Color superconductivity in the static Einstein Universe

We study the behavior of quark and diquark condensates in dense quark matter under the influence of a gravitational field adopting as a simple model the static $D-$dimensional Einstein Universe. Calculations are performed in the framework of the extended Nambu--Jona-Lasinio model at finite temperature and quark density on the basis of the thermodynamic potential and the gap equations. Quark and diquark condensates as functions of the chemical potential and temperature at different values of the curvature have been studied. Phase portraits of the system have been constructed

Gapless Color Superconductivity

We present the dispersion relations for quasiparticle excitations about the color-flavor locked ground state of QCD at high baryon density. In the presence of condensates which pair light and strange quarks there need not be an energy gap in the quasiparticle spectrum. This raises the possibility of gapless color superconductivity, with a Meissner effect but no minimum excitation energy. Analysis within a toy model suggests that gapless color superconductivity may occur only as a metastable phase.Comment: 4 pages, Revtex, eps figures include

Inhomogeneity driven by Higgs instability in gapless superconductor

The fluctuations of the Higgs and pseudo Nambu-Goldstone fields in the 2SC phase with mismatched pairing are described in the nonlinear realization framework of the gauged Nambu--Jona-Lasinio model. In the gapless 2SC phase, not only Nambu-Goldstone currents can be spontaneously generated, but the Higgs field also exhibits instablity. The Nambu-Goldstone currents generation indicates the formation of the single plane wave LOFF state and breaks rotation symmetry, while the Higgs instability favors spatial inhomogeneity and breaks translation invariance. In this paper, we focus on the Higgs instability which has not drawn much attention yet. The Higgs instability cannot be removed without a long range force, thus it persists in the gapless superfluidity and induces phase separation. In the case of g2SC state, the Higgs instability can only be partially removed by the electric Coulomb energy. However, it is not excluded that the Higgs instability might be completely removed in the charge neutral gCFL phase by the color Coulomb energy.Comment: 21 pages, 5 figure

Random matrix models for phase diagrams

We describe a random matrix approach that can provide generic and readily soluble mean-field descriptions of the phase diagram for a variety of systems ranging from QCD to high-T_c materials. Instead of working from specific models, phase diagrams are constructed by averaging over the ensemble of theories that possesses the relevant symmetries of the problem. Although approximate in nature, this approach has a number of advantages. First, it can be useful in distinguishing generic features from model-dependent details. Second, it can help in understanding the `minimal' number of symmetry constraints required to reproduce specific phase structures. Third, the robustness of predictions can be checked with respect to variations in the detailed description of the interactions. Finally, near critical points, random matrix models bear strong similarities to Ginsburg-Landau theories with the advantage of additional constraints inherited from the symmetries of the underlying interaction. These constraints can be helpful in ruling out certain topologies in the phase diagram. In this Key Issue, we illustrate the basic structure of random matrix models, discuss their strengths and weaknesses, and consider the kinds of system to which they can be applied.Comment: 29 pages, 2 figures, uses iopart.sty. Author's postprint versio

Gluonic phases, vector condensates, and exotic hadrons in dense QCD

We study the dynamics in phases with vector condensates of gluons (gluonic phases) in dense two-flavor quark matter. These phases yield an example of dynamics in which the Higgs mechanism is provided by condensates of gauge (or gauge plus scalar) fields. Because vacuum expectation values of spatial components of vector fields break the rotational symmetry, it is naturally to have a spontaneous breakdown both of external and internal symmetries in this case. In particular, by using the Ginzburg-Landau approach, we establish the existence of a gluonic phase with both the rotational symmetry and the electromagnetic U(1) being spontaneously broken. In other words, this phase describes an anisotropic medium in which the color and electric superconductivities coexist. It is shown that this phase corresponds to a minimum of the Ginzburg-Landau potential and, unlike the two-flavor superconducting (2SC) phase, it does not suffer from the chromomagnetic instability. The dual (confinement) description of its dynamics is developed and it is shown that there are light exotic vector hadrons in the spectrum, some of which condense. Because most of the initial symmetries in this system are spontaneously broken, its dynamics is very rich.Comment: 33 pages, RevTeX; v.2: Published PRD versio

