Eigenvalue bounds for a class of singular potentials in N dimensions

The eigenvalue bounds obtained earlier [J. Phys. A: Math. Gen. 31 (1998) 963] for smooth transformations of the form V(x) = g(x^2) + f(1/x^2) are extended to N-dimensions. In particular a simple formula is derived which bounds the eigenvalues for the spiked harmonic oscillator potential V(x) = x^2 + lambda/x^alpha, alpha > 0, lambda > 0, and is valid for all discrete eigenvalues, arbitrary angular momentum ell, and spatial dimension N.Comment: 10 pages (plain tex with 2 ps figures). J.Phys.A:Math.Gen.(In Press

Effect of inversion asymmetry on the intrinsic anomalous Hall effect in ferromagnetic (Ga,Mn)As

The relativistic nature of the electron motion underlies the intrinsic part of the anomalous Hall effect, believed to dominate in ferromagnetic (Ga,Mn)As. In this paper, we concentrate on the crystal band structure as an important facet to the description of this phenomenon. Using different k.p and tight-binding computational schemes, we capture the strong effect of the bulk inversion asymmetry on the Berry curvature and the anomalous Hall conductivity. At the same time, we find it not to affect other important characteristics of (Ga,Mn)As, namely the Curie temperature and uniaxial anisotropy fields. Our results extend the established theories of the anomalous Hall effect in ferromagnetic semiconductors and shed new light on its puzzling nature

Global three-dimensional flow of a neutron superfluid in a spherical shell in a neutron star

We integrate for the first time the hydrodynamic Hall-Vinen-Bekarevich-Khalatnikov equations of motion of a $^{1}S_{0}$-paired neutron superfluid in a rotating spherical shell, using a pseudospectral collocation algorithm coupled with a time-split fractional scheme. Numerical instabilities are smoothed by spectral filtering. Three numerical experiments are conducted, with the following results. (i) When the inner and outer spheres are put into steady differential rotation, the viscous torque exerted on the spheres oscillates quasiperiodically and persistently (after an initial transient). The fractional oscillation amplitude ($\sim 10^{-2}$) increases with the angular shear and decreases with the gap width. (ii) When the outer sphere is accelerated impulsively after an interval of steady differential rotation, the torque increases suddenly, relaxes exponentially, then oscillates persistently as in (i). The relaxation time-scale is determined principally by the angular velocity jump, whereas the oscillation amplitude is determined principally by the gap width. (iii) When the mutual friction force changes suddenly from Hall-Vinen to Gorter-Mellink form, as happens when a rectilinear array of quantized Feynman-Onsager vortices is destabilized by a counterflow to form a reconnecting vortex tangle, the relaxation time-scale is reduced by a factor of $\sim 3$ compared to (ii), and the system reaches a stationary state where the torque oscillates with fractional amplitude $\sim 10^{-3}$ about a constant mean value. Preliminary scalings are computed for observable quantities like angular velocity and acceleration as functions of Reynolds number, angular shear, and gap width. The results are applied to the timing irregularities (e.g., glitches and timing noise) observed in radio pulsars.Comment: 6 figures, 23 pages. Accepted for publication in Astrophysical Journa

Gravitational radiation from nonaxisymmetric spherical Couette flow in a neutron star

The gravitational wave signal generated by global, nonaxisymmetric shear flows in a neutron star is calculated numerically by integrating the incompressible Navier--Stokes equation in a spherical, differentially rotating shell. At Reynolds numbers \Rey \gsim 3 \times 10^{3}, the laminar Stokes flow is unstable and helical, oscillating Taylor--G\"ortler vortices develop. The gravitational wave strain generated by the resulting kinetic-energy fluctuations is computed in both $+$ and $\times$ polarizations as a function of time. It is found that the signal-to-noise ratio for a coherent, $10^{8}$-{\rm s} integration with LIGO II scales as $6.5 (\Omega_*/10^{4} {\rm rad} {\rm s}^{-1})^{7/2}$ for a star at 1 {\rm kpc} with angular velocity $\Omega_*$. This should be regarded as a lower limit: it excludes pressure fluctuations, herringbone flows, Stuart vortices, and fully developed turbulence (for \Rey \gsim 10^{6}).Comment: (1) School of Physics, University of Melbourne, Parkville, VIC 3010, Australia. (2) Departamento de Fisica, Escuela de Ciencias,Universidad de Oriente, Cumana, Venezuela, (3) Department of Mechanical Engineering, University of Melbourne, Parkville, VIC 3010, Australia. Accepted for publication in The Astrophysical Journal Letter

