Equivariant quantization of orbifolds

Equivariant quantization is a new theory that highlights the role of symmetries in the relationship between classical and quantum dynamical systems. These symmetries are also one of the reasons for the recent interest in quantization of singular spaces, orbifolds, stratified spaces... In this work, we prove existence of an equivariant quantization for orbifolds. Our construction combines an appropriate desingularization of any Riemannian orbifold by a foliated smooth manifold, with the foliated equivariant quantization that we built in \cite{PoRaWo}. Further, we suggest definitions of the common geometric objects on orbifolds, which capture the nature of these spaces and guarantee, together with the properties of the mentioned foliated resolution, the needed correspondences between singular objects of the orbifold and the respective foliated objects of its desingularization.Comment: 13 page

Building a path-integral calculus: a covariant discretization approach

Path integrals are a central tool when it comes to describing quantum or thermal fluctuations of particles or fields. Their success dates back to Feynman who showed how to use them within the framework of quantum mechanics. Since then, path integrals have pervaded all areas of physics where fluctuation effects, quantum and/or thermal, are of paramount importance. Their appeal is based on the fact that one converts a problem formulated in terms of operators into one of sampling classical paths with a given weight. Path integrals are the mirror image of our conventional Riemann integrals, with functions replacing the real numbers one usually sums over. However, unlike conventional integrals, path integration suffers a serious drawback: in general, one cannot make non-linear changes of variables without committing an error of some sort. Thus, no path-integral based calculus is possible. Here we identify which are the deep mathematical reasons causing this important caveat, and we come up with cures for systems described by one degree of freedom. Our main result is a construction of path integration free of this longstanding problem, through a direct time-discretization procedure.Comment: 22 pages, 2 figures, 1 table. Typos correcte

Comparison between high-energy proton and charged pion induced damage in Lead Tungstate calorimeter crystals

A Lead Tungstate crystal produced for the electromagnetic calorimeter of the CMS experiment at the LHC was cut into three equal-length sections. The central one was irradiated with 290 MeV/c positive pions up to a fluence of (5.67 +- 0.46)x10^13 /cm^2, while the other two were exposed to a 24 GeV/c proton fluence of (1.17 +- 0.11) x 10^13/ cm^2. The damage recovery in these crystals, stored in the dark at room temperature, has been followed over two years. The comparison of the radiation-induced changes in light transmission for these crystals shows that damage is proportional to the star densities produced by the irradiation.Comment: 7 pages, 4 figure

First results on radiation damage in PbWO4 crystals exposed to a 20 GeV/c proton beam

We have exposed seven full length production quality crystals of the electromagnetic calorimeter (ECAL) of the CMS detector to a 20 GeV/c proton beam at the CERN PS accelerator. The exposure was done at fluxes of 10**12 p/cm**2/h and 10**13 p/cm**2/h and integral fluences of 10**12 p/cm**2 and 10**13 p/cm**2 were reached at both rates. The light transmission of the crystals was measured after irradiation and suitable cooling time for induced radioactivity to decrease to a safe level. First results of these measurements are shown. The possible damage mechanisms are discussed and simulations based on one possible model are presented. The implications for long-term operation of CMS are discussed and it is shown that in the whole barrel and at least most of the ECAL endcap hadron damage alone - even if cumulative - should not cause the crystals to fail the CMS specification of an induced absorption coefficient muIND < 1.5 /m during the first 10 years of LHC operation.Comment: 5 pages, to be published in Proc. ICATPP Conference on Astroparticle, Particle, Space Physics, Detectors and Medical Physics Applications (Como, Italy, 6 to 10 October 2003

High-energy proton induced damage study of scintillation light output from PbWO4 calorimeter crystals

Eight PbWO4 crystals produced for the electromagnetic calorimeter of the CMS experiment at LHC have been irradiated in a 20 GeV/c proton beam up to fluences of 5.4 E13 p/cm2. The damage recovery in these crystals, stored in the dark at room temperature, has been followed for over a year. Comparative irradiations with 60Co photons have been performed on seven other crystals using a dose rate of 1 kGy/h. The issue whether hadrons cause a specific damage to the scintillation mechanism has been studied through light output measurements on the irradiated crystals using cosmic rays. The correlation between light output changes and light transmission changes is measured to be the same for proton-irradiated crystals and for gamma-irradiated crystals. Thus, within the precision of the measurements and for the explored range of proton fluences, no additional, hadron-specific damage to the scintillation mechanism is observed.Comment: 7 pages, 4 figure

Decomposition of symmetric tensor fields in the presence of a flat contact projective structure

Let $M$ be an odd-dimensional Euclidean space endowed with a contact 1-form $\alpha$. We investigate the space of symmetric contravariant tensor fields on $M$ as a module over the Lie algebra of contact vector fields, i.e. over the Lie subalgebra made up by those vector fields that preserve the contact structure. If we consider symmetric tensor fields with coefficients in tensor densities, the vertical cotangent lift of contact form $\alpha$ is a contact invariant operator. We also extend the classical contact Hamiltonian to the space of symmetric density valued tensor fields. This generalized Hamiltonian operator on the symbol space is invariant with respect to the action of the projective contact algebra $sp(2n+2)$. The preceding invariant operators lead to a decomposition of the symbol space (expect for some critical density weights), which generalizes a splitting proposed by V. Ovsienko

A study of high-energy proton induced damage in Cerium Fluoride in comparison with measurements in Lead Tungstate calorimeter crystals

A Cerium Fluoride crystal produced during early R&D studies for calorimetry at the CERN Large Hadron Collider was exposed to a 24 GeV/c proton fluence Phi_p=(2.78 +- 0.20) x 10EE13 cm-2 and, after one year of measurements tracking its recovery, to a fluence Phi_p=(2.12 +- 0.15) x 10EE14 cm-2. Results on proton-induced damage to the crystal and its spontaneous recovery after both irradiations are presented here, along with some new, complementary data on proton-damage in Lead Tungstate. A comparison with FLUKA Monte Carlo simulation results is performed and a qualitative understanding of high-energy damage mechanism is attempted.Comment: Submitted to Elsevier Science on May 6th, 2010; 11 pages, 8 figure

Thick films of YSZ electrolytes by dip-coating process

Yttria stabilized zirconia (YSZ, 8% Y2O3) thick films were coated on porous Ni-YSZ substrates using the dip-coating process and a suspension with a new formulation. The suspension was obtained by addition of a polymeric matrix in a stable suspension of a commercial YSZ (Tosoh) powders dispersed in an azeotropic MEK-EtOH mixture. The green layers were densified after an optimization of the suspension composition. YSZ Tosoh particles encapsulated by a zirconium alkoxide sol and added with colloidal alkoxide precursor are used to load the suspension. The in situ growth of these colloids increases significantly the layers density after an appropriated heat treatment. The obtained films are continuous, homogeneous and 20 μm thick. Different microstructures are obtained depending on the synthesis parameters of the suspension

A numerical approach to large deviations in continuous-time

We present an algorithm to evaluate the large deviation functions associated to history-dependent observables. Instead of relying on a time discretisation procedure to approximate the dynamics, we provide a direct continuous-time algorithm, valuable for systems with multiple time scales, thus extending the work of Giardin\`a, Kurchan and Peliti (PRL 96, 120603 (2006)). The procedure is supplemented with a thermodynamic-integration scheme, which improves its efficiency. We also show how the method can be used to probe large deviation functions in systems with a dynamical phase transition -- revealed in our context through the appearance of a non-analyticity in the large deviation functions.Comment: Submitted to J. Stat. Mec