119346040
Separation of variables and the XXZ Gaudin magnet
In this work we generalise previous results connecting (rational) Gaudin magnet models and classical separation of variables. It is shown that the connection persists for the case of linear r-matrix algebra which corresponds to the trigonometric 4 × 4 r-matrix (of the XXZ type). We comment also on the corresponding problem for the elliptic (XYZ) r-matrix. A prescription for obtaining integrable systems associated with multiple poles of an L-operator is given.
122430224
Lie theory and separation of variables. 7. The harmonic oscillator in elliptic coordinates and Ince polynomials
As a continuation of Paper 6 we study the separable basis eigenfunctions and their relationships for the harmonic oscillator Hamiltonian in two space variables with special emphasis on products of Ince polynomials, the eigenfunctions obtained when one separates variables in elliptic coordinates. The overlaps connecting this basis to the polar and Cartesian coordinate bases are obtained by computing in a simpler Bargmann Hilbert space model of the problem. We also show that Ince polynomials are intimately connected with the representation theory of SU (2), the group responsible for the eigenvalue degeneracy of the oscillator Hamiltonian.
119430316
Complete sets of commuting operators and O (3) scalars in the enveloping algebra of SU (3)
We consider the ``missing label'' problem for basis vectors of SU(3) representations in a basis corresponding to the group reduction SU(3)⊃O(3)⊃O(2). We prove that only two independent O (3) scalars exist in the enveloping algebra of S U (3), in addition to the obvious ones, namely the angular momentum L2 and the two SU(3) Casimir operators C(2) and C(3). Any one of these two operators (of third and fourth order in the generators) can be added to C(2), C(3), L2, and L3 to form a complete set of commuting operators. The eigenvalues of the third and fourth order scalars X(3) and X(4) are calculated analytically or numerically for many cases of physical interest. The methods developed in this article can be used to resolve a missing label problem for any semisimple group G, when reduced to any semisimple subgroup H.
120822220
Separation of variables in Einstein spaces. I. Two ignorable and one null coordinate
Computes and classifies all Einstein spaces and their corresponding coordinate systems such that the Hamilton-Jacobi equation admits a separation of variables with two ignorable and one essential null coordinates. The authors find that all such spaces correspond to plane-fronted gravitational waves of Petrov type N. They also give necessary conditions which a general space-time must have in order to admit coordinates of the type studied. Furthermore, the integrability conditions for Helmholtz (Schrodinger) separability are completely solved.
17212560
Superintegrability on the two-dimensional hyperboloid. II
In this work we examine the basis functions for classical and quantum mechanical systems on the two-dimensional hyperboloid that admit separation of variables in at least two coordinate systems. We present all of these cases from a unified point of view. In particular, all of the special functions that arise via variable separation have their essential features expressed in terms of their zeros. The principal new results are the details of the polynomial bases for each of the nonsubgroup bases, not just the subgroup spherical coordinate cases, and the details of the structure of the quadratic symmetry algebras.
120152328
Lie theory and separation of variables. 11. The EPD equation
We show that the Euler–Poisson–Darboux equation {∂tt−∂rr−[(2m+1)/r]∂r}Θ=0 separates in exactly nine coordinate systems corresponding to nine orbits of symmetric second‐order operators in the enveloping algebra of SL(2,R), the symmetry group of this equation. We employ techniques developed in earlier papers from this series and use the representation theory of SL(2,R) to derive special function identities relating the separated solutions. We also show that the complex EPD equation separates in exactly five coordinate systems corresponding to five orbits of symmetric second‐order operators in the enveloping algebra of SL(2,C).
110729769
ATLAS pixel detector electronics and sensors
The silicon pixel tracking system for the ATLAS experiment at the Large Hadron Collider is described and the performance requirements are summarized. Detailed descriptions of the pixel detector electronics and the silicon sensors are given. The design, fabrication, assembly and performance of the pixel detector modules are presented. Data obtained from test beams as well as studies using cosmic rays are also discussed.
1036381
Measurement of neutrino oscillations with the MINOS detectors in the NuMI beam.
This Letter reports new results from the MINOS experiment based on a two-year exposure to muon neutrinos from the Fermilab NuMI beam. Our data are consistent with quantum-mechanical oscillations of neutrino flavor with mass splitting |Deltam2| = (2.43+/-0.13) x 10(-3) eV2 (68% C.L.) and mixing angle sin2(2theta) > 0.90 (90% C.L.). Our data disfavor two alternative explanations for the disappearance of neutrinos in flight: namely, neutrino decays into lighter particles and quantum decoherence of neutrinos, at the 3.7 and 5.7 standard-deviation levels, respectively.
118841620
Cosmic ray events in Soudan 2
The Soudan 2 detector is located at a depth of 2090 meters-water equivalent (mwe). About 2 million muon events have been recorded. Here we report on our plans to analyze them for comparison with expectations from atmospheric cosmic ray models. Plans and capabilities to analyze multiple muons and monopoles are also discussed. 3 refs., 5 figs.
118474942
R&D Argon Detector at Ash River (RADAR) - Letter of Intent
In the RADAR project described in this Letter of Intent, we propose to deploy a 6 kton liquid argon TPC at the NOvA Far Detector building in Ash River, Minnesota, and expose it to the NuMI beam during NOvA running. It will significantly add to the physics capabilities of the NOvA program while providing LBNE with an R&D program based on full-scale TPC module assemblies. RADAR offers an excellent opportunity to improve the full Homestake LBNE project in physics reach, timeline, costs, and fostering international partnership. The anticipated duration of the project's construction is 5 years, with running happening between 2018 and 2023.
122916605
The SOUDAN 2 detector: the operation and performance of the tracking calorimeter modules
SOUDAN 2 is a 960-ton tracking calorimeter which has been constructed to search for nucleon decay and other phenomena. The full detector consists of 224 calorimeter modules each weighing 4.3 tons. The modules consist of finely segmented iron instrumented with 1 m long drift tubes of 15 mm internal diameter. The tubes enable three spatial coordinates and dEdx to be recorded for charged particles traversing the tubes. The spatial resolution is 0.38 cm in the x−y plane and 0.65 cm in the z, or drift, direction. The operation and performance of the modules are discussed.