Semiclassical approximations for Hamiltonians with operator-valued symbols

We consider the semiclassical limit of quantum systems with a Hamiltonian given by the Weyl quantization of an operator valued symbol. Systems composed of slow and fast degrees of freedom are of this form. Typically a small dimensionless parameter $\varepsilon\ll 1$ controls the separation of time scales and the limit $\varepsilon\to 0$ corresponds to an adiabatic limit, in which the slow and fast degrees of freedom decouple. At the same time $\varepsilon\to 0$ is the semiclassical limit for the slow degrees of freedom. In this paper we show that the $\varepsilon$-dependent classical flow for the slow degrees of freedom first discovered by Littlejohn and Flynn, coming from an \epsi-dependent classical Hamilton function and an $\varepsilon$-dependent symplectic form, has a concrete mathematical and physical meaning: Based on this flow we prove a formula for equilibrium expectations, an Egorov theorem and transport of Wigner functions, thereby approximating properties of the quantum system up to errors of order $\varepsilon^2$. In the context of Bloch electrons formal use of this classical system has triggered considerable progress in solid state physics. Hence we discuss in some detail the application of the general results to the Hofstadter model, which describes a two-dimensional gas of non-interacting electrons in a constant magnetic field in the tight-binding approximation.Comment: Final version to appear in Commun. Math. Phys. Results have been strengthened with only minor changes to the proofs. A section on the Hofstadter model as an application of the general theory was added and the previous section on other applications was remove

Design, construction, and quality tests of the large Al-alloy mandrels for the CMS coil

The Compact Muon Solenoid (CMS) is one of the general-purpose detectors to be provided for the LHC project at CERN. The design field of the CMS superconducting magnet is 4 T, the magnetic length is 12.5 m and the free bore is 6 m. Almost all large indirectly cooled solenoids constructed to date (e.g., Zeus, Aleph, Delphi, Finuda, Babar) comprise Al-alloy mandrels fabricated by welding together plates bent to the correct radius. The external cylinder of CMS will consist of five modules having an inner diameter of 6.8 m, a thickness of 50 mm and an individual length of 2.5 m. It will be manufactured by bending and welding thick plates (75 mm) of the strain hardened aluminum alloy EN AW-5083-H321. The required high geometrical tolerances and mechanical strength (a yield strength of 209 MPa at 4.2 K) impose a critical appraisal of the design, the fabrication techniques, the welding procedures and the quality controls. The thick flanges at both ends of each module will be fabricated as seamless rolled rings, circumferentially welded to the body of the modules. The developed procedures and manufacturing methods will be validated by the construction of a prototype mandrel of full diameter and reduced length (670 mm). (7 refs)

Development and Coil Fabrication Test of the Nb3Sn Dipole Magnet PRESCA2

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Multiple shades of grey: Opening the black box of public sector executives' hybrid role identities

Public sector reforms of recent decades in Europe have promoted managerialism and aimed at introducing private sector thinking and practices. However, with regard to public sector executives' self-understanding, managerial role identities have not replaced bureaucratic ones; rather, components from both paradigms have combined. In this article, we introduce a bi-dimensional approach (attitudes and practices) that allows for different combinations and forms of hybridity. Empirically, we explore the role identities of public sector executives across Europe, building on survey data from over 7,000 top public officials in 19 countries (COCOPS survey). We identify country-level profiles, as well as patterns across countries, and find that administrative traditions can account for these profiles and patterns only to a limited extent. Rather, they have to be complemented by factors such as stability of the institutional environment (indicating lower shares of hybrid combinations) or extent of reform pressures (indicating higher shares of hybrid combinations)

Intercalibration of the barrel electromagnetic calorimeter of the CMS experiment at start-up

Calibration of the relative response of the individual channels of the barrel electromagnetic calorimeter of the CMS detector was accomplished, before installation, with cosmic ray muons and test beams. One fourth of the calorimeter was exposed to a beam of high energy electrons and the relative calibration of the channels, the intercalibration, was found to be reproducible to a precision of about 0.3%. Additionally, data were collected with cosmic rays for the entire ECAL barrel during the commissioning phase. By comparing the intercalibration constants obtained with the electron beam data with those from the cosmic ray data, it is demonstrated that the latter provide an intercalibration precision of 1.5% over most of the barrel ECAL. The best intercalibration precision is expected to come from the analysis of events collected in situ during the LHC operation. Using data collected with both electrons and pion beams, several aspects of the intercalibration procedures based on electrons or neutral pions were investigated

CMS physics technical design report : Addendum on high density QCD with heavy ions

Peer reviewe

Energy Resolution Performance of the CMS Electromagnetic Calorimeter

The energy resolution performance of the CMS lead tungstate crystal electromagnetic calorimeter is presented. Measurements were made with an electron beam using a fully equipped supermodule of the calorimeter barrel. Results are given both for electrons incident on the centre of crystals and for electrons distributed uniformly over the calorimeter surface. The electron energy is reconstructed in matrices of 3 times 3 or 5 times 5 crystals centred on the crystal containing the maximum energy. Corrections for variations in the shower containment are applied in the case of uniform incidence. The resolution measured is consistent with the design goals

Longitudinal and Transverse Dimensional Changes During Heat Treatment of the Nb3_3Sn Cables for the Graded Research Racetrack Dipole Demonstrator (R2D2)

The Research Racetrack Dipole Demonstrator (R2D2) is a Nb$_3$Sn graded magnet developed in the framework of the CEA-CERN collaboration with the goal to assess key technologies for future high field accelerator magnets. This demonstrator magnet features two 1.7 m long racetrack coils, designed in the graded configuration needed for compact and efficient high field magnets. Each coil is made of two different Nb$_3$Sn cables wound around each other and submitted together to the high temperature heat treatment needed for Nb$_3$Sn compound formation. The experience on Nb$_3$Sn coils has taught us that the management of the deformations undergone by the Nb$_3$Sn cable during its formation must be a priority in the definition and the dimensioning of the tools and the manufacturing processes of the coils. This paper reports the results of the test campaigns carried out at CEA Saclay to study the behavior of R2D2 cables during heat treatment. The first campaign consisted of reduced-coils made of a few turns of each cable, with representative lengths. For each coil, the winding is performed with gaps in the components, and the gaps are measured before and after the heat treatment to quantify the coil length variations. A second campaign consisted in measuring the thickness variations of cable stacks in various configurations. The results allowed validating the choices made for the final R2D2 coils and heat treatment tooling to manage the longitudinal contraction and the transverse expansion