25 research outputs found
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 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
Supersymmetric BCS
We implement relativistic BCS superconductivity in N=1 supersymmetric field
theories with a U(1)_R symmetry. The simplest model contains two chiral
superfields with a Kahler potential modified by quartic terms. We study the
phase diagram of the gap as a function of the temperature and the specific
heat. The superconducting phase transition turns out to be first order, due to
the scalar contribution to the one-loop potential. By virtue of supersymmetry,
the critical curves depend logarithmically with the UV cutoff, rather than
quadratically as in standard BCS theory. We comment on the difficulties in
having fermion condensates when the chemical potential is instead coupled to a
baryonic U(1)_B current. We also discuss supersymmetric models of BCS with
canonical Kahler potential constructed by "integrating-in" chiral superfields.Comment: 26 pages, 5 figure
Ultrarelativistic electron-hole pairing in graphene bilayer
We consider ground state of electron-hole graphene bilayer composed of two
independently doped graphene layers when a condensate of spatially separated
electron-hole pairs is formed. In the weak coupling regime the pairing affects
only conduction band of electron-doped layer and valence band of hole-doped
layer, thus the ground state is similar to ordinary BCS condensate. At strong
coupling, an ultrarelativistic character of electron dynamics reveals and the
bands which are remote from Fermi surfaces (valence band of electron-doped
layer and conduction band of hole-doped layer) are also affected by the
pairing. The analysis of instability of unpaired state shows that s-wave
pairing with band-diagonal condensate structure, described by two gaps, is
preferable. A relative phase of the gaps is fixed, however at weak coupling
this fixation diminishes allowing gapped and soliton-like excitations. The
coupled self-consistent gap equations for these two gaps are solved at zero
temperature in the constant-gap approximation and in the approximation of
separable potential. It is shown that, if characteristic width of the pairing
region is of the order of magnitude of chemical potential, then the value of
the gap in the spectrum is not much different from the BCS estimation. However,
if the pairing region is wider, then the gap value can be much larger and
depends exponentially on its energy width.Comment: 13 pages with 8 figures; accepted to Eur. Phys. J.
BCS and generalized BCS superconductivity in relativistic quantum field theory. I. formulation
We investigate the BCS and generalized BCS theories in the relativistic
quantum field theory. We select the gauge freedom as U(1), and introduce a
BCS-type effective attractive interaction. After introducing the Gor'kov
formalism and performing the group theoretical consideration of the mean
fields, we solve the relativistic Gor'kov equation and obtain the Green's
functions in analytical forms. We obtain various types of gap equations.Comment: 31 page
Topological superfluid He-B: fermion zero modes on interfaces and in the vortex core
Many quantum condensed matter systems are strongly correlated and strongly
interacting fermionic systems, which cannot be treated perturbatively. However,
topology allows us to determine generic features of their fermionic spectrum,
which are robust to perturbation and interaction. We discuss the nodeless 3D
system, such as superfluid He-B, vacuum of Dirac fermions, and relativistic
singlet and triplet supercondutors which may arise in quark matter. The
systems, which have nonzero value of topological invariant, have gapless
fermions on the boundary and in the core of quantized vortices. We discuss the
index theorem which relates fermion zero modes on vortices with the topological
invariants in combined momentum and coordinate space.Comment: paper is prepared for Proceedings of the Workshop on Vortices,
Superfluid Dynamics, and Quantum Turbulence held on 11-16 April 2010, Lammi,
Finlan
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
Relation Between Chiral Susceptibility and Solutions of Gap Equation in Nambu--Jona-Lasinio Model
We study the solutions of the gap equation, the thermodynamic potential and
the chiral susceptibility in and beyond the chiral limit at finite chemical
potential in the Nambu--Jona-Lasinio (NJL) model. We give an explicit relation
between the chiral susceptibility and the thermodynamic potential in the NJL
model. We find that the chiral susceptibility is a quantity being able to
represent the furcation of the solutions of the gap equation and the
concavo-convexity of the thermodynamic potential in NJL model. It indicates
that the chiral susceptibility can identify the stable state and the
possibility of the chiral phase transition in NJL model.Comment: 21 pages, 6 figures, misprints are correcte
Pion condensation of quark matter in the static Einstein universe
In the framework of an extended Nambu--Jona-Lasinio model we are studying
pion condensation in quark matter with an asymmetric isospin composition in a
gravitational field of the static Einstein universe at finite temperature and
chemical potential. This particular choice of the gravitational field
configuration enables us to investigate phase transitions of the system with
exact consideration of the role of this field in the formation of quark and
pion condensates and to point out its influence on the phase portraits. We
demonstrate the effect of oscillations of the thermodynamic quantities as
functions of the curvature and also refer to a certain similarity between the
behavior of these quantities as functions of curvature and finite temperature.
Finally, the role of quantum fluctuations for spontaneous symmetry breaking in
the case of a finite volume of the universe is shortly discussed.Comment: RevTex4; 15 pages, 10 figure
Chiral Modulations in Curved Space II: Conifold Geometries
In this paper, we extend our previous analysis concerning the formation of
inhomogeneous condensates in strongly-coupled fermion effective field theories
on curved spaces and include the case of conifold geometries that represent the
simplest tractable case of manifolds with curvature singularities. In the
set-up considered here, by keeping the genuine thermodynamical temperature
constant, we may single out the role that curvature effects play on the
breaking/restoration of chiral symmetry and on the appearance of inhomogeneous
phases. The first goal of this paper is to construct a general expression of
the finite temperature effective action for inhomogeneous condensates in the
case of four-fermion effective field theories on conifold geometries with
generic Riemannian smooth base (generalised cones). The other goal is to
implement numerically the above formal results and construct self-consistent
solutions for the condensate. We explicitly show that the condensate assumes a
kink-like profile, vanishing at the singularity that is surrounded by a bubble
of restored chiral symmetry phase.Comment: 14 pages; 4 figure