251 research outputs found
Quantitative comparison of filtering methods in lattice QCD
We systematically compare filtering methods used to extract topological
excitations (like instantons, calorons, monopoles and vortices) from lattice
gauge configurations, namely APE-smearing and spectral decompositions based on
lattice Dirac and Laplace operators. Each of these techniques introduces
ambiguities, which can invalidate the interpretation of the results. We show,
however, that all these methods, when handled with care, reveal very similar
topological structures. Hence, these common structures are free of ambiguities
and faithfully represent infrared degrees of freedom in the QCD vacuum. As an
application we discuss an interesting power-law for the clusters of filtered
topological charge.Comment: 6 pages, 18 plots in 5 figures; final version as published in EPJ A;
section 4 was adde
Rest-to-Rest Trajectory Planning for Underactuated Cable-Driven Parallel Robots
This article studies the trajectory planning for underactuated cable-driven parallel robots (CDPRs) in the case of rest-to-rest motions, when both the motion time and the path geometry are prescribed. For underactuated manipulators, it is possible to prescribe a control law only for a subset of the generalized coordinates of the system. However, if an arbitrary trajectory is prescribed for a suitable subset of these coordinates, the constraint deficiency on the end-effector leads to the impossibility of bringing the system at rest in a prescribed time. In addition, the behavior of the system may not be stable, that is, unbounded oscillatory motions of the end-effector may arise. In this article, we propose a novel trajectory-planning technique that allows the end effector to track a constrained geometric path in a specified time, and allows it to transition between stable static poses. The design of such a motion is based on the solution of a boundary value problem, aimed at a finding solution to the differential equations of motion with constraints on position and velocity at start and end times. To prove the effectiveness of such a method, the trajectory planning of a six-degrees-of-freedom spatial CDPR suspended by three cables is investigated. Trajectories of a reference point on the moving platform are designed so as to ensure that the assigned path is tracked accurately, and the system is brought to a static condition in a prescribed time. Experimental validation is presented and discussed
Calorons with non-trivial holonomy on and off the lattice
We discuss recent solutions for SU(2) calorons with non-trivial holonomy at
higher charge, both through analytic means and using cooling, as well as
extensive lattice studies for SU(3).Comment: 12 pages, 16 figures in 34 parts, 4 talks presented at Lattice
2004(topology
Probing for Instanton Quarks with epsilon-Cooling
We use epsilon-cooling, adjusting at will the order a^2 corrections to the
lattice action, to study the parameter space of instantons in the background of
non-trivial holonomy and to determine the presence and nature of constituents
with fractional topological charge at finite and zero temperature for SU(2). As
an additional tool, zero temperature configurations were generated from those
at finite temperature with well-separated constituents. This is achieved by
"adiabatically" adjusting the anisotropic coupling used to implement finite
temperature on a symmetric lattice. The action and topological charge density,
as well as the Polyakov loop and chiral zero-modes are used to analyse these
configurations. We also show how cooling histories themselves can reveal the
presence of constituents with fractional topological charge. We comment on the
interpretation of recent fermion zero-mode studies for thermalized ensembles at
small temperatures.Comment: 26 pages, 14 figures in 33 part
Improved superposition schemes for approximate multi-caloron configurations
Two improved superposition schemes for the construction of approximate
multi-caloron-anticaloron configurations, using exact single (anti)caloron
gauge fields as underlying building blocks, are introduced in this paper. The
first improvement deals with possible monopole-Dirac string interactions
between different calorons with non-trivial holonomy. The second one, based on
the ADHM formalism, improves the (anti-)selfduality in the case of small
caloron separations. It conforms with Shuryak's well-known ratio-ansatz when
applied to instantons. Both superposition techniques provide a higher degree of
(anti-)selfduality than the widely used sum-ansatz, which simply adds the
(anti)caloron vector potentials in an appropriate gauge. Furthermore, the
improved configurations (when discretized onto a lattice) are characterized by
a higher stability when they are exposed to lattice cooling techniques.Comment: New version accepted for publication in Nucl. Phys. B. Text partly
shortened, changes in the introduction, new results added on the comparison
with exact solution
Calorons, Nahm's equations on S^1 and bundles over P^1xP^1
The moduli space of solutions to Nahm's equations of rank (k,k+j) on the
circle, and hence, of SU(2) calorons of charge (k,j), is shown to be equivalent
to the moduli of holomorphic rank 2 bundles on P^1xP^1 trivialized at infinity
with c_2=k and equipped with a flag of degree j along P^1x{0}. An explicit
matrix description of these spaces is given by a monad constructio
An SU(2) KvBLL caloron gas model and confinement
A semi-classical model is developed to describe pure SU(2) Yang-Mills
gluodynamics at finite temperature as a dilute, non-interacting gas of
Kraan-van Baal-Lee-Lu calorons including the case of non-trivial holonomy.
