Singular projective varieties and quantization

By the quantization condition compact quantizable Kaehler manifolds can be embedded into projective space. In this way they become projective varieties. The quantum Hilbert space of the Berezin-Toeplitz quantization (and of the geometric quantization) is the projective coordinate ring of the embedded manifold. This allows for generalization to the case of singular varieties. The set-up is explained in the first part of the contribution. The second part of the contribution is of tutorial nature. Necessary notions, concepts, and results of algebraic geometry appearing in this approach to quantization are explained. In particular, the notions of projective varieties, embeddings, singularities, and quotients appearing in geometric invariant theory are recalled.Comment: 21 pages, 3 figure

Identification of Berezin-Toeplitz deformation quantization

We give a complete identification of the deformation quantization which was obtained from the Berezin-Toeplitz quantization on an arbitrary compact Kaehler manifold. The deformation quantization with the opposite star-product proves to be a differential deformation quantization with separation of variables whose classifying form is explicitly calculated. Its characteristic class (which classifies star-products up to equivalence) is obtained. The proof is based on the microlocal description of the Szegoe kernel of a strictly pseudoconvex domain given by Boutet de Monvel and Sjoestrand.Comment: 26 page

Effective Rheology of Bubbles Moving in a Capillary Tube

We calculate the average volumetric flux versus pressure drop of bubbles moving in a single capillary tube with varying diameter, finding a square-root relation from mapping the flow equations onto that of a driven overdamped pendulum. The calculation is based on a derivation of the equation of motion of a bubble train from considering the capillary forces and the entropy production associated with the viscous flow. We also calculate the configurational probability of the positions of the bubbles.Comment: 4 pages, 1 figur

Particle identification in ALICE : a Bayesian approach

Peer reviewe

Measurement of electrons from beauty-hadron decays in p-Pb collisions at root(NN)-N-S=5.02 TeV and Pb-Pb collisions at. root(NN)-N-S=2.76 TeV

The production of beauty hadrons was measured via semi-leptonic decays at mid-rapidity with the ALICE detector at the LHC in the transverse momentum interval 1<pT< 8 GeV/c in minimum-bias p-Pb collisions at sNN=5.02 TeV and in 1.3 < pT< 8 GeV/c in the 20% most central Pb-Pb collisions at sNN=2.76 TeV. The pp reference spectra at sNN=5.02 TeV and s=2.76 TeV, needed for the calculation of the nuclear modification factors RpPb and RPbPb, were obtained by a pQCD-driven scaling of the cross section of electrons from beauty-hadron decays measured at s=7 TeV. In the pT interval 3 < pT< 8 GeV/c, a suppression of the yield of electrons from beauty-hadron decays is observed in Pb-Pb compared to pp collisions. Towards lower pT, the RPbPb values increase with large systematic uncertainties. The RpPb is consistent with unity within systematic uncertainties and is well described by theoretical calculations that include cold nuclear matter effects in p-Pb collisions. The measured RpPb and these calculations indicate that cold nuclear matter effects are small at high transverse momentum also in Pb-Pb collisions. Therefore., the observed reduction of RPbPb below unity at high pT may be ascribed to an effect of the hot and dense medium formed in Pb-Pb collisions.[Figure not available: see fulltext.

清涼飮料税論

The production of J/\).psi\) and $\psi(2S)$ was measured with the ALICE detector in Pb-Pb collisions at the LHC. The measurement was performed at forward rapidity 2.5 < y < 4 \() down to zero transverse momentum \(p_{\rm T} in the dimuon decay channel. Inclusive J/\).psi\) yields were extracted in different centrality classes and the centrality dependence of the average $p_{\rm T}$ is presented. The J/\).psi\) suppression, quantified with the nuclear modification factor $R_{\rm AA}$ , was studied as a function of centrality, transverse momentum and rapidity. Comparisons with similar measurements at lower collision energy and theoretical models indicate that the J/\).psi\) production is the result of an interplay between color screening and recombination mechanisms in a deconfined partonic medium, or at its hadronization. Results on the $\psi(2S)$ suppression are provided via the ratio of $\psi(2S)$ over J/\).psi\) measured in pp and Pb-Pb collisions

