Numerical solution of the color superconductivity gap in a weak coupling constant

We present the numerical solution of the full gap equation in a weak coupling constant $g$. It is found that the standard approximations to derive the gap equation to the leading order of coupling constant are essential for a secure numerical evaluation of the logarithmic singularity with a small coupling constant. The approximate integral gap equation with a very small $g$ should be inverted to a soft integral equation to smooth the logarithmic singularity near the Fermi surface. The full gap equation is solved for a rather large coupling constant $g\ge 2.0$. The approximate and soft integral gap equations are solved for small $g$ values. When their solutions are extrapolated to larger $g$ values, they coincide the full gap equation solution near the Fermi surface. Furthermore, the analytical solution matches the numerical one up to the order one O(1). Our results confirm the previous estimates that the gap energy is of the order tens to 100 MeV for the chemical potential $\mu\le 1000$ MeV. They also support the validity of leading approximations applied to the full gap equation to derive the soft integral gap equation and its analytical solution near the Fermi surface.Comment: 7 pages+ 6 figs, Stanford, Frankfurt and Bethlehe

Dense quark matter in compact stars

The densest predicted state of matter is colour-superconducting quark matter, in which quarks near the Fermi surface form a condensate of Cooper pairs. This form of matter may well exist in the core of compact stars, and the search for signatures of its presence is an ongoing enterprise. Using a bag model of quark matter, I discuss the effects of colour superconductivity on the mass-radius relationship of compact stars, showing that colour superconducting quark matter can occur in compact stars at values of the bag constant where ordinary quark matter would not be allowed. The resultant ``hybrid'' stars with colour superconducting quark matter interior and nuclear matter surface have masses in the range 1.3-1.6 Msolar and radii 8-11 km. Once perturbative corrections are included, quark matter can show a mass-radius relationship very similar to that of nuclear matter, and the mass of a hybrid star can reach 1.8 \Msolar.Comment: 11 pages, for proceedings of SQM 2003 conference; references added, abstract reworde

Enforced Electrical Neutrality of the Color-Flavor Locked Phase

We demonstrate that quark matter in the color-flavor locked phase of QCD is rigorously electrically neutral, despite the unequal quark masses, and even in the presence of an electron chemical potential. As long as the strange quark mass and the electron chemical potential do not preclude the color-flavor locked phase, quark matter is automatically neutral. No electrons are required and none are admitted.Comment: 4 pages, revtex. v2: very minor changes only. v3: small clarifications; reference added; version to appear in Phys. Rev. Lett. v4, posted in 2008: typo in Eq. 14 correcte

Spin-one color superconductivity in compact stars?- an analysis within NJL-type models

We present results of a microscopic calculation using NJL-type model of possible spin-one pairings in two flavor quark matter for applications in compact star phenomenology. We focus on the color-spin locking phase (CSL) in which all quarks pair in a symmetric way, in which color and spin states are locked. The CSL condensate is particularly interesting for compact star applications since it is flavor symmetric and could easily satisfy charge neutrality. Moreover, the fact that in this phase all quarks are gapped might help to suppress the direct Urca process, consistent with cooling models. The order of magnitude of these small gaps (~1 MeV) will not influence the EoS, but their also small critical temperatures (T_c ~800 keV) could be relevant in the late stages neutron star evolution, when the temperature falls below this value and a CSL quark core could form.Comment: 7 pages, 7 figures, revised version, accepted for the Conference Proceedings of "Isolated Neutron Stars: from the Interior to the Surface", London, 24-28. April 200

A Diagrammatic Approach to Crystalline Color Superconductivity

We present a derivation of the gap equation for the crystalline color superconducting phase of QCD which begins from a one-loop Schwinger-Dyson equation written using a Nambu-Gorkov propagator modified to describe the spatially varying condensate. Some aspects of previous variational calculations become more straightforward when rephrased beginning from a diagrammatic starting point. This derivation also provides a natural base from which to generalize the analysis to include quark masses, nontrivial crystal structures, gluon propagation at asymptotic densities, and nonzero temperature. In this paper, we analyze the effects of nonzero temperature on the crystalline color superconducting phase.Comment: 15 pages. 2 eps figure

