Matrix representation of the time operator

In quantum mechanics the time operator $\Theta$ satisfies the commutation relation $[\Theta,H]=i$, and thus it may be thought of as being canonically conjugate to the Hamiltonian $H$. The time operator associated with a given Hamiltonian $H$ is not unique because one can replace $\Theta$ by $\Theta+ \Theta_{\rm hom}$, where $\Theta_{\rm hom}$ satisfies the homogeneous condition $[\Theta_{\rm hom},H]=0$. To study this nonuniqueness the matrix elements of $\Theta$ for the harmonic-oscillator Hamiltonian are calculated in the eigenstate basis. This calculation requires the summation of divergent series, and the summation is accomplished by using zeta-summation techniques. It is shown that by including appropriate homogeneous contributions, the matrix elements of $\Theta$ simplify dramatically. However, it is still not clear whether there is an optimally simple representation of the time operator.Comment: 13 pages, 3 figure

Total knee arthroplasty in valgus knee

SummaryTotal knee arthroplasty (TKA) in valgus knee has the reputation of being more difficult than in well aligned or varus knee, and there is no management consensus. Results on a continuous series of 100 TKAs on valgus knee were compared to the literature data, to define surgical strategy adapted to the various types of valgus knee

The Level-0 Muon Trigger for the LHCb Experiment

A very compact architecture has been developed for the first level Muon Trigger of the LHCb experiment that processes 40 millions of proton-proton collisions per second. For each collision, it receives 3.2 kBytes of data and it finds straight tracks within a 1.2 microseconds latency. The trigger implementation is massively parallel, pipelined and fully synchronous with the LHC clock. It relies on 248 high density Field Programable Gate arrays and on the massive use of multigigabit serial link transceivers embedded inside FPGAs.Comment: 33 pages, 16 figures, submitted to NIM

Adiabatic passage and ensemble control of quantum systems

This paper considers population transfer between eigenstates of a finite quantum ladder controlled by a classical electric field. Using an appropriate change of variables, we show that this setting can be set in the framework of adiabatic passage, which is known to facilitate ensemble control of quantum systems. Building on this insight, we present a mathematical proof of robustness for a control protocol -- chirped pulse -- practiced by experimentalists to drive an ensemble of quantum systems from the ground state to the most excited state. We then propose new adiabatic control protocols using a single chirped and amplitude shaped pulse, to robustly perform any permutation of eigenstate populations, on an ensemble of systems with badly known coupling strengths. Such adiabatic control protocols are illustrated by simulations achieving all 24 permutations for a 4-level ladder

The deep-sea hub of the ANTARES neutrino telescope

The ANTARES neutrino telescope, currently under construction at 2500 m depth off the French Mediterranean coast, will contain 12 detection lines, powered and read out through a deep-sea junction box (JB) hub. Electrical energy from the shore station is distributed through a transformer with multiple secondary windings and a plugboard with 16 deep sea-mateable electro-optic connectors. Connections are made to the JB outputs using manned or remotely operated submersible vehicles. The triply redundant power management and slow control system is based on two identical AC-powered systems, communicating with the shore through 160 Mb/s fibre G-links and a third battery-powered system using a slower link. We describe the power and slow control systems of the underwater hub

E2-quasi-exact solvability for non-Hermitian models

We propose the notion of E2-quasi-exact solvability and apply this idea to find explicit solutions to the eigenvalue problem for a non-Hermitian Hamiltonian system depending on two parameters. The model considered reduces to the complex Mathieu Hamiltonian in a double scaling limit, which enables us to compute the exceptional points in the energy spectrum of the latter as a limiting process of the zeros for some algebraic equations. The coefficient functions in the quasi-exact eigenfunctions are univariate polynomials in the energy obeying a three-term recurrence relation. The latter property guarantees the existence of a linear functional such that the polynomials become orthogonal. The polynomials are shown to factorize for all levels above the quantization condition leading to vanishing norms rendering them to be weakly orthogonal. In two concrete examples we compute the explicit expressions for the Stieltjes measure

The ANTARES Optical Beacon System

ANTARES is a neutrino telescope being deployed in the Mediterranean Sea. It consists of a three dimensional array of photomultiplier tubes that can detect the Cherenkov light induced by charged particles produced in the interactions of neutrinos with the surrounding medium. High angular resolution can be achieved, in particular when a muon is produced, provided that the Cherenkov photons are detected with sufficient timing precision. Considerations of the intrinsic time uncertainties stemming from the transit time spread in the photomultiplier tubes and the mechanism of transmission of light in sea water lead to the conclusion that a relative time accuracy of the order of 0.5 ns is desirable. Accordingly, different time calibration systems have been developed for the ANTARES telescope. In this article, a system based on Optical Beacons, a set of external and well-controlled pulsed light sources located throughout the detector, is described. This calibration system takes into account the optical properties of sea water, which is used as the detection volume of the ANTARES telescope. The design, tests, construction and first results of the two types of beacons, LED and laser-based, are presented.Comment: 21 pages, 18 figures, submitted to Nucl. Instr. and Meth. Phys. Res.

The impact of Stieltjes' work on continued fractions and orthogonal polynomials

Stieltjes' work on continued fractions and the orthogonal polynomials related to continued fraction expansions is summarized and an attempt is made to describe the influence of Stieltjes' ideas and work in research done after his death, with an emphasis on the theory of orthogonal polynomials

Cadaveric and three-dimensional computed tomography study of the morphology of the scapula with reference to reversed shoulder prosthesis

<p>Abstract</p> <p>Purpose</p> <p>The purpose of this study is to analyze the morphology of the scapula with reference to the glenoid component implantation in reversed shoulder prosthesis, in order to improve primary fixation of the component.</p> <p>Methods</p> <p>Seventy-three 3-dimensional computed tomography of the scapula and 108 scapular dry specimens were analyzed to determine the anterior and posterior length of the glenoid neck, the angle between the glenoid surface and the upper posterior column of the scapula and the angle between the major craneo-caudal glenoid axis and the base of the coracoid process and the upper posterior column.</p> <p>Results</p> <p>The anterior and posterior length of glenoid neck was classified into two groups named "short-neck" and "long-neck" with significant differences between them. The angle between the glenoid surface and the upper posterior column of the scapula was also classified into two different types: type I (mean 50°–52°) and type II (mean 62,50°–64°), with significant differences between them (p < 0,001). The angle between the major craneo-caudal glenoid axis and the base of the coracoid process averaged 18,25° while the angle with the upper posterior column of the scapula averaged 8°.</p> <p>Conclusion</p> <p>Scapular morphological variability advices for individual adjustments of glenoid component implantation in reversed total shoulder prosthesis. Three-dimensional computed tomography of the scapula constitutes an important tool when planning reversed prostheses implantation.</p