105 research outputs found
Macdonald Polynomials from Sklyanin Algebras: A Conceptual Basis for the -Adics-Quantum Group Connection
We establish a previously conjectured connection between -adics and
quantum groups. We find in Sklyanin's two parameter elliptic quantum algebra
and its generalizations, the conceptual basis for the Macdonald polynomials,
which ``interpolate'' between the zonal spherical functions of related real and
\--adic symmetric spaces. The elliptic quantum algebras underlie the
\--Baxter models. We show that in the n \air \infty limit, the Jost
function for the scattering of {\em first} level excitations in the
\--Baxter model coincides with the Harish\--Chandra\--like \--function
constructed from the Macdonald polynomials associated to the root system .
The partition function of the \--Baxter model itself is also expressed in
terms of this Macdonald\--Harish\--Chandra\ \--function, albeit in a less
simple way. We relate the two parameters and of the Macdonald
polynomials to the anisotropy and modular parameters of the Baxter model. In
particular the \--adic ``regimes'' in the Macdonald polynomials correspond
to a discrete sequence of XXZ models. We also discuss the possibility of
``\--deforming'' Euler products.Comment: 25 page
CP violating neutrino oscillation and uncertainties in Earth matter density
We propose a statistical formulation to estimate possible errors in long
baseline neutrino oscillation experiments caused by uncertainties in the Earth
matter density. A quantitative investigation of the effect is made on the CP
asymmetry in future neutrino factory experiments.Comment: Latex, 10 pages, 5 figure
Gravitational excitons from extra dimensions
Inhomogeneous multidimensional cosmological models with a higher dimensional
space-time manifold are investigated under dimensional reduction. In the
Einstein conformal frame, small excitations of the scale factors of the
internal spaces near minima of an effective potential have a form of massive
scalar fields in the external space-time. Parameters of models which ensure
minima of the effective potentials are obtained for particular cases and masses
of gravitational excitons are estimated.Comment: Revised version --- 12 references added, Introduction enlarged, 20
pages, LaTeX, to appear in Phys.Rev.D56 (15.11.97
Nonlinear multidimensional cosmological models with form fields: stabilization of extra dimensions and the cosmological constant problem
We consider multidimensional gravitational models with a nonlinear scalar
curvature term and form fields in the action functional. In our scenario it is
assumed that the higher dimensional spacetime undergoes a spontaneous
compactification to a warped product manifold. Particular attention is paid to
models with quadratic scalar curvature terms and a Freund-Rubin-like ansatz for
solitonic form fields. It is shown that for certain parameter ranges the extra
dimensions are stabilized. In particular, stabilization is possible for any
sign of the internal space curvature, the bulk cosmological constant and of the
effective four-dimensional cosmological constant. Moreover, the effective
cosmological constant can satisfy the observable limit on the dark energy
density. Finally, we discuss the restrictions on the parameters of the
considered nonlinear models and how they follow from the connection between the
D-dimensional and the four-dimensional fundamental mass scales.Comment: 21 pages, LaTeX2e, minor changes, improved references, fonts include
Quantum Creation of an Open Inflationary Universe
We discuss a dramatic difference between the description of the quantum
creation of an open universe using the Hartle-Hawking wave function and the
tunneling wave function. Recently Hawking and Turok have found that the
Hartle-Hawking wave function leads to a universe with Omega = 0.01, which is
much smaller that the observed value of Omega > 0.3. Galaxies in such a
universe would be about light years away from each other, so the
universe would be practically structureless. We will argue that the
Hartle-Hawking wave function does not describe the probability of the universe
creation. If one uses the tunneling wave function for the description of
creation of the universe, then in most inflationary models the universe should
have Omega = 1, which agrees with the standard expectation that inflation makes
the universe flat. The same result can be obtained in the theory of a
self-reproducing inflationary universe, independently of the issue of initial
conditions. However, there exist two classes of models where Omega may take any
value, from Omega > 1 to Omega << 1.Comment: 23 pages, 4 figures. New materials are added. In particular, we show
that boundary terms do not help to solve the problem of unacceptably small
Omega in the new model proposed by Hawking and Turok in hep-th/9803156. A
possibility to solve the cosmological constant problem in this model using
the tunneling wave function is discusse
Experimental Study of the Shortest Reset Word of Random Automata
In this paper we describe an approach to finding the shortest reset word of a
finite synchronizing automaton by using a SAT solver. We use this approach to
perform an experimental study of the length of the shortest reset word of a
finite synchronizing automaton. The largest automata we considered had 100
states. The results of the experiments allow us to formulate a hypothesis that
the length of the shortest reset word of a random finite automaton with
states and 2 input letters with high probability is sublinear with respect to
and can be estimated as $1.95 n^{0.55}.