QCD at finite isospin density

QCD at finite isospin chemical potential mu_I has no fermion sign problem and can be studied on the lattice. We solve this theory analytically in two limits: at low mu_I where chiral perturbation theory is applicable, and at asymptotically high mu_I where perturbative QCD works. At low isospin density the ground state is a pion condensate, whereas at high density it is a Fermi liquid with Cooper pairing. The pairs carry the same quantum numbers as the pion. This leads us to a conjecture that the transition from hadron to quark matter is smooth, which passes several tests. Our results imply a nontrivial phase diagram in the space of temperature and chemical potentials of isospin and baryon number.Comment: 4 pages, 1 figure, version to appear in PR

QCD-like Theories at Finite Baryon and Isospin Density

We use 2-color QCD as a model to study the effects of simultaneous presence of chemical potentials for isospin charge, $\mu_I$, and for baryon number, $\mu_B$. We determine the phase diagrams for 2 and 4 flavor theories using the method of effective chiral Lagrangians at low densities and weak coupling perturbation theory at high densities. We determine the values of various condensates and densities as well as the spectrum of excitations as functions of $\mu_I$ and $\mu_B$. A similar analysis of QCD with quarks in the adjoint representation is also presented. Our results can be of relevance for lattice simulations of these theories. We predict a phase of inhomogeneous condensation (Fulde-Ferrel-Larkin-Ovchinnikov phase) in the 2 colour 2 flavor theory, while we do not expect it the 4 flavor case or in other realizations of QCD with a positive measure.Comment: 17 pages, 14 figure

Numerical Portrait of a Relativistic BCS Gapped Superfluid

We present results of numerical simulations of the 3+1 dimensional Nambu - Jona-Lasinio (NJL) model with a non-zero baryon density enforced via the introduction of a chemical potential mu not equal to 0. The triviality of the model with a number of dimensions d>=4 is dealt with by fitting low energy constants, calculated analytically in the large number of colors (Hartree) limit, to phenomenological values. Non-perturbative measurements of local order parameters for superfluidity and their related susceptibilities show that, in contrast to the 2+1 dimensional model, the ground-state at high chemical potential and low temperature is that of a traditional BCS superfluid. This conclusion is supported by the direct observation of a gap in the dispersion relation for 0.5<=(mu a)<=0.85, which at (mu a)=0.8 is found to be roughly 15% the size of the vacuum fermion mass. We also present results of an initial investigation of the stability of the BCS phase against thermal fluctuations. Finally, we discuss the effect of splitting the Fermi surfaces of the pairing partners by the introduction of a non-zero isospin chemical potential.Comment: 41 pages, 19 figures, uses axodraw.sty, v2: minor typographical correction

Obtaining strong ferromagnetism in diluted Gd-doped ZnO thin films through controlled Gd-defect complexes

We demonstrate the fabrication of reproducible long-range ferromagnetism (FM) in highly crystalline Gdx Zn 1−xO thin films by controlling the defects. Films are grown on lattice-matched substrates by pulsed laser deposition at low oxygen pressures (≤25 mTorr) and low Gd concentrations (x ≤ 0.009). These films feature strong FM (10 μB per Gd atom) at room temperature. While films deposited at higher oxygen pressure do not exhibit FM, FM is recovered by post-annealing these films under vacuum. These findings reveal the contribution of oxygen deficiency defects to the long-range FM. We demonstrate the possible FM mechanisms, which are confirmed by density functional theory study, and show that Gd dopants are essential for establishing FM that is induced by intrinsic defects in these films

Ultra-High Energy Cosmic Rays and Stable H-dibaryon

It is shown that an instanton induced interaction between quarks produces a very deeply bound H-dibaryon with mass below 2M_N, M_H=1718 MeV. Therefore the H-dibaryon is predicted to be a stable particle. The reaction of photodisintegration of H-dibaryon to $2\Lambda$ in during of its penetration into cosmic microwave background will result in a new possible cut-off in the cosmic-ray spectrum. This provides an explanation of ultra-high energy cosmic ray events observed above the GZK cut-off as a result of the strong interaction of high energy H-dibaryons from cosmic rays with nuclei in Earth's atmosphere.Comment: 5 pages, Late