27 research outputs found
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
The Crystallography of Color Superconductivity
We develop the Ginzburg-Landau approach to comparing different possible
crystal structures for the crystalline color superconducting phase of QCD, the
QCD incarnation of the Larkin-Ovchinnikov-Fulde-Ferrell phase. In this phase,
quarks of different flavor with differing Fermi momenta form Cooper pairs with
nonzero total momentum, yielding a condensate that varies in space like a sum
of plane waves. We work at zero temperature, as is relevant for compact star
physics. The Ginzburg-Landau approach predicts a strong first-order phase
transition (as a function of the chemical potential difference between quarks)
and for this reason is not under quantitative control. Nevertheless, by
organizing the comparison between different possible arrangements of plane
waves (i.e. different crystal structures) it provides considerable qualitative
insight into what makes a crystal structure favorable. Together, the
qualitative insights and the quantitative, but not controlled, calculations
make a compelling case that the favored pairing pattern yields a condensate
which is a sum of eight plane waves forming a face-centered cubic structure.
They also predict that the phase is quite robust, with gaps comparable in
magnitude to the BCS gap that would form if the Fermi momenta were degenerate.
These predictions may be tested in ultracold gases made of fermionic atoms. In
a QCD context, our results lay the foundation for a calculation of vortex
pinning in a crystalline color superconductor, and thus for the analysis of
pulsar glitches that may originate within the core of a compact star.Comment: 41 pages, 13 figures, 1 tabl
Breaking rotational symmetry in two-flavor color superconductors
The color superconductivity under flavor asymmetric conditions relevant to
the compact star phenomenology is studied within the Nambu-Jona-Lasinio model.
We focus on the effect of the deformation of the Fermi surfaces on the pairing
properties and the energy budget of the superconducting state. We find that at
finite flavor asymmetries the color superconducting BCS state is unstable
towards spontaneous quadrupole deformation of the Fermi surfaces of the and
quarks into ellipsoidal form. The ground state of the phase with deformed
Fermi surfaces corresponds to a superposition of prolate and oblate deformed
Fermi ellipsoids of and quarks.Comment: 6 pages, 4 figures. Parameter changes, references added, conclusions
unchange
Breached Pairing Superfluidity at Finite Temperature and Density
A general analysis on Fermion pairing at finite temperature and density
between different species with mismatched Fermi surfaces is presented. Very
different from the temperature effect of BCS phase, the recently found breached
pairing phase resulted from density difference of the two species lies in a
region with calabash-like shape in the plane, and the most probable
temperature for the new phase's creation is finite but not zero.Comment: 5 papes, 5 figures. Comments are welcome to
[email protected]
Phases of asymmetric nuclear matter with broken space symmetries
Isoscalar Cooper pairing in isospin asymmetric nuclear matter occurs between
states populating two distinct Fermi surfaces, each for neutrons and protons.
The transition from a BCS-like to the normal (unpaired) state, as the isospin
asymmetry is increased, is intervened by superconducting phases which
spontaneously break translational and rotational symmetries. One possibility is
the formation of a condensate with a periodic crystallinelike structure where
Cooper pairs carry net momentum (the nuclear
Larkin-Ovchinnikov-Fulde-Ferrell-phase). Alternatively, perturbations of the
Fermi surfaces away from spherical symmetry allow for minima in the condensate
free energy which correspond to a states with quadrupole deformations of Fermi
surfaces and zero momentum of the Cooper pairs. In a combined treatment of
these phases we show that, although the Cooper pairing with finite momentum
might arise as a local minimum, the lowest energy state features are deformed
Fermi surfaces and Cooper pairs with vanishing total momentum.Comment: 22 pages, 6 figures, RevTex; v2: matches published version; v3:
changes in the frontmatter, content unchange
Color-Neutral Superconducting Quark Matter
We investigate the consequences of enforcing local color neutrality on the
color superconducting phases of quark matter by utilizing the
Nambu-Jona-Lasinio model supplemented by diquark and the t'Hooft six-fermion
interactions. In neutrino free matter at zero temperature, color neutrality
guarantees that the number densities of u, d, and s quarks in the
Color-Flavor-Locked (CFL) phase will be equal even with physical current quark
masses. Electric charge neutrality follows as a consequence and without the
presence of electrons. In contrast, electric charge neutrality in the less
symmetric 2-flavor superconducting (2SC) phase with ud pairing requires more
electrons than the normal quark phase. The free energy density cost of
enforcing color and electric charge neutrality in the CFL phase is lower than
that in the 2SC phase, which favors the formation of the CFL phase. With
increasing temperature and neutrino content, an unlocking transition occurs
from the CFL phase to the 2SC phase with the order of the transition depending
on the temperature, the quark and lepton number chemical potentials. The
astrophysical implications of this rich structure in the phase diagram,
including estimates of the effects from Goldstone bosons in the CFL phase, are
discussed.Comment: 20 pages, 4 figures; version to appear in Phys. Rev.
