1,707 research outputs found
Vector Positronium States in QED3
The homogeneous Bethe-Salpeter equation is solved in the quenched ladder
approximation for the vector positronium states of 4-component quantum
electrodynamics in 2 space and 1 time dimensions. Fermion propagator input is
from a Rainbow approximation Dyson-Schwinger solution, with a broad range of
fermion masses considered. This work is an extension of earlier work on the
scalar spectrum of the same model. The non-relativistic limit is also
considered via the large fermion mass limit. Classification of states via their
transformation properties under discrete parity transformations allows
analogies to be drawn with the meson spectrum of QCD.Comment: 24 pages, 2 encapsulated postscript figure
The analytic structure of heavy quark propagators
The renormalised quark Dyson-Schwinger equation is studied in the limit of
the renormalised current heavy quark mass m_R --> infinity. We are particularly
interested in the analytic pole structure of the heavy quark propagator in the
complex momentum plane. Approximations in which the quark-gluon vertex is
modelled by either the bare vertex or the Ball-Chiu Ansatz, and the Landau
gauge gluon propagator takes either a gaussian form or a gaussian form with an
ultraviolet asymptotic tail are used.Comment: 21 pages Latex and 5 postscript figures. The original version of this
paper has been considerably extended to include a formalism dealing with the
renormalised heavy quark Dyson-Schwinger equation and uses a more realistic
Ansatz for the gluon propagator
Collective phase synchronization in locally-coupled limit-cycle oscillators
We study collective behavior of locally-coupled limit-cycle oscillators with
scattered intrinsic frequencies on -dimensional lattices. A linear analysis
shows that the system should be always desynchronized up to . On the other
hand, numerical investigation for and 6 reveals the emergence of the
synchronized (ordered) phase via a continuous transition from the fully random
desynchronized phase. This demonstrates that the lower critical dimension for
the phase synchronization in this system is $d_{l}=4
Extrapolation-CAM Theory for Critical Exponents
By intentionally underestimating the rate of convergence of
exact-diagonalization values for the mass or energy gaps of finite systems, we
form families of sequences of gap estimates. The gap estimates cross zero with
generically nonzero linear terms in their Taylor expansions, so that
for each member of these sequences of estimates. Thus, the Coherent Anomaly
Method can be used to determine . Our freedom in deciding exactly how to
underestimate the convergence allows us to choose the sequence that displays
the clearest coherent anomaly. We demonstrate this approach on the
two-dimensional ferromagnetic Ising model, for which . We also use it
on the three-dimensional ferromagnetic Ising model, finding , in good agreement with other estimates.Comment: 21 pages, Submitted to Journal of Physics A; new section added
discussing rate of convergence and relation to Finite-Size Scalin
Collective synchronization in spatially extended systems of coupled oscillators with random frequencies
We study collective behavior of locally coupled limit-cycle oscillators with
random intrinsic frequencies, spatially extended over -dimensional
hypercubic lattices. Phase synchronization as well as frequency entrainment are
explored analytically in the linear (strong-coupling) regime and numerically in
the nonlinear (weak-coupling) regime. Our analysis shows that the oscillator
phases are always desynchronized up to , which implies the lower critical
dimension for phase synchronization. On the other hand, the
oscillators behave collectively in frequency (phase velocity) even in three
dimensions (), indicating that the lower critical dimension for frequency
entrainment is . Nonlinear effects due to periodic nature of
limit-cycle oscillators are found to become significant in the weak-coupling
regime: So-called {\em runaway oscillators} destroy the synchronized (ordered)
phase and there emerges a fully random (disordered) phase. Critical behavior
near the synchronization transition into the fully random phase is unveiled via
numerical investigation. Collective behavior of globally-coupled oscillators is
also examined and compared with that of locally coupled oscillators.Comment: 18 pages, 18 figure
Approximation of the Schwinger--Dyson and the Bethe--Salpeter Equations and Chiral Symmetry of QCD
The Bethe--Salpeter equation for the pion in chiral symmetric models is
studied with a special care to consistency with low-energy relations. We
propose a reduction of the rainbow Schwinger--Dyson and the ladder
Bethe--Salpeter equations with a dressed gluon propagator. We prove that the
reduction preserves the Ward--Takahashi identity for the axial-vector current
and the PCAC relation.Comment: 10 pages, LaTe
Adsorption models of hybridization and post-hybridisation behaviour on oligonucleotide microarrays
Analysis of data from an Affymetrix Latin Square spike-in experiment
indicates that measured fluorescence intensities of features on an
oligonucleotide microarray are related to spike-in RNA target concentrations
via a hyperbolic response function, generally identified as a Langmuir
adsorption isotherm. Furthermore the asymptotic signal at high spike-in
concentrations is almost invariably lower for a mismatch feature than for its
partner perfect match feature. We survey a number of theoretical adsorption
models of hybridization at the microarray surface and find that in general they
are unable to explain the differing saturation responses of perfect and
mismatch features. On the other hand, we find that a simple and consistent
explanation can be found in a model in which equilibrium hybridization followed
by partial dissociation of duplexes during the post-hybridization washing
phase.Comment: 26 pages, 6 figures, some rearrangement of sections and some
additions. To appear in J.Phys.(condensed matter
Singular Liouville fields and spiky strings in \rr^{1,2} and SL(2,\rr)
The closed string dynamics in \rr^{1,2} and SL(2,\rr) is studied within
the scheme of Pohlmeyer reduction. In both spaces two different classes of
string surfaces are specified by the structure of the fundamental quadratic
forms. The first class in \rr^{1,2} is associated with the standard lightcone
gauge strings and the second class describes spiky strings and their conformal
deformations on the Virasoro coadjoint orbits. These orbits correspond to
singular Liouville fields with the monodromy matrixes . The first class
in SL(2,\rr) is parameterized by the Liouville fields with vanishing chiral
energy functional. Similarly to \rr^{1,2}, the second class in SL(2,\rr)
describes spiky strings, related to the vacuum configurations of the
SL(2,\rr)/U(1) coset model.Comment: 37 p. 6 fi
Ground-state Spectrum of Light-quark Mesons
A confining, Goldstone theorem preserving, separable Ansatz for the ladder
kernel of the two-body Bethe-Salpeter equation is constructed from
phenomenologically efficacious , and dressed-quark propagators. The
simplicity of the approach is its merit. It provides a good description of the
ground-state isovector-pseudoscalar, vector and axial-vector meson spectrum;
facilitates an exploration of the relative importance of various components of
the two-body Bethe-Salpeter amplitudes, showing that sub-leading Dirac
components are quantitatively important in the isovector-pseudoscalar meson
channels; and allows a scrutiny of the domain of applicability of ladder
truncation studies. A colour-antitriplet diquark spectrum is obtained.
Shortcomings of separable Ans\"atze and the ladder kernel are highlighted.Comment: 30 pages, LaTeX/REVTEX 3.0, no figure
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