Temperature dependent parameters of the model (asymptotic caloron holonomy,
caloron density and caloron size distribution) are discussed from the point of
view of lattice observations and of in-medium modifications of the one-loop
caloron amplitude. Space-like string tensions running into plateaux at
distances R \approx 0.8 - 1.3 fm are obtained and compared to lattice results
in order to find more precisely the average caloron size. Then, the
quark-antiquark free energy as predicted by the model is considered. In the
confined phase a linear rise with the separation can be observed up to R
\approx 4 fm, whereas it runs into plateaux above T_c. Screening effects in the
adjoint potentials are observed together with an approximate Casimir scaling of
the caloron contribution to the fundamental and adjoint forces. In Abelian
projection, space-like percolation of monopoles is found in the confined phase
only. Thus, taking the non-trivial holonomy into account, confinement
properties of pure SU(2) Yang-Mills gluodynamics can be described by a
semi-classical approach up to distances one order of magnitude larger than the
caloron size.Comment: 26 pages, 14 figures, textheight change
Polyakov loops and spectral properties of the staggered Dirac operator
We study the spectrum of the staggered Dirac operator in SU(2) gauge fields
close to the free limit, for both the fundamental and the adjoint
representation. Numerically we find a characteristic cluster structure with
spacings of adjacent levels separating into three scales. We derive an
analytical formula which explains the emergence of these different spectral
scales. The behavior on the two coarser scales is determined by the lattice
geometry and the Polyakov loops, respectively. Furthermore, we analyze the
spectral statistics on all three scales, comparing to predictions from random
matrix theory.Comment: 11 pages, 25 figures; v2: minor changes, as published in Phys. Rev.
Decomposition of meron configuration of SU(2) gauge field
For the meron configuration of the SU(2) gauge field in the four dimensional
Minkowskii spacetime, the decomposition into an isovector field \bn,
isoscalar fields and , and a U(1) gauge field is
attained by solving the consistency condition for \bn. The resulting \bn
turns out to possess two singular points, behave like a monopole-antimonopole
pair and reduce to the conventional hedgehog in a special case. The
field also possesses singular points, while and are regular
everywhere.Comment: 18 pages, 5 figures, Sec.4 rewritten. 5 refs. adde
2+1 Dimensional Georgi-Glashow Instantons in Weyl Gauge
Semiclassical instanton solutions in the 3D SU(2) Georgi-Glashow model are
transformed into the Weyl gauge. This illustrates the tunneling interpretation
of these instantons and provides a smooth regularization of the singular
unitary gauge. The 3D Georgi-Glashow model has both instanton and sphaleron
solutions, in contrast to 3D Yang-Mills theory which has neither, and 4D
Yang-Mills theory which has instantons but no sphaleron, and 4D electroweak
theory which has a sphaleron but no instantons. We also discuss the spectral
flow picture of fundamental fermions in a Georgi-Glashow instanton background.Comment: 22 pages, 8 figures, revtex4; v2 - references and comments adde
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