More on quantum groups from the the quantization point of view

Star products on the classical double group of a simple Lie group and on corresponding symplectic grupoids are given so that the quantum double and the "quantized tangent bundle" are obtained in the deformation description. "Complex" quantum groups and bicovariant quantum Lie algebras are discused from this point of view. Further we discuss the quantization of the Poisson structure on symmetric algebra $S(g)$ leading to the quantized enveloping algebra $U_{h}(g)$ as an example of biquantization in the sense of Turaev. Description of $U_{h}(g)$ in terms of the generators of the bicovariant differential calculus on $F(G_q)$ is very convenient for this purpose. Finally we interpret in the deformation framework some well known properties of compact quantum groups as simple consequences of corresponding properties of classical compact Lie groups. An analogue of the classical Kirillov's universal character formula is given for the unitary irreducible representation in the compact case.Comment: 18 page

Poisson-Lie generalization of the Kazhdan-Kostant-Sternberg reduction

The trigonometric Ruijsenaars-Schneider model is derived by symplectic reduction of Poisson-Lie symmetric free motion on the group U(n). The commuting flows of the model are effortlessly obtained by reducing canonical free flows on the Heisenberg double of U(n). The free flows are associated with a very simple Lax matrix, which is shown to yield the Ruijsenaars-Schneider Lax matrix upon reduction.Comment: 13 pages, LaTeX, minor modifications and references added in v

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 $n$ states and 2 input letters with high probability is sublinear with respect to $n$ 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.

Measurement of Bottom versus Charm as a Function of Transverse Momentum with Electron-Hadron Correlations in p+p Collisions at sqrt(s)=200 GeV

The momentum distribution of electrons from semi-leptonic decays of charm and bottom for mid-rapidity |y|<0.35 in p+p collisions at sqrt(s)=200 GeV is measured by the PHENIX experiment at the Relativistic Heavy Ion Collider (RHIC) over the transverse momentum range 2 < p_T < 7 GeV/c. The ratio of the yield of electrons from bottom to that from charm is presented. The ratio is determined using partial D/D^bar --> e^{+/-} K^{-/+} X (K unidentified) reconstruction. It is found that the yield of electrons from bottom becomes significant above 4 GeV/c in p_T. A fixed-order-plus-next-to-leading-log (FONLL) perturbative quantum chromodynamics (pQCD) calculation agrees with the data within the theoretical and experimental uncertainties. The extracted total bottom production cross section at this energy is \sigma_{b\b^bar}= 3.2 ^{+1.2}_{-1.1}(stat) ^{+1.4}_{-1.3}(syst) micro b.Comment: 432 authors, 6 pages text, 3 figures. Submitted to Phys. Rev. Lett. Plain text data tables for the points plotted in figures for this and previous PHENIX publications are (or will be) publicly available at http://www.phenix.bnl.gov/papers.htm

Identified charged hadron production in p+p collisions at sqrt(s)=200 and 62.4 GeV

Transverse momentum distributions and yields for $\pi^{\pm}$, $K^{\pm}$, $p$ and $\bar{p}$ in $p+p$ collisions at $\sqrt{s}$=200 and 62.4 GeV at midrapidity are measured by the PHENIX experiment at the Relativistic Heavy Ion Collider (RHIC). These data provide important baseline spectra for comparisons with identified particle spectra in heavy ion collisions at RHIC. We present the inverse slope parameter $T_{\rm inv}$, mean transverse momentum $$ and yield per unit rapidity $dN/dy$ at each energy, and compare them to other measurements at different $\sqrt{s}$ in $p+p$ and $p+\bar{p}$ collisions. We also present the scaling properties such as $m_T$ scaling, $x_T$ scaling on the $p_T$ spectra between different energies. To discuss the mechanism of the particle production in $p+p$ collisions, the measured spectra are compared to next-to-leading-order or next-to-leading-logarithmic perturbative quantum chromodynamics calculations.Comment: 431 authors from 62 institutions, 32 pages, 23 figures, and 18 tables. Submitted to Physical Review C. Plain text data tables for the points plotted in figures for this and previous PHENIX publications are (or will be) publicly available at http://www.phenix.bnl.gov/papers.htm

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

Study of doubly strange systems using stored antiprotons

Bound nuclear systems with two units of strangeness are still poorly known despite their importance for many strong interaction phenomena. Stored antiprotons beams in the GeV range represent an unparalleled factory for various hyperon-antihyperon pairs. Their outstanding large production probability in antiproton collisions will open the floodgates for a series of new studies of systems which contain two or even more units of strangeness at the P‾ANDA experiment at FAIR. For the first time, high resolution γ-spectroscopy of doubly strange ΛΛ-hypernuclei will be performed, thus complementing measurements of ground state decays of ΛΛ-hypernuclei at J-PARC or possible decays of particle unstable hypernuclei in heavy ion reactions. High resolution spectroscopy of multistrange Ξ−-atoms will be feasible and even the production of Ω−-atoms will be within reach. The latter might open the door to the |S|=3 world in strangeness nuclear physics, by the study of the hadronic Ω−-nucleus interaction. For the first time it will be possible to study the behavior of Ξ‾+ in nuclear systems under well controlled conditions