Opening the Crystalline Color Superconductivity Window
Cold dense quark matter is in a crystalline color superconducting phase
wherever pairing occurs between species of quarks with chemical potentials
whose difference \delta\mu lies within an appropriate window. If the
interaction between quarks is modeled as point-like, this window is rather
narrow. We show that when the interaction between quarks is modeled as
single-gluon exchange, the window widens by about a factor of ten at accessible
densities and by much larger factors at higher density. This striking
enhancement reflects the increasingly (1+1)-dimensional nature of the physics
at weaker and weaker coupling. Our results indicate that crystalline color
superconductivity is a generic feature of the phase diagram of cold dense quark
matter, occurring wherever one finds quark matter which is not in the
color-flavor locked phase. If it occurs within the cores of compact stars, a
crystalline color superconducting region may provide a new locus for glitch
phenomena.Comment: 14 pages, 2 figure
Spontaneous symmetry breaking in strong-coupling lattice QCD at high density
We determine the patterns of spontaneous symmetry breaking in strong-coupling
lattice QCD in a fixed background baryon density. We employ a
next-nearest-neighbor fermion formulation that possesses the SU(N_f)xSU(N_f)
chiral symmetry of the continuum theory. We find that the global symmetry of
the ground state varies with N_f and with the background baryon density. In all
cases the condensate breaks the discrete rotational symmetry of the lattice as
well as part of the chiral symmetry group.Comment: 10 pages, RevTeX 4; added discussion of accidental degeneracy of
vacuum after Eq. (35
The Minimal CFL-Nuclear Interface
At nuclear matter density, electrically neutral strongly interacting matter
in weak equilibrium is made of neutrons, protons and electrons. At sufficiently
high density, such matter is made of up, down and strange quarks in the
color-flavor locked phase, with no electrons. As a function of increasing
density (or, perhaps, increasing depth in a compact star) other phases may
intervene between these two phases which are guaranteed to be present. The
simplest possibility, however, is a single first order phase transition between
CFL and nuclear matter. Such a transition, in space, could take place either
through a mixed phase region or at a single sharp interface with electron-free
CFL and electron-rich nuclear matter in stable contact. Here we construct a
model for such an interface. It is characterized by a region of separated
charge, similar to an inversion layer at a metal-insulator boundary. On the CFL
side, the charged boundary layer is dominated by a condensate of negative
kaons. We then consider the energetics of the mixed phase alternative. We find
that the mixed phase will occur only if the nuclear-CFL surface tension is
significantly smaller than dimensional analysis would indicate.Comment: 30 pages, 7 figure
Chiral Modulations in Curved Space I: Formalism
The goal of this paper is to present a formalism that allows to handle
four-fermion effective theories at finite temperature and density in curved
space. The formalism is based on the use of the effective action and zeta
function regularization, supports the inclusion of inhomogeneous and
anisotropic phases. One of the key points of the method is the use of a
non-perturbative ansatz for the heat-kernel that returns the effective action
in partially resummed form, providing a way to go beyond the approximations
based on the Ginzburg-Landau expansion for the partition function. The
effective action for the case of ultra-static Riemannian spacetimes with
compact spatial section is discussed in general and a series representation,
valid when the chemical potential satisfies a certain constraint, is derived.
To see the formalism at work, we consider the case of static Einstein spaces at
zero chemical potential. Although in this case we expect inhomogeneous phases
to occur only as meta-stable states, the problem is complex enough and allows
to illustrate how to implement numerical studies of inhomogeneous phases in
curved space. Finally, we extend the formalism to include arbitrary chemical
potentials and obtain the analytical continuation of the effective action in
curved space.Comment: 22 pages, 3 figures; version to appear in JHE