5,334 research outputs found
Stringy K-theory and the Chern character
For a finite group G acting on a smooth projective variety X, we construct
two new G-equivariant rings: first the stringy K-theory of X, and second the
stringy cohomology of X. For a smooth Deligne-Mumford stack Y we also construct
a new ring called the full orbifold K-theory of Y. For a global quotient
Y=[X/G], the ring of G-invariants of the stringy K-theory of X is a subalgebra
of the full orbifold K-theory of the the stack Y and is linearly isomorphic to
the ``orbifold K-theory'' of Adem-Ruan (and hence Atiyah-Segal), but carries a
different, ``quantum,'' product, which respects the natural group grading. We
prove there is a ring isomorphism, the stringy Chern character, from stringy
K-theory to stringy cohomology, and a ring homomorphism from full orbifold
K-theory to Chen-Ruan orbifold cohomology. These Chern characters satisfy
Grothendieck-Riemann-Roch for etale maps.
We prove that stringy cohomology is isomorphic to Fantechi and Goettsche's
construction. Since our constructions do not use complex curves, stable maps,
admissible covers, or moduli spaces, our results simplify the definitions of
Fantechi-Goettsche's ring, of Chen-Ruan's orbifold cohomology, and of
Abramovich-Graber-Vistoli's orbifold Chow.
We conclude by showing that a K-theoretic version of Ruan's Hyper-Kaehler
Resolution Conjecture holds for symmetric products.
Our results hold both in the algebro-geometric category and in the
topological category for equivariant almost complex manifolds.Comment: Exposition improved and additional details provided. To appear in
Inventiones Mathematica
Precise Experimental Investigation of Eigenmodes in a Planar Ion Crystal
The accurate characterization of eigenmodes and eigenfrequencies of
two-dimensional ion crystals provides the foundation for the use of such
structures for quantum simulation purposes. We present a combined experimental
and theoretical study of two-dimensional ion crystals. We demonstrate that
standard pseudopotential theory accurately predicts the positions of the ions
and the location of structural transitions between different crystal
configurations. However, pseudopotential theory is insufficient to determine
eigenfrequencies of the two-dimensional ion crystals accurately but shows
significant deviations from the experimental data obtained from resolved
sideband spectroscopy. Agreement at the level of 2.5 x 10^(-3) is found with
the full time-dependent Coulomb theory using the Floquet-Lyapunov approach and
the effect is understood from the dynamics of two-dimensional ion crystals in
the Paul trap. The results represent initial steps towards an exploitation of
these structures for quantum simulation schemes.Comment: 5 pages, 4 figures, supplemental material (mathematica and matlab
files) available upon reques
Energy dependence of pion double charge exchange
The energy dependence of forward angle pion double charge exchange is calculated in the energy range of 0–250 MeV. The most striking feature is a peak around 40 MeV which is in excellent agreement with the data when distorted waves obtained from a realistic optical model are used. Two possible short-range corrections to the reaction mechanism are addressed
Finite size scaling for quantum criticality using the finite-element method
Finite size scaling for the Schr\"{o}dinger equation is a systematic approach
to calculate the quantum critical parameters for a given Hamiltonian. This
approach has been shown to give very accurate results for critical parameters
by using a systematic expansion with global basis-type functions. Recently, the
finite element method was shown to be a powerful numerical method for ab initio
electronic structure calculations with a variable real-space resolution. In
this work, we demonstrate how to obtain quantum critical parameters by
combining the finite element method (FEM) with finite size scaling (FSS) using
different ab initio approximations and exact formulations. The critical
parameters could be atomic nuclear charges, internuclear distances, electron
density, disorder, lattice structure, and external fields for stability of
atomic, molecular systems and quantum phase transitions of extended systems. To
illustrate the effectiveness of this approach we provide detailed calculations
of applying FEM to approximate solutions for the two-electron atom with varying
nuclear charge; these include Hartree-Fock, density functional theory under the
local density approximation, and an "exact"' formulation using FEM. We then use
the FSS approach to determine its critical nuclear charge for stability; here,
the size of the system is related to the number of elements used in the
calculations. Results prove to be in good agreement with previous Slater-basis
set calculations and demonstrate that it is possible to combine finite size
scaling with the finite-element method by using ab initio calculations to
obtain quantum critical parameters. The combined approach provides a promising
first-principles approach to describe quantum phase transitions for materials
and extended systems.Comment: 15 pages, 19 figures, revision based on suggestions by referee,
accepted in Phys. Rev.
Analytic Solution of the Pion-Laser Model
Brooding over bosons, wave packets and Bose - Einstein correlations, we find
that a generalization of the pion-laser model for the case of overlapping
wave-packets is analytically solvable with complete n-particle symmetrization.
The effective radius parameter of the two-particle correlation function is
reduced for low values and enlargened for high values of the mean momentum in
the rare gas limiting case, as compared to the case when multi-particle
symmetrization effects are neglected.
These results explicitly depend on the multiplicity, providing a theoretical
basis for event-by-event analysis of high energy heavy ion reactions.Comment: LaTeX, ReVTeX 3.1, 7 pages, uses 1 eps figure and epsfig.sty
(shortened version
Towards an understanding of isospin violation in pion-nucleon scattering
We investigate isospin breaking in low-energy pion-nucleon scattering in the
framework of chiral perturbation theory. This work extends the systematic
analysis of [1] to the energy range above threshold. Various relations, which
identically vanish in the limit of isospin symmetry, are used to quantify
isospin breaking effects. We study the energy dependence of the S- and P-wave
projections of these ratios and find dramatic effects in the S-waves of those
two relations which are given in terms of isoscalar quantities only. This
effect drops rather quickly with growing center-of-mass energy.Comment: 12 pp, REVTeX, 8 figs, FZJ-IKP(TH)-2000-2
Charge Symmetry Violation Effects in Pion Scattering off the Deuteron
We discuss the theoretical and experimental situations for charge symmetry
violation (CSV) effects in the elastic scattering of pi+ and pi- on deuterium
(D) and 3He/3H. Accurate comparison of data for both types of targets provides
evidence for the presence of CSV effects. While there are indications of a CSV
effect in deuterium, it is much more pronounced in the case of 3He/3H. We
provide a description of the CSV effect on the deuteron in terms of single- and
double- scattering amplitudes. The Delta-mass splitting is taken into account.
Theoretical predictions are compared with existing experimental data for pi-d
scattering; a future article will speak to the pi-three nucleon case.Comment: 16 pages of RevTeX, 7 postscript figure
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