536 research outputs found
Chiral perturbation theory for lattice QCD including O(a^2)
The O(a^2) contributions to the chiral effective Lagrangian for lattice QCD
with Wilson fermions are constructed. The results are generalized to partially
quenched QCD with Wilson fermions as well as to the "mixed'' lattice theory
with Wilson sea quarks and Ginsparg-Wilson valence quarks.Comment: 3 pages, Lattice2003 (spectrum
Excited-state contribution to the axial-vector and pseudo-scalar correlators with two extra pions
We study multi-particle state contributions to the QCD two-point functions of
the axial-vector and pseudo-scalar quark bilinears in a finite spatial volume.
For sufficiently small quark masses one expects three-meson states with two
additional pions at rest to have the lowest total energy after the ground
state. We calculate this three-meson state contribution using chiral
perturbation theory. We find it to be strongly suppressed and too small to be
seen in present-day lattice simulations.Comment: 17 pages, 5 figure
DNA mixtures: biostatistics for mixed stains with haplotypic genetic markers
The conventional theory for interpreting forensic DNA evidence developed for the autosomal genetic markers is not applicable in the case of haplotypic markers, specifically for Y-STR based data. The reason is, that in contrast to the case of autosomal markers, single alleles found in the mixed stain cannot be assigned to unknown stain contributors independently of each other, while the assignable entities are sets of linked alleles which should be treated as non-separable units. It is shown that the conventional theory cannot be extended to this situation. A novel theory which accounts for the features of haplotypic markers has been developed within the general framework of the hypotheses testing approach. This theory opens the way for the use of haplotypic markers in the analysis of mixed stains with the arbitrary numbers of unknown contributors and linked loci. A numerical example demonstrates the application of the theor
A remark on the space of metrics having non-trivial harmonic spinors
Let M be a closed spin manifold of dimension congruent to 3 modulo 4. We give a simple proof of the fact that the space of metrics on M with invertible Dirac operator is either empty or it has infinitely many path components
Dirac-harmonic maps from index theory
We prove existence results for Dirac-harmonic maps using index theoretical
tools. They are mainly interesting if the source manifold has dimension 1 or 2
modulo 8. Our solutions are uncoupled in the sense that the underlying map
between the source and target manifolds is a harmonic map.Comment: 26 pages, no figur
Generic metrics and the mass endomorphism on spin three-manifolds
Let be a closed Riemannian spin manifold. The constant term in the
expansion of the Green function for the Dirac operator at a fixed point is called the mass endomorphism in associated to the metric due to
an analogy to the mass in the Yamabe problem. We show that the mass
endomorphism of a generic metric on a three-dimensional spin manifold is
nonzero. This implies a strict inequality which can be used to avoid
bubbling-off phenomena in conformal spin geometry.Comment: 8 page
Manifolds with small Dirac eigenvalues are nilmanifolds
Consider the class of n-dimensional Riemannian spin manifolds with bounded
sectional curvatures and diameter, and almost non-negative scalar curvature.
Let r=1 if n=2,3 and r=2^{[n/2]-1}+1 if n\geq 4. We show that if the square of
the Dirac operator on such a manifold has small eigenvalues, then the
manifold is diffeomorphic to a nilmanifold and has trivial spin structure.
Equivalently, if M is not a nilmanifold or if M is a nilmanifold with a
non-trivial spin structure, then there exists a uniform lower bound on the r-th
eigenvalue of the square of the Dirac operator. If a manifold with almost
nonnegative scalar curvature has one small Dirac eigenvalue, and if the volume
is not too small, then we show that the metric is close to a Ricci-flat metric
on M with a parallel spinor. In dimension 4 this implies that M is either a
torus or a K3-surface
Spiral waves in a surface reaction: Model calculations
A systematic study of spiral waves in a realistic reactionâdiffusion model describing the isothermal CO oxidation on Pt(110) is carried out. Spirals exist under oscillatory, excitable, and bistable (doubly metastable) conditions. In the excitable region, two separate meandering transitions occur, both when the time scales become strongly different and when they become comparable. By the assumption of surface defects of the order of 10 ÎŒm, to which the spirals can be pinned, the continuous distribution of wavelengths observed experimentally can be explained. An external periodic perturbation generally causes a meandering motion of a free spiral, while a straight drift results, if the period of the perturbation divided by the rotation period is a natural number
The Dirac operator on untrapped surfaces
We establish a sharp extrinsic lower bound for the first eigenvalue of the
Dirac operator of an untrapped surface in initial data sets without apparent
horizon in terms of the norm of its mean curvature vector. The equality case
leads to rigidity results for the constraint equations with spherical boundary
as well as uniqueness results for constant mean curvature surfaces in Minkowski
space.Comment: 16 page
Spectral Bounds for Dirac Operators on Open Manifolds
We extend several classical eigenvalue estimates for Dirac operators on
compact manifolds to noncompact, even incomplete manifolds. This includes
Friedrich's estimate for manifolds with positive scalar curvature as well as
the author's estimate on surfaces.Comment: pdflatex, 14 pages, 3 figure
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