Exclusive J/psi Photoproduction off Protons in Ultraperipheral p-Pb Collisions at root s(NN)=5.02 TeV

We present the first measurement at the LHC of exclusive J/psi photoproduction off protons, in ultraperipheral proton-lead collisions at root s(NN) = 5.02 TeV. Events are selected with a dimuon pair produced either in the rapidity interval, in the laboratory frame, 2.5 J/psi + p) are 33.2 +/- 2.2(stat) +/- 3.2(syst) +/- 0.7(theor) nb in p-Pb and 284 +/- 36(stat)(-32)(+27)(syst) +/- 26(theor) nb in Pb-p collisions. We measure this process up to about 700 GeV in the gamma p center of mass, which is a factor of two larger than the highest energy studied at HERA. The data are consistent with a power law dependence of the J/psi photoproduction cross section in gamma p energies from about 20 to 700 GeV, or equivalently, from Bjorken x scaling variable between similar to 2 x 10(-2) and similar to 2 x 10(-5), thus indicating no significant change in the gluon density behavior of the proton between HERA and LHC energies

Measurement of charged jet suppression in Pb-Pb collisions at sNN\sqrt{s_{NN}}=2.76TeV

A measurement of the transverse momentum spectra of jets in Pb-Pb collisions at $\sqrt{s_{NN}}$=2.76TeV is reported. Jets are reconstructed from charged particles using the anti-$k_T$ jet algorithm with jet resolution parameters R of 0.2 and 0.3 in pseudo-rapidity |$\eta$|<0.5. The transverse momentum p_T of charged particles is measured down to 0.15 GeV/c which gives access to the low p_T fragments of the jet. Jets found in heavy-ion collisions are corrected event-by-event for average background density and on an inclusive basis (via unfolding) for residual background fluctuations and detector effects. A strong suppression of jet production in central events with respect to peripheral events is observed. The suppression is found to be similar to the suppression of charged hadrons, which suggests that substantial energy is radiated at angles larger than the jet resolution parameter R=0.3 considered in the analysis. The fragmentation bias introduced by selecting jets with a high p_T leading particle, which rejects jets with a soft fragmentation pattern, has a similar effect on the jet yield for central and peripheral events. The ratio of jet spectra with R=0.2 and R=0.3 is found to be similar in Pb-Pb and simulated PYTHIA pp events, indicating no strong broadening of the radial jet structure in the reconstructed jets with R<0.3.A measurement of the transverse momentum spectra of jets in Pb-Pb collisions at $\sqrt{s_{\rm NN}}=2.76$ TeV is reported. Jets are reconstructed from charged particles using the anti-$k_{\rm T}$ jet algorithm with jet resolution parameters $R$ of $0.2$ and $0.3$ in pseudo-rapidity $|\eta|<0.5$. The transverse momentum $p_{\rm T}$ of charged particles is measured down to $0.15$ GeV/$c$ which gives access to the low $p_{\rm T}$ fragments of the jet. Jets found in heavy-ion collisions are corrected event-by-event for average background density and on an inclusive basis (via unfolding) for residual background fluctuations and detector effects. A strong suppression of jet production in central events with respect to peripheral events is observed. The suppression is found to be similar to the suppression of charged hadrons, which suggests that substantial energy is radiated at angles larger than the jet resolution parameter $R=0.3$ considered in the analysis. The fragmentation bias introduced by selecting jets with a high $p_{\rm T}$ leading particle, which rejects jets with a soft fragmentation pattern, has a similar effect on the jet yield for central and peripheral events. The ratio of jet spectra with $R=0.2$ and $R=0.3$ is found to be similar in Pb-Pb and simulated PYTHIA pp events, indicating no strong broadening of the radial jet structure in the reconstructed jets with $R<0.3$