821 research outputs found
Quantum cohomology via vicious and osculating walkers
We relate the counting of rational curves intersecting Schubert varieties of the Grassmannian to the counting of certain non-intersecting lattice paths on the cylinder, so-called vicious and osculating walkers. These lattice paths form exactly solvable statistical mechanics models and are obtained from solutions to the Yang–Baxter equation. The eigenvectors of the transfer matrices of these models yield the idempotents of the Verlinde algebra of the gauged u^(n)k -WZNW model. The latter is known to be closely related to the small quantum cohomology ring of the Grassmannian. We establish further that the partition functions of the vicious and osculating walker model are given in terms of Postnikov’s toric Schur functions and can be interpreted as generating functions for Gromov–Witten invariants. We reveal an underlying quantum group structure in terms of Yang–Baxter algebras and use it to give a generating formula for toric Schur functions in terms of divided difference operators which appear in known representations of the nil-Hecke algebra
Decomposable representations and Lagrangian submanifolds of moduli spaces associated to surface groups
In this paper, we construct a Lagrangian submanifold of the moduli space
associated to the fundamental group of a punctured Riemann surface (the space
of representations of this fundamental group into a compact connected Lie
group). This Lagrangian submanifold is obtained as the fixed-point set of an
anti-symplectic involution defined on the moduli space. The notion of
decomposable representation provides a geometric interpretation of this
Lagrangian submanifold
Systematics of Inclusive Photon Production in 158 AGeV Pb Induced Reactions on Ni, Nb, and Pb Targets
The multiplicity of inclusive photons has been measured on an event-by-event
basis for 158 AGeV Pb induced reactions on Ni, Nb, and Pb targets. The
systematics of the pseudorapidity densities at midrapidity (rho_max) and the
width of the pseudorapidity distributions have been studied for varying
centralities for these collisions. A power law fit to the photon yield as a
function of the number of participating nucleons gives a value of 1.13+-0.03
for the exponent. The mean transverse momentum, , of photons determined
from the ratio of the measured electromagnetic transverse energy and photon
multiplicity, remains almost constant with increasing rho_max. Results are
compared with model predictions.Comment: 16 pages including 4 figure
Scaling of Particle and Transverse Energy Production in 208Pb+208Pb collisions at 158 A GeV
Transverse energy, charged particle pseudorapidity distributions and photon
transverse momentum spectra have been studied as a function of the number of
participants (N_{part}) and the number of binary nucleon-nucleon collisions
(N_{coll}) in 158 A GeV Pb+Pb collisions over a wide impact parameter range. A
scaling of the transverse energy pseudorapidity density at midrapidity as
N_{part}^{1.08 \pm 0.06} and N_{coll}^{0.83 \pm 0.05} is observed. For the
charged particle pseudorapidity density at midrapidity we find a scaling as
N_{part}^{1.07 \pm 0.04} and N_{coll}^{0.82 \pm 0.03}. This faster than linear
scaling with N_{part} indicates a violation of the naive Wounded Nucleon Model.Comment: 13 pages, 16 figures, submitted to European Physical Journal C
(revised results for scaling exponents
Centrality Dependence of Neutral Pion Production in 158 A GeV Pb + Pb Collisions
The production of neutral pions in 158AGeV Pb+Pb collisions has been studied
in the WA98 experiment at the CERN SPS. Transverse momentum spectra are studied
for the range 0.3 GeV/c < mT-m0 < 4.0 GeV/c. The results for central collisions
are compared to various models. The centrality dependence of the neutral pion
spectral shape and yield is investigated. An invariance of the spectral shape
and a simple scaling of the yield with the number of participating nucleons is
observed for centralities with greater than about 30 participating nucleons
which is most naturally explained by assuming an equilibrated system.Comment: 5 pages, Latex, including 3 eps figures, submitted to Phys.Rev.Lett;
updated pQCD comparison due to new input from the author, updated references,
corrected plotting error in figure
Deformation effects in Ni nuclei produced in Si+Si at 112 MeV
Velocity and energy spectra of the light charged particles (protons and
-particles) emitted in the Si(E = 112 MeV) + Si
reaction have been measured at the Strasbourg VIVITRON Tandem facility. The
ICARE charged particle multidetector array was used to obtain exclusive spectra
of the light particles in the angular range 15 - 150 degree and to determine
the angular correlations of these particles with respect to the emission angles
of the evaporation residues. The experimental data are analysed in the
framework of the statistical model. The exclusive energy spectra of
-particles emitted from the Si + Si compound system are
generally well reproduced by Monte Carlo calculations using spin-dependent
level densities. This spin dependence approach suggests the onset of large
deformations at high spin. A re-analysis of previous -particle data
from the Si + Si compound system, using the same spin-dependent
parametrization, is also presented in the framework of a general discussion of
the occurrence of large deformation effects in the A ~ 60 mass region.Comment: 25 pages, 6 figure
A Preshower Photon Multiplicity Detector for the WA98 Experiment
A high granularity preshower detector has been fabricated and installed in the WA98 Experiment at the CERN SPS for measuring the spatial distribution of photons produced in the forward region in lead ion induced interactions. Photons are counted by detecting the preshower signal in plastic scintillator pads placed behind a 3 radiation length thick lead converter and applying a threshold on the scintillator signal to reject the minimum ionizing particles. Techniques to improve the imaging of the fibre and performance of the detector in the high multiplicity environment of lead-lead collisions are described. Using Monte-Carlo simulation methods and test beam data of pi- and e- at various energies the photon counting efficiency is estimated to be 68% for central and 73% for peripheral Pb+Pb collisions
Multiplicity Distributions and Charged-neutral Fluctuations
Results from the multiplicity distributions of inclusive photons and charged
particles, scaling of particle multiplicities, event-by-event multiplicity
fluctuations, and charged-neutral fluctuations in 158 GeV Pb+Pb
collisions are presented and discussed. A scaling of charged particle
multiplicity as and photons as have been observed, indicating violation of naive wounded nucleon model.
The analysis of localized charged-neutral fluctuation indicates a
model-independent demonstration of non-statistical fluctuations in both charged
particles and photons in limited azimuthal regions. However, no correlated
charged-neutral fluctuations are observed.Comment: Talk given at the International Symposium on Nuclear Physics
(ISNP-2000), Mumbai, India, 18-22 Dec 2000, Proceedings to be published in
Pramana, Journal of Physic
Search for DCC in 158A GeV Pb+Pb Collisions
A detailed analysis of the phase space distributions of charged particles and
photons have been carried out using two independent methods. The results
indicate the presence of nonstatistical fluctuations in localized regions of
phase space.Comment: Talk at the PANIC99 Conference, June 9-16, 199
Present Status and Future of DCC Analysis
Disoriented Chiral Condensates (DCC) have been predicted to form in high
energy heavy ion collisions where the approximate chiral symmetry of QCD has
been restored. This leads to large imbalances in the production of charged to
neutral pions. Sophisticated analysis methods are being developed to
disentangle DCC events out of the large background of events with
conventionally produced particles. We present a short review of current
analysis methods and future prospects.Comment: 12 pages, 5 figures. Invited talk presented at the 13th International
Conference on Ultrarelativistic Nucleus-Nucleus Collisions (Quark Matter 97),
Tsukuba, Japan, 1-5 Dec 199
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