Gapless phases of color-superconducting matter

We discuss gapless color superconductivity for neutral quark matter in beta equilibrium at zero as well as at nonzero temperature. Basic properties of gapless superconductors are reviewed. The current progress and the remaining problems in the understanding of the phase diagram of strange quark matter are discussed.Comment: 8 pages, 2 figures. Plenary talk at Strangeness in Quark Matter 2004 (SQM2004), Cape Town, South Africa, 15-20 September 2004. Minor correction

Thermodynamic Curvature of the BTZ Black Hole

Some thermodynamic properties of the Ba\~nados-Teitelboim-Zanelli (BTZ) black hole are studied to get the effective dimension of its corresponding statistical model. For this purpose, we make use of the geometrical approach to the thermodynamics: Considering the black hole as a thermodynamic system with two thermodynamic variables (the mass $M$ and the angular momemtum $J$), we obtain two-dimensional Riemannian thermodynamic geometry described by positive definite Ruppeiner metric. From the thermodynamic curvature we find that the extremal limit is the critical point. The effective spatial dimension of the statistical system corresponding to the near-extremal BTZ black holes is one. Far from the extremal point, the effective dimension becomes less than one, which leads to one possible speculation on the underlying structure for the corresponding statistical model.Comment: 19 pages, LaTeX with revtex macro, 4 figures in eps file

Conformal Invariance and Degrees of Freedom in the QCD String

We demonstrate that the Hagedorn-like growth of the number of observed meson states can be used to constrain the degrees of freedom of the underlying effective QCD string. We find that the temperature relevant for such string theories is not given by the usual Hagedorn value $T_H\approx 160$ MeV, but is considerably higher. This resolves an apparent conflict with the results from a static quark-potential analysis, and suggests that conformal invariance and modular invariance are indeed reflected in the hadronic spectrum. We also find that the $D_\perp=2$ scalar string is in excellent agreement with data.Comment: 13 pages (Standard LaTeX); --> replaced version emphasizes new results, and agrees with version to appear in Physical Review Letters (Jan 1994

Superfluid phase transition and strong-coupling effects in an ultracold Fermi gas with mass imbalance

We investigate the superfluid phase transition and effects of mass imbalance in the BCS (Bardeen-Cooper-Schrieffer)-BEC (Bose-Einstein condensation) crossover regime of an cold Fermi gas. We point out that the Gaussian fluctuation theory developed by Nozi\`eres and Schmitt-Rink and the $T$-matrix theory, that are now widely used to study strong-coupling physics of cold Fermi gases, give unphysical results in the presence of mass imbalance. To overcome this problem, we extend the $T$-matrix theory to include higher-order pairing fluctuations. Using this, we examine how the mass imbalance affects the superfluid phase transition. Since the mass imbalance is an important key in various Fermi superfluids, such as $^{40}$K-$^6$Li Fermi gas mixture, exciton condensate, and color superconductivity in a dense quark matter, our results would be useful for the study of these recently developing superfluid systems.Comment: 7 pages, 4 figures, Proceedings of QFS-201

Microcanonical statistics of black holes and bootstrap condition

The microcanonical statistics of the Schwarzschild black holes as well as the Reissner-Nordstr$\sf \ddot{o}$m black holes are analyzed. In both cases we set up the inequalities in the microcanonical density of states. These are then used to show that the most probable configuration in the gases of black holes is that one black hole acquires all of the mass and all of the charge at high energy limit. Thus the black holes obey the statistical bootstrap condition and, in contrast to the other investigation, we see that U(1) charge does not break the bootstrap property.Comment: 16 pages. late