Variational analysis for a generalized spiked harmonic oscillator

A variational analysis is presented for the generalized spiked harmonic oscillator Hamiltonian operator H, where H = -(d/dx)^2 + Bx^2+ A/x^2 + lambda/x^alpha, and alpha and lambda are real positive parameters. The formalism makes use of a basis provided by exact solutions of Schroedinger's equation for the Gol'dman and Krivchenkov Hamiltonian (alpha = 2), and the corresponding matrix elements that were previously found. For all the discrete eigenvalues the method provides bounds which improve as the dimension of the basis set is increased. Extension to the N-dimensional case in arbitrary angular-momentum subspaces is also presented. By minimizing over the free parameter A, we are able to reduce substantially the number of basis functions needed for a given accuracy.Comment: 15 pages, 1 figur

Semiclassical energy formulas for power-law and log potentials in quantum mechanics

We study a single particle which obeys non-relativistic quantum mechanics in R^N and has Hamiltonian H = -Delta + V(r), where V(r) = sgn(q)r^q. If N \geq 2, then q > -2, and if N = 1, then q > -1. The discrete eigenvalues E_{n\ell} may be represented exactly by the semiclassical expression E_{n\ell}(q) = min_{r>0}\{P_{n\ell}(q)^2/r^2+ V(r)}. The case q = 0 corresponds to V(r) = ln(r). By writing one power as a smooth transformation of another, and using envelope theory, it has earlier been proved that the P_{n\ell}(q) functions are monotone increasing. Recent refinements to the comparison theorem of QM in which comparison potentials can cross over, allow us to prove for n = 1 that Q(q)=Z(q)P(q) is monotone increasing, even though the factor Z(q)=(1+q/N)^{1/q} is monotone decreasing. Thus P(q) cannot increase too slowly. This result yields some sharper estimates for power-potential eigenvlaues at the bottom of each angular-momentum subspace.Comment: 20 pages, 5 figure

Cosmological Constraints on Dissipative Models of Inflation

(Abridged) We study dissipative inflation in the regime where the dissipative term takes a specific form, \Gamma=\Gamma(\phi), analyzing two models in the weak and strong dissipative regimes with a SUSY breaking potential. After developing intuition about the predictions from these models through analytic approximations, we compute the predicted cosmological observables through full numerical evolution of the equations of motion, relating the mass scale and scale of dissipation to the characteristic amplitude and shape of the primordial power spectrum. We then use Markov Chain Monte Carlo techniques to constrain a subset of the models with cosmological data from the cosmic microwave background (WMAP three-year data) and large scale structure (SDSS Luminous Red Galaxy power spectrum). We find that the posterior distributions of the dissipative parameters are highly non-Gaussian and their allowed ranges agree well with the expectations obtained using analytic approximations. In the weak regime, only the mass scale is tightly constrained; conversely, in the strong regime, only the dissipative coefficient is tightly constrained. A lower limit is seen on the inflation scale: a sub-Planckian inflaton is disfavoured by the data. In both weak and strong regimes, we reconstruct the limits on the primordial power spectrum and show that these models prefer a {\it red} spectrum, with no significant running of the index. We calculate the reheat temperature and show that the gravitino problem can be overcome with large dissipation, which in turn leads to large levels of non-Gaussianity: if dissipative inflation is to evade the gravitino problem, the predicted level of non-Gaussianity might be seen by the Planck satellite.Comment: 14 pages, 9 figures, Accepted by JCAP without text changes, References adde

Measurements in SUGRA Models with Large tan beta at LHC

We present an example of a scenario of particle production and decay in supersymmetry models in which the supersymmetry breaking is transmitted to the observable world via gravitational interactions. The case is chosen so that there is a large production of tau leptons in the final state. It is characteristic of large tan beta in that decays into muons and electrons may be suppressed. It is shown that hadronic tau decays can be used to reconstruct final states.Comment: 15 pages, 12 figure