1,282 research outputs found
Low-Dimensional Long-Range Topological Charge Structure in the QCD Vacuum
While sign-coherent 4-dimensional structures cannot dominate topological
charge fluctuations in the QCD vacuum at all scales due to reflection
positivity, it is possible that enhanced coherence exists over extended
space-time regions of lower dimension. Using the overlap Dirac operator to
calculate topological charge density, we present evidence for such structure in
pure-glue SU(3) lattice gauge theory. It is found that a typical equilibrium
configuration is dominated by two oppositely-charged sign-coherent connected
structures (``sheets'') covering about 80% of space-time. Each sheet is built
from elementary 3-d cubes connected through 2-d faces, and approximates a
low-dimensional curved manifold (or possibly a fractal structure) embedded in
the 4-d space. At the heart of the sheet is a ``skeleton'' formed by about 18%
of the most intense space-time points organized into a global long-range
structure, involving connected parts spreading over maximal possible distances.
We find that the skeleton is locally 1-dimensional and propose that its
geometrical properties might be relevant for understanding the possible role of
topological charge fluctuations in the physics of chiral symmetry breaking.Comment: 4 pages RevTeX, 4 figures; v2: 6 pages, 5 figures, more explanations
provided, figure and references added, published versio
Topological Charge Fluctuations and Low-Lying Dirac Eigenmodes
We discuss the utility of low-lying Dirac eigenmodes for studying the nature
of topological charge fluctuations in QCD. The implications of previous results
using the local chirality histogram method are discussed, and the new results
using the overlap Dirac operator in Wilson gauge backgrounds at lattice
spacings ranging from a~0.04 fm to a~0.12 fm are reported. While the degree of
local chirality does not change appreciably closer to the continuum limit, we
find that the size and density of local structures responsible for chiral
peaking do change significantly. The resulting values are in disagreement with
the assumptions of the Instanton Liquid Model. We conclude that the
fluctuations of topological charge in the QCD vacuum are not locally quantized.Comment: 3 pages, 4 figures, Lattice2001(confinement
Instanton dominance of topological charge fluctuations in QCD?
We consider the local chirality of near-zero eigenvectors from Wilson-Dirac
and clover improved Wilson-Dirac lattice operators as proposed recently by
Horv\'ath et al. We studied finer lattices and repaired for the loss of
orthogonality due to the non-normality of the Wilson-Dirac matrix. As a result
we do see a clear double peak structure on lattices with resolutions higher
than 0.1 fm. We found that the lattice artifacts can be considerably reduced by
exploiting the biorthogonal system of left and right eigenvectors. We conclude
that the dominance of instantons on topological charge fluctuations is not
ruled out by local chirality measurements.Comment: 10 pages, 6 figure
QUANTENCHEMISCHE RECHNUNGEN AUF DER ELEKTRONISCHEN RECHENANLAGE RAZDAN-3. IV. MODIFIZIERTES PROGRAMM FÜR LCAO-MO-SCF-PPP-CI-RECHNUNGEN
Topological Structure of the QCD Vacuum Revealed by Overlap Fermions
Overlap fermions preserve a remnant of chiral symmetry on the lattice. They
are a powerful tool to investigate the topological structure of the vacuum of
Yang-Mills theory and full QCD. Recent results concerning the localization of
topological charge and the localization and local chirality of the overlap
eigenmodes are reported. The charge distribution is radically different, if a
spectral cut-off for the Dirac eigenmodes is applied. The density q(x) is
changing from the scale-a charge density (with full lattice resolution) to the
ultraviolet filtered charge density. The scale-a density, computed on the Linux
cluster of LRZ, has a singular, sign-coherent global structure of co-dimension
1 first described by the Kentucky group. We stress, however, the cluster
properties of the UV filtered topological density resembling the instanton
picture. The spectral cut-off can be mapped to a bosonic smearing procedure.
The UV filtered field strength reveals a high degree of (anti)selfduality at
"hot spots" of the action. The fermionic eigenmodes show a high degree of local
chirality. The lowest modes are seen to be localized in low-dimensional
space-time regions.Comment: 13 pages, 11 figures, accepted to appear in the Proceedings of "HLRB,
KONWIHR and Linux-Cluster: Review, Results and Future Projects Workshop",
Leibniz Rechenzentrum Munich, December 200
The local structure of topological charge fluctuations in QCD
We introduce the Dirac eigenmode filtering of topological charge density
associated with Ginsparg-Wilson fermions as a tool to investigate the local
structure of topological charge fluctuations in QCD. The resulting framework is
used to demonstrate that the bulk of topological charge in QCD does not appear
in the form of unit quantized lumps. This means that the mixing of "would-be"
zeromodes associated with such lumps is probably not the prevalent microscopic
mechanism for spontaneous chiral symmetry breaking in QCD. To characterize the
coherent local behavior in topological charge density at low energy, we compute
the charges contained in maximal coherent spheres enclosing non-overlapping
peaks. We find a continuous distribution essentially ending at ~0.5. Finally,
we study, for the first time, the overlap-operator topological-charge-density
correlators and find consistency with non-positivity at nonzero physical
distance. This represents a non-trivial check on the locality (in gauge paths)
of the overlap Dirac operator for realistic gauge backgrounds.Comment: 3 pages, 4 figures, talk, Lattice2002(topology
Computation of the radiation amplitude of oscillons
The radiation loss of small amplitude oscillons (very long-living, spatially
localized, time dependent solutions) in one dimensional scalar field theories
is computed in the small-amplitude expansion analytically using matched
asymptotic series expansions and Borel summation. The amplitude of the
radiation is beyond all orders in perturbation theory and the method used has
been developed by Segur and Kruskal in Phys. Rev. Lett. 58, 747 (1987). Our
results are in good agreement with those of long time numerical simulations of
oscillons.Comment: 22 pages, 9 figure
Local Chirality of Low-Lying Dirac Eigenmodes and the Instanton Liquid Model
The reasons for using low-lying Dirac eigenmodes to probe the local structure
of topological charge fluctuations in QCD are discussed, and it is pointed out
that the qualitative double-peaked behavior of the local chiral orientation
probability distribution in these modes is necessary, but not sufficient for
dominance of instanton-like fluctuations. The results with overlap Dirac
operator in Wilson gauge backgrounds at lattice spacings ranging from a~0.04 fm
to a~0.12 fm are reported, and it is found that the size and density of local
structures responsible for double-peaking of the distribution are in
disagreement with the assumptions of the Instanton Liquid Model. More
generally, our results suggest that vacuum fluctuations of topological charge
are not effectively dominated by locally quantized (integer-valued) lumps in
QCD.Comment: 29 pages, 13 figures; v2: minor improvements in presentation, results
and conclusions unchanged, version to appear in PR
Calorons, instantons and constituent monopoles in SU(3) lattice gauge theory
We analyze the zero-modes of the Dirac operator in quenched SU(3) gauge
configurations at non-zero temperature and compare periodic and anti-periodic
temporal boundary conditions for the fermions. It is demonstrated that for the
different boundary conditions often the modes are localized at different
space-time points and have different sizes. Our observations are consistent
with patterns expected for Kraan - van Baal solutions of the classical
Yang-Mills equations. These solutions consist of constituent monopoles and the
zero-modes are localized on different constituents for different boundary
conditions. Our findings indicate that the excitations of the QCD vacuum are
more structured than simple instanton-like lumps.Comment: Remarks added. To appear in Phys. Rev.
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