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.
15381990
Superintegrability and higher order integrals for quantum systems
We refine a method for finding a canonical form of symmetry operators of arbitrary order for the Schrodinger eigenvalue equation HΨ ≡ (Δ2 + V)Ψ = EΨ on any 2D Riemannian manifold, real or complex, that admits a separation of variables in some orthogonal coordinate system. The flat space equations with potentials V = α(x + iy)k − 1/(x − iy)k + 1 in Cartesian coordinates, and V = αr2 + β/r2cos 2kθ + γ/r2sin 2kθ (the Tremblay, Turbiner and Winternitz system) in polar coordinates, have each been shown to be classically superintegrable for all rational numbers k. We apply the canonical operator method to give a constructive proof that each of these systems is also quantum superintegrable for all rational k. We develop the classical analog of the quantum canonical form for a symmetry. It is clear that our methods will generalize to other Hamiltonian systems.
11831934
Infinite order symmetries for two-dimensional separable Schrödinger equations
W. MILLER †, E. KALNINS ‡ and G. POGOSYAN § † School of Mathematics, University of Minnesota, Minneapolis, Minnesota, 55455, U.S.A. E-mail: miller@ima.umn.edu ‡ Department of Mathematics, University of Waikato, Hamilton, New Zealand E-mail: e.kalnins@waikato.ac.nz § Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, 14980 Dubna, Moscow Region, Russia E-mail: pogosyan@thsun1.jinr.dubna.su
123571163
A classification of second‐order raising operators for Hamiltonians in two variables
We develop a group theoretic method based on results of Winternitz et al. to compute and classify all first‐ and second‐order raising and lowering operators admitted by Hamiltonians of the form H¯=−(1/2)Δ2+V(x,y). The key to our results, which generalize to higher dimensions, is a proof that H¯ admits a second‐order raising operator only if the Schrodinger equation separates in Cartesian, polar, or elliptic coordinates.
55017968
Series solutions for the Dirac equation in Kerr-Newman space-time
The Dirac equation is solved for an electron in a Kerr–Newman geometry using an adaptation of the procedure of Chandrasekhar. The corresponding eigenfunctions obtained can be represented as series of Jacobi polynomials. The spectrum of eigenvalues can be calculated using continued fraction techniques. Representations for the eigenvalues and eigenfunctions are obtained for various ranges of the parameters appearing in the Kerr–Newman metric. Some comments concerning the bag model of nucleons are made.
36369065
Comparisons of annual modulations in MINOS with the event rate modulation in CoGeNT
The CoGeNT Collaboration has recently published results from a fifteen month data set which indicate an annual modulation in the event rate similar to what is expected from weakly interacting massive particle interactions. It has been suggested that the CoGeNT modulation may actually be caused by other annually modulating phenomena, specifically the flux of atmospheric muons underground or the radon level in the laboratory. We have compared the phase of the CoGeNT data modulation to that of the concurrent atmospheric muon and radon data collected by the MINOS experiment which occupies an adjacent experimental hall in the Soudan Underground Laboratory. The results presented are obtained by performing a shape-free χ^2 data-to-data comparison and from a simultaneous fit of the MINOS and CoGeNT data to phase-shifted sinusoidal functions. Both tests indicate that the phase of the CoGeNT modulation is inconsistent with the phases of the MINOS muon and radon modulations at the 3.0σ level.
6943412
Active to sterile neutrino mixing limits from neutral-current interactions in MINOS.
Results are reported from a search for active to sterile neutrino oscillations in the MINOS long-baseline experiment, based on the observation of neutral-current neutrino interactions, from an exposure to the NuMI neutrino beam of 7.07×10(20) protons on target. A total of 802 neutral-current event candidates is observed in the Far Detector, compared to an expected number of 754 ± 28(stat) ± 37(syst) for oscillations among three active flavors. The fraction f(s) of disappearing ν(μ) that may transition to ν(s) is found to be less than 22% at the 90% C.L.
17785120
The silicon tracker of the beam test engineering model of the GLAST large-area telescope
The silicon tracker for the engineering model of the GLAST Large Area Telescope(LAT) has at least two unique features: it employs self triggering readout electronics, dissipating less than 200 mu-W per channel and to date represents the largest surface of silicon microstrip detectors assembled in a tracker (2.7 m{sup 2}). It demonstrates the feasibility of employing this technology for satellite based experiments, in which low power consumption, large effective areas and high reliability are required. This note describes the construction of this silicon tracker, which was installed in a beam test of positrons, hadrons and tagged photons at SLAC in December of 1999 and January of 2000.
2264842
Measurement of the neutrino mass splitting and flavor mixing by MINOS.
Measurements of neutrino oscillations using the disappearance of muon neutrinos from the Fermilab NuMI neutrino beam as observed by the two MINOS detectors are reported. New analysis methods have been applied to an enlarged data sample from an exposure of 7.25×10(20) protons on target. A fit to neutrino oscillations yields values of |Δm(2)|=(2.32(-0.08)(+0.12))×10(-3) eV(2) for the atmospheric mass splitting and sin(2)(2θ)>0.90 (90% C.L.) for the mixing angle. Pure neutrino decay and quantum decoherence hypotheses are excluded at 7 and 9 standard deviations, respectively.
16147937
New constraints on muon-neutrino to electron-neutrino transitions in MINOS
This paper reports results from a search for ν_μ → ν_e transitions by the MINOS experiment based on a 7×10^(20) protons-on-target exposure. Our observation of 54 candidate ν_e events in the far detector with a background of 49.1±7.0(stat)±2.7(syst) events predicted by the measurements in the near detector requires 2sin^2(2θ_(13))sin^2θ_(23)<0.12(0.20) at the 90% C.L. for the normal (inverted) mass hierarchy at δ_(CP)=0. The experiment sets the tightest limits to date on the value of θ_(13) for nearly all values of δ_(CP) for the normal neutrino mass hierarchy and maximal sin^2(2θ_(23)).