8,194 research outputs found
Direct instantons, topological charge screening and QCD glueball sum rules
Nonperturbative Wilson coefficients of the operator product expansion (OPE)
for the spin-0 glueball correlators are derived and analyzed. A systematic
treatment of the direct instanton contributions is given, based on realistic
instanton size distributions and renormalization at the operator scale. In the
pseudoscalar channel, topological charge screening is identified as an
additional source of (semi-) hard nonperturbative physics. The screening
contributions are shown to be vital for consistency with the anomalous axial
Ward identity, and previously encountered pathologies (positivity violations
and the disappearance of the 0^{-+} glueball signal) are traced to their
neglect. On the basis of the extended OPE, a comprehensive quantitative
analysis of eight Borel-moment sum rules in both spin-0 glueball channels is
then performed. The nonperturbative OPE coefficients turn out to be
indispensable for consistent sum rules and for their reconciliation with the
underlying low-energy theorems. The topological short-distance physics strongly
affects the sum rule results and reveals a rather diverse pattern of glueball
properties. New predictions for the spin-0 glueball masses and decay constants
and an estimate of the scalar glueball width are given, and several
implications for glueball structure and experimental glueball searches are
discussed.Comment: 49 pages, 8 figure
Normal Mode Determination of Perovskite Crystal Structures with Octahedral Rotations: Theory and Applications
Nuclear site analysis methods are used to enumerate the normal modes of
perovskite polymorphs with octahedral rotations. We provide the modes
of the fourteen subgroups of the cubic aristotype describing the Glazer
octahedral tilt patterns, which are obtained from rotations of the
octahedra with different sense and amplitude about high symmetry axes. We
tabulate all normal modes of each tilt system and specify the contribution of
each atomic species to the mode displacement pattern, elucidating the physical
meaning of the symmetry unique modes. We have systematically generated 705
schematic atomic displacement patterns for the normal modes of all 15 (14
rotated + 1 unrotated) Glazer tilt systems. We show through some illustrative
examples how to use these tables to identify the octahedral rotations,
symmetric breathing, and first-order Jahn-Teller anti-symmetric breathing
distortions of the octahedra, and the associated Raman selection
rules. We anticipate that these tables and schematics will be useful in
understanding the lattice dynamics of bulk perovskites and would serve as
reference point in elucidating the atomic origin of a wide range of physical
properties in synthetic perovskite thin films and superlattices.Comment: 17 pages, 3 figures, 17 tables. Supporting information accessed
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Cauchy's formulas for random walks in bounded domains
Cauchy's formula was originally established for random straight paths
crossing a body and basically relates the average
chord length through to the ratio between the volume and the surface of the
body itself. The original statement was later extended in the context of
transport theory so as to cover the stochastic paths of Pearson random walks
with exponentially distributed flight lengths traversing a bounded domain. Some
heuristic arguments suggest that Cauchy's formula may also hold true for
Pearson random walks with arbitrarily distributed flight lengths. For such a
broad class of stochastic processes, we rigorously derive a generalized
Cauchy's formula for the average length travelled by the walkers in the body,
and show that this quantity depends indeed only on the ratio between the volume
and the surface, provided that some constraints are imposed on the entrance
step of the walker in . Similar results are obtained also for the average
number of collisions performed by the walker in , and an extension to
absorbing media is discussed.Comment: 12 pages, 6 figure
Particle scattering in turbulent plasmas with amplified wave modes
High-energy particles stream during coronal mass ejections or flares through the plasma of the solar wind. This causes instabilities, which lead to wave growth at specific resonant wave numbers, especially within shock regions. These amplified wave modes influence the turbulent scattering process significantly. In this paper, results of particle transport and scattering in turbulent plasmas with excited wave modes are presented. The method used is a hybrid simulation code, which treats the heliospheric turbulence by an incompressible magnetohydrodynamic approach separately from a kinetic particle description. Furthermore, a semi-analytical model using quasilinear theory (QLT) is compared to the numerical results. This paper aims at a more fundamental understanding and interpretation of the pitch-angle scattering coefficients. Our calculations show a good agreement of particle simulations and the QLT for broad-band turbulent spectra; for higher turbulence levels and particle beam driven plasmas, the QLT approximation gets worse. Especially the resonance gap at μ = 0 poses a well-known problem for QLT for steep turbulence spectra, whereas test-particle computations show no problems for the particles to scatter across this region. The reason is that the sharp resonant wave-particle interactions in QLT are an oversimplification of the broader resonances in test-particle calculations, which result from nonlinear effects not included in the QLT. We emphasise the importance of these results for both numerical simulations and analytical particle transport approaches, especially the validity of the QLT.
Appendices A-D are available in electronic form at http://www.aanda.or
On extending actions of groups
Problems of dense and closed extension of actions of compact transformation
groups are solved. The method developed in the paper is applied to problems of
extension of equivariant maps and of construction of equivariant
compactifications
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