76,919 research outputs found

### Classical mappings of the symplectic model and their application to the theory of large-amplitude collective motion

We study the algebra Sp(n,R) of the symplectic model, in particular for the
cases n=1,2,3, in a new way. Starting from the Poisson-bracket realization we
derive a set of partial differential equations for the generators as functions
of classical canonical variables. We obtain a solution to these equations that
represents the classical limit of a boson mapping of the algebra. The
relationship to the collective dynamics is formulated as a theorem that
associates the mapping with an exact solution of the time-dependent Hartree
approximation. This solution determines a decoupled classical symplectic
manifold, thus satisfying the criteria that define an exactly solvable model in
the theory of large amplitude collective motion. The models thus obtained also
provide a test of methods for constructing an approximately decoupled manifold
in fully realistic cases. We show that an algorithm developed in one of our
earlier works reproduces the main results of the theorem.Comment: 23 pages, LaTeX using REVTeX 3.

### Exact relativistic treatment of stationary counter-rotating dust disks III. Physical Properties

This is the third in a series of papers on the construction of explicit
solutions to the stationary axisymmetric Einstein equations which can be
interpreted as counter-rotating disks of dust. We discuss the physical
properties of a class of solutions to the Einstein equations for disks with
constant angular velocity and constant relative density which was constructed
in the first part. The metric for these spacetimes is given in terms of theta
functions on a Riemann surface of genus 2. It is parameterized by two physical
parameters, the central redshift and the relative density of the two
counter-rotating streams in the disk. We discuss the dependence of the metric
on these parameters using a combination of analytical and numerical methods.
Interesting limiting cases are the Maclaurin disk in the Newtonian limit, the
static limit which gives a solution of the Morgan and Morgan class and the
limit of a disk without counter-rotation. We study the mass and the angular
momentum of the spacetime. At the disk we discuss the energy-momentum tensor,
i.e. the angular velocities of the dust streams and the energy density of the
disk. The solutions have ergospheres in strongly relativistic situations. The
ultrarelativistic limit of the solution in which the central redshift diverges
is discussed in detail: In the case of two counter-rotating dust components in
the disk, the solutions describe a disk with diverging central density but
finite mass. In the case of a disk made up of one component, the exterior of
the disks can be interpreted as the extreme Kerr solution.Comment: 30 pages, 20 figures; to appear in Phys. Rev.

### Novel multipurpose timer for laboratories

Multipurpose digital delay timer simultaneously controls both a buffer pump and a fraction-collector. Timing and control may be in 30-second increments for up to 15 hours. Use of glassware and scintillation vials make it economical

### Asymptotic Inverse Problem for Almost-Periodically Perturbed Quantum Harmonic Oscillator

Consider quantum harmonic oscillator, perturbed by an even almost-periodic
complex-valued potential with bounded derivative and primitive. Suppose that we
know the first correction to the spectral asymptotics
$\{\Delta\mu_n\}_{n=0}^\infty$ ($\Delta\mu_n=\mu_n-\mu_n^0+o(n^{-1/4})$, where
$\mu_n^0$ and $\mu_n$ is the spectrum of the unperturbed and the perturbed
operators, respectively). We obtain the formula that recovers the frequencies
and the Fourier coefficients of the perturbation.Comment: 6 page

### Tritiated alumina serves as reagent for self-labeling analysis

Tritiated alumina, prepared by exchange of the surface hydroxyl groups with tritiated water, is a suitable reagent for exchange-labeling of specific compounds in low concentrations prior to chromatographic analysis. In a chromatographic column, it detects and measures submicrogram quantities of material

### Interplay of Fulde-Ferrell-Larkin-Ovchinnikov and Vortex states in two-dimensional Superconductors

Clean superconductors with weakly coupled conducting planes have been
suggested as promising candidates for observing the
Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state. We consider here a layered
superconductor in a magnetic field of arbitrary orientation with respect to the
conducting plane. In this case there is competition of spin-pair-breaking and
orbital-pair-breaking effects. In previous work, phase boundaries characterized
by Landau quantum numbers n > 0 have been predicted. Here, we calculate the
actual structure of the stable states below Hc2 by minimizing the free energy.
We find several new order parameter structures differing from both the
traditional Abrikosov and FFLO solutions. Some interesting unsolved questions
appear in the limit of large n.Comment: 13 pages, 3 figure

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