Surprises in the suddenly-expanded infinite well

I study the time-evolution of a particle prepared in the ground state of an infinite well after the latter is suddenly expanded. It turns out that the probability density $|\Psi(x, t)|^{2}$ shows up quite a surprising behaviour: for definite times, {\it plateaux} appear for which $|\Psi(x, t)|^{2}$ is constant on finite intervals for $x$. Elements of theoretical explanation are given by analyzing the singular component of the second derivative $\partial_{xx}\Psi(x, t)$. Analytical closed expressions are obtained for some specific times, which easily allow to show that, at these times, the density organizes itself into regular patterns provided the size of the box in large enough; more, above some critical time-dependent size, the density patterns are independent of the expansion parameter. It is seen how the density at these times simply results from a construction game with definite rules acting on the pieces of the initial density.Comment: 24 pages, 14 figure

Discrete Spectra of Semirelativistic Hamiltonians

We review various attempts to localize the discrete spectra of semirelativistic Hamiltonians of the form H = \beta \sqrt{m^2 + p^2} + V(r) (w.l.o.g. in three spatial dimensions) as entering, for instance, in the spinless Salpeter equation. Every Hamiltonian in this class of operators consists of the relativistic kinetic energy \beta \sqrt{m^2 + p^2} (where \beta > 0 allows for the possibility of more than one particles of mass m) and a spherically symmetric attractive potential V(r), r = |x|. In general, accurate eigenvalues of a nonlocal Hamiltonian operator can only be found by the use of a numerical approximation procedure. Our main emphasis, however, is on the derivation of rigorous semi-analytical expressions for both upper and lower bounds to the energy levels of such operators. We compare the bounds obtained within different approaches and present relationships existing between the bounds.Comment: 21 pages, 3 figure

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

Unravelling quantum carpets: a travelling wave approach

Quantum carpets are generic spacetime patterns formed in the probability distributions P(x,t) of one-dimensional quantum particles, first discovered in 1995. For the case of an infinite square well potential, these patterns are shown to have a detailed quantitative explanation in terms of a travelling-wave decomposition of P(x,t). Each wave directly yields the time-averaged structure of P(x,t) along the (quantised)spacetime direction in which the wave propagates. The decomposition leads to new predictions of locations, widths depths and shapes of carpet structures, and results are also applicable to light diffracted by a periodic grating and to the quantum rotator. A simple connection between the waves and the Wigner function of the initial state of the particle is demonstrated, and some results for more general potentials are given.Comment: Latex, 26 pages + 6 figures, submitted to J. Phys. A (connections with prior literature clarified

TB6: Importance of Entomogenous Fungi in Controlling Aphids on Potatoes in Northeastern Maine

This publication reports on field studies of aphid biology and of associated ecological factors made near Presque Isle, Maine. Results showed that, among the biological agents affecting aphid population trends from 1952 through 1962, entomogenous fungi were outstanding in reducing the size of populations of the potato aphid developing on potatoes treated with fungicides but not with insecticides. The potato aphid was most affected by fungi and the buckthorn aphid least affected by them. The green peach and foxglove aphids were intermediate. Predators exerted a noticeably adverse effect upon aphid population trends in two of the 11 years.https://digitalcommons.library.umaine.edu/aes_techbulletin/1188/thumbnail.jp

Vertex Corrections on the Anomalous Hall Effect in Spin-polarized Two-dimensional Electron Gases with Rashba Spin-orbit Interaction

We study the effect of disorder on the intrinsic anomalous Hall (AH) conductivity in a spin-polarized two-dimensional electron gas with a Rashba-type spin-orbit interaction. We find that AH conductivity vanishes unless the lifetime is spin-dependent, similar to the spin Hall (SH) conductivity in the non-magnetic system. In addition, we find that the SH conductivity does not vanish in the presence of magnetic scatterers. We show that the SH conductivity can be controlled by changing the amount of the magnetic impurities.Comment: Tex file only, no figure

A Consistent Dark Matter Interpretation For CoGeNT and DAMA/LIBRA

In this paper, we study the recent excess of low energy events observed by the CoGeNT collaboration and the annual modulation reported by the DAMA/LIBRA collaboration, and discuss whether these signals could both be the result of the same elastically scattering dark matter particle. We find that, without channeling but when taking into account uncertainties in the relevant quenching factors, a dark matter candidate with a mass of approximately ~7.0 GeV and a cross section with nucleons of sigma_{DM-N} ~2x10^-4 pb (2x10^-40 cm^2) could account for both of these observations. We also comment on the events recently observed in the oxygen band of the CRESST experiment and point out that these could potentially be explained by such a particle. Lastly, we compare the region of parameter space favored by DAMA/LIBRA and CoGeNT to the constraints from XENON 10, XENON 100, and CDMS (Si) and find that these experiments cannot at this time rule out a dark matter interpretation of these signals.Comment: 8 pages, 6 figure

Addiction, neuroscience and ethics

Neuroscience models have much to offer the field of addiction, but they will be self-defeating if they lead to severe restrictions on the type of neuroscience research that can conducted in future. A major challenge for the addiction field is to integrate the insights that neuroscience research has provided on drug use and addiction with those provided about drug use and addiction by clinical, epidemiological, sociological and economic research. The challenge is (1) to develop theories of addiction that take seriously the neurobiological bases for drug effects and addictive phenomena; (2) without depicting addicts as automatons whose behaviour is under the control of the drugs acting on the receptors sites in their brains; and (3) while recognizing the opportunities for individual decision, interpersonal influence and social policy to affect the drug use and the behaviour of drug-dependent people

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