldstone bosons is less than the number of broken generators. Both phenomena are familiar in non-relativistic systems. We interpret our results in terms of a Goldstone boson counting rule found previously by Nielsen and Chadha. We also formulate a criterion sufficient for the equality between the number of Goldstone bosons and the number of broken generators., Comment: 13 pages, 1 figure, Latex

We review recent work on how the superfluid state of three flavor quark matter is affected by non-zero quark masses and chemical potentials., Comment: 7 pages. To appear in the proceedings of 6th Workshop on Non-Perturbative QCD, Paris, France, 5-9 Jun 2001

We discuss recent results on color superconductivity in QCD at large chemical potential., Comment: to appear in the Proceedings of the 10th International Conference on Recent Progress in Many-Body Theories (MBX), Seattle, WA, 10-15 Sep 1999, R. F. Bishop et al. (eds.), World Scientific (Singapore)

We comment on the recent paper (hep-lat/0005006) by Isgur and Thacker on the origin of the OZI rule in QCD. We show that instantons explain the sign and magnitude of the observed OZI-violating amplitude in all mesonic channels, not just in the $\eta'$ channel. We comment on the role of instantons in hadronic spectroscopy and the relation between instantons and the large $N_c$ limit of QCD., Comment: 5 pages, 3 figures

We summarize some recent results on the structure of QCD at very high baryon density., 4 pages, to appear in the proceedings of Quark Matter 99

We study flavor mixing and the axial anomaly in QCD at zero and finite temperature. Using the instanton liquid model, we show that the strength of the anomaly is essentially unchanged near the critical temperature for chiral symmetry restoration. We demonstrate that nevertheless, chiral symmetry restoration has important consequences for the eta and eta prime. In particular, the strange and non-strange components of the eta unmix near T_c. The anomaly does not affect the strange eta, so we expect a light purely strange pseudoscalar meson near the phase transition., 11 pages, 5 figures

Strongly correlated quantum fluids are phases of matter that are intrinsically quantum mechanical, and that do not have a simple description in terms of weakly interacting quasi-particles. Two systems that have recently attracted a great deal of interest are the quark-gluon plasma, a plasma of strongly interacting quarks and gluons produced in relativistic heavy ion collisions, and ultracold atomic Fermi gases, very dilute clouds of atomic gases confined in optical or magnetic traps. These systems differ by more than 20 orders of magnitude in temperature, but they were shown to exhibit very similar hydrodynamic flow. In particular, both fluids exhibit a robustly low shear viscosity to entropy density ratio which is characteristic of quantum fluids described by holographic duality, a mapping from strongly correlated quantum field theories to weakly curved higher dimensional classical gravity. This review explores the connection between these fields, and it also serves as an introduction to the Focus Issue of New Journal of Physics on Strongly Correlated Quantum Fluids: from Ultracold Quantum Gases to QCD Plasmas. The presentation is made accessible to the general physics reader and includes discussions of the latest research developments in all three areas., Comment: 138 pages, 25 figures, review associated with New Journal of Physics special issue "Focus on Strongly Correlated Quantum Fluids: from Ultracold Quantum Gases to QCD Plasmas" (http://iopscience.iop.org/1367-2630/focus/Focus%20on%20Strongly%20Correlated%20Quantum%20Fluids%20-%20from%20Ultracold%20Quantum%20Gases%20to%20QCD%20Plasmas)

International audience; The non-monotonic beam energy dependence of the higher cumulants of net-proton fluctuations is a widely studied signature of the conjectured presence of a critical point in the QCD phase diagram. In this work we study the effect of resonance decays on critical fluctuations. We show that resonance effects reduce the signatures of critical fluctuations, but that for reasonable parameter choices critical effects in the net-proton cumulants survive. The relative role of resonance decays has a weak dependence on the order of the cumulants studied with a slightly stronger suppression of critical effects for higher-order cumulants.

We provide a summary of our current knowledge of the phase structure of very dense quark matter. We concentrate on the question how the ground state at asymptotically high density -- color-flavor-locked (CFL) matter -- is modified as the density is lowered. We discuss the nature of the quasi-particle excitations, and present work on the transport properties of dense QCD matter., Comment: To appear in Proceedings for "Compact stars in the QCD phase diagram II (CSQCD II), May 20-24, 2009, KIAA at Peking University, Beijing - P. R. China [http://vega.bac.pku.edu.cn/rxxu/csqcd.htm]