38 research outputs found
On gap equations and color-flavor locking in cold dense QCD with three massless flavors
The superconductivity in cold dense QCD with three massless flavors is
analyzed in the framework of the Schwinger-Dyson equation. The set of two
coupled gap equations for the color antitriplet, flavor antitriplet
(bar{3},bar{3}) and the color sextet, flavor sextet (6,6) order parameters is
derived. It is shown that the antitriplet-antitriplet gives the dominant
contribution to the color-flavor locked order parameter, while the
sextet-sextet is small but nonzero.Comment: 9 pages, no figures, REVTe
The effective potential of composite diquark fields and the spectrum of resonances in dense QCD
The effective potential of composite diquark fields responsible for color
symmetry breaking in cold very dense QCD, in which long-range interactions
dominate, is derived. The spectrum of excitations and the universality class of
this dynamics are described.Comment: 8 pages, 1 figure (new), REVTeX. The latest version to appear in
Phys. Lett. B. References added, discussion improve
Gluonic phase versus LOFF phase in two-flavor quark matter
We study the gluonic phase in a two-flavor color superconductor as a function
of the ratio of the gap over the chemical potential
mismatch,. We find that the gluonic phase resolves the
chromomagnetic instability encountered in a two-flavor color superconductor for
. We also calculate approximately the free
energies of the gluonic phase and the single plane-wave LOFF phase and show
that the former is favored over the latter for a wide range of coupling
strengths.Comment: 6 pages, 3 figures, references added, revisions to text, version
accepted for publication in Phys. Lett.
Optically opaque color-flavor locked phase inside compact stars
The contribution of thermally excited electron-positron pairs to the bulk
properties of the color-flavor locked quark phase inside compact stars is
examined. The presence of these pairs causes the photon mean free path to be
much smaller than a typical core radius ( km) for all
temperatures above 25 keV so that the photon contribution to the thermal
conductivity is much smaller than that of the Nambu-Goldstone bosons. We also
find that the electrons and positrons dominate the electrical conductivity,
while their contributions to the total thermal energy is negligible.Comment: 3 pages, 2 figures. Published versio
Edge states in quantum Hall effect in graphene (Review Article)
We review recent results concerning the spectrum of edge states in the quantum Hall effect in graphene.
In particular, a special attention is payed to the derivation of the conditions under which gapless edge states
exist in the spectrum of graphene with zigzag and armchair edges.We find that in the case of a half-plane or a
ribbon with a zigzag edges, there are gapless edge states only when a spin gap dominates over a Dirac mass
gap. In the case of a half-plane with an armchair edge, the existence of the gapless edge states depends on the
specific type of Dirac mass gaps. The implications of these results for the dynamics in the quantum Hall effect
in graphene are discussed
Dimensional Reduction and Dynamical Chiral Symmetry Breaking by a Magnetic Field in Dimensions
It is shown that in dimensions, a constant magnetic field is a catalyst
of dynamical chiral symmetry breaking, leading to generating a fermion mass
even at the weakest attractive interaction between fermions. The essence of
this effect is the dimensional reduction () in the dynamics of fermion pairing in a magnetic field. The effect is
illustrated in the Nambu-Jona-Lasinio model. Possible applications of this
effect are briefly discussed.Comment: 13 pages, LaTeX, no figure
Collective modes of color-flavor locked phase of dense QCD at finite temperature
A detailed analysis of collective modes that couple to either vector or axial
color currents in color-flavor locked phase of color superconducting dense
quark matter at finite temperature is presented. Among the realm of collective
modes, including the plasmons and the Nambu-Goldstone bosons, we also reveal
the gapless Carlson-Goldman modes, resembling the scalar Nambu-Golstone bosons.
These latter exist only in a close vicinity of the critical line. Their
presence does not eliminate the Meissner effect, proving that the system
remains in the color broken phase. The finite temperature properties of the
plasmons and the Nambu-Goldstone bosons are also studied. In addition to the
ordinary plasmon, we also reveal a "light" plasmon which has a narrow width and
whose mass is of the order of the superconducting gap.Comment: 28 pages, 8 figures. REVTeX. Two references added and minor
modifications introduced (see p. 5 and pp. 13,14). To appear in Nucl. Phys.
Theory of the Magnetic Catalysis of Chiral Symmetry Breaking in QED
The theory of the magnetic catalysis of chiral symmetry breaking in QED is
developed. An approximation for the Schwinger-Dyson equations describing
reliably this phenomenon is established, i.e., it is shown that there exists a
consistent truncation of those equations in this problem. The equations are
solved both analytically and numerically, and the dynamical mass of fermions is
determined.Comment: 22 pages, 5 figures, REVTe
Abnormal number of Nambu-Goldstone bosons in the color-asymmetric 2SC phase of an NJL-type model
We consider an extended Nambu--Jona-Lasinio model including both (q \bar q)-
and (qq)-interactions with two light-quark flavors in the presence of a single
(quark density) chemical potential. In the color superconducting phase of the
quark matter the color SU(3) symmetry is spontaneously broken down to SU(2). If
the usual counting of Goldstone bosons would apply, five Nambu-Goldstone (NG)
bosons corresponding to the five broken color generators should appear in the
mass spectrum. Unlike that expectation, we find only three gapless diquark
excitations of quark matter. One of them is an SU(2)-singlet, the remaining two
form an SU(2)-(anti)doublet and have a quadratic dispersion law in the small
momentum limit. These results are in agreement with the Nielsen-Chadha theorem,
according to which NG-bosons in Lorentz-noninvariant systems, having a
quadratic dispersion law, must be counted differently. The origin of the
abnormal number of NG-bosons is shown to be related to a nonvanishing
expectation value of the color charge operator Q_8 reflecting the lack of color
neutrality of the ground state. Finally, by requiring color neutrality, two
massive diquarks are argued to become massless, resulting in a normal number of
five NG-bosons with usual linear dispersion laws.Comment: 13 pages, 4 figures, revtex
How the quark self-energy affects the color-superconducting gap
We consider color superconductivity with two flavors of massless quarks which
form Cooper pairs with total spin zero. We solve the gap equation for the
color-superconducting gap parameter to subleading order in the QCD coupling
constant at zero temperature. At this order in , there is also a
previously neglected contribution from the real part of the quark self-energy
to the gap equation. Including this contribution leads to a reduction of the
color-superconducting gap parameter \f_0 by a factor b_0'=\exp \big[ -(\p
^2+4)/8 \big]\simeq 0.177. On the other hand, the BCS relation T_c\simeq
0.57\f_0 between \f_0 and the transition temperature is shown to
remain valid after taking into account corrections from the quark self-energy.
The resulting value for confirms a result obtained previously with a
different method.Comment: Revtex, 8 pages, no figur