Two-proton correlations from 158 AGeV Pb+Pb central collisions
The two-proton correlation function at midrapidity from Pb+Pb central
collisions at 158 AGeV has been measured by the NA49 experiment. The results
are compared to model predictions from static thermal Gaussian proton source
distributions and transport models RQMD and VENUS. An effective proton source
size is determined by minimizing CHI-square/ndf between the correlation
functions of the data and those calculated for the Gaussian sources, yielding
3.85 +-0.15(stat.) +0.60-0.25(syst.) fm. Both the RQMD and the VENUS model are
consistent with the data within the error in the correlation peak region.Comment: RevTeX style, 6 pages, 4 figures, 1 table. More discussion are added
about the structure on the tail of the correlation function. The systematic
error is revised. To appear in Phys. Lett.
Event-by-event fluctuations of average transverse momentum in central Pb+Pb collisions at 158 GeV per nucleon
We present first data on event-by-event fluctuations in the average
transverse momentum of charged particles produced in Pb+Pb collisions at the
CERN SPS. This measurement provides previously unavailable information allowing
sensitive tests of microscopic and thermodynamic collision models and to search
for fluctuations expected to occur in the vicinity of the predicted QCD phase
transition. We find that the observed variance of the event-by-event average
transverse momentum is consistent with independent particle production modified
by the known two-particle correlations due to quantum statistics and final
state interactions and folded with the resolution of the NA49 apparatus. For
two specific models of non-statistical fluctuations in transverse momentum
limits are derived in terms of fluctuation amplitude. We show that a
significant part of the parameter space for a model of isospin fluctuations
predicted as a consequence of chiral symmetry restoration in a non-equilibrium
scenario is excluded by our measurement.Comment: 6 pages, 2 figures, submitted to Phys. Lett.
NA49 Results on Single Particle and Correlation Measurements in Central Pb+Pb Collisions
Single-particle spectra and two-particle correlation functions measured by the NA49 collaboration in central Pb+Pb collisions at 158 GeV/nucleon are presented. These measurements are used to study the kinetic and chemical freeze-out conditions in heavy ion collisions. We conclude that large baryon stopping, high baryon density and strong transverse radial flow are achieved in central Pb+Pb collisions at the SPS.Single-particle spectra and two-particle correlation functions measured by the NA49 collaboration in central Pb+Pb collisions at 158 GeV/nucleon are presented. These measurements are used to study the kinetic and chemical freeze-out conditions in heavy ion collisions. We conclude that large baryon stopping, high baryon density and strong transverse radial flow are achieved in central Pb+Pb collisions at the SPS
Xi and Xi-bar Production in 158 GeV/Nucleon Pb+Pb Collisions
We report measurements of Xi and Xi-bar hyperon absolute yields as a function
of rapidity in 158 GeV/c Pb+Pb collisions. At midrapidity, dN/dy = 2.29 +/-
0.12 for Xi, and 0.52 +/- 0.05 for Xi-bar, leading to the ratio of Xi-bar/Xi =
0.23 +/- 0.03. Inverse slope parameters fitted to the measured transverse mass
spectra are of the order of 300 MeV near mid-rapidity. The estimated total
yield of Xi particles in Pb+Pb central interactions amounts to 7.4 +/- 1.0 per
collision. Comparison to Xi production in properly scaled p+p reactions at the
same energy reveals a dramatic enhancement (about one order of magnitude) of Xi
production in Pb+Pb central collisions over elementary hadron interactions.Comment: 15 page
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