31,195 research outputs found
Coherent states and the quantization of 1+1-dimensional Yang-Mills theory
This paper discusses the canonical quantization of 1+1-dimensional Yang-Mills
theory on a spacetime cylinder, from the point of view of coherent states, or
equivalently, the Segal-Bargmann transform. Before gauge symmetry is imposed,
the coherent states are simply ordinary coherent states labeled by points in an
infinite-dimensional linear phase space. Gauge symmetry is imposed by
projecting the original coherent states onto the gauge-invariant subspace,
using a suitable regularization procedure. We obtain in this way a new family
of "reduced" coherent states labeled by points in the reduced phase space,
which in this case is simply the cotangent bundle of the structure group K.
The main result explained here, obtained originally in a joint work of the
author with B. Driver, is this: The reduced coherent states are precisely those
associated to the generalized Segal-Bargmann transform for K, as introduced by
the author from a different point of view. This result agrees with that of K.
Wren, who uses a different method of implementing the gauge symmetry. The
coherent states also provide a rigorous way of making sense out of the quantum
Hamiltonian for the unreduced system.
Various related issues are discussed, including the complex structure on the
reduced phase space and the question of whether quantization commutes with
reduction
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
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 -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 () 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 compared to (ii), and the system reaches a stationary state
where the torque oscillates with fractional amplitude 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
General energy bounds for systems of bosons with soft cores
We study a bound system of N identical bosons interacting by model pair
potentials of the form V(r) = A sgn(p)r^p + B/r^2, A > 0, B >= 0. By using a
variational trial function and the `equivalent 2-body method', we find explicit
upper and lower bound formulas for the N-particle ground-state energy in
arbitrary spatial dimensions d > 2 for the two cases p = 2 and p = -1. It is
demonstrated that the upper bound can be systematically improved with the aid
of a special large-N limit in collective field theory
Equivalence of operator-splitting schemes for the integration of the Langevin equation
We investigate the equivalence of different operator-splitting schemes for
the integration of the Langevin equation. We consider a specific problem, so
called the directed percolation process, which can be extended to a wider class
of problems. We first give a compact mathematical description of the
operator-splitting method and introduce two typical splitting schemes that will
be useful in numerical studies. We show that the two schemes are essentially
equivalent through the map that turns out to be an automorphism. An associated
equivalent class of operator-splitting integrations is also defined by
generalizing the specified equivalence.Comment: 4 page
Scattering of first and second sound waves by quantum vorticity in superfluid Helium
We study the scattering of first and second sound waves by quantum vorticity
in superfluid Helium using two-fluid hydrodynamics. The vorticity of the
superfluid component and the sound interact because of the nonlinear character
of these equations. Explicit expressions for the scattered pressure and
temperature are worked out in a first Born approximation, and care is exercised
in delimiting the range of validity of the assumptions needed for this
approximation to hold. An incident second sound wave will partly convert into
first sound, and an incident first sound wave will partly convert into second
sound. General considerations show that most incident first sound converts into
second sound, but not the other way around. These considerations are validated
using a vortex dipole as an explicitely worked out example.Comment: 24 pages, Latex, to appear in Journal of Low Temperature Physic
Limiting Behaviour of the Mean Residual Life
In survival or reliability studies, the mean residual life or life expectancy
is an important characteristic of the model. Here, we study the limiting
behaviour of the mean residual life, and derive an asymptotic expansion which
can be used to obtain a good approximation for large values of the time
variable. The asymptotic expansion is valid for a quite general class of
failure rate distributions--perhaps the largest class that can be expected
given that the terms depend only on the failure rate and its derivatives.Comment: 19 page
Experiments on a videotape atom chip: fragmentation and transport studies
This paper reports on experiments with ultra-cold rubidium atoms confined in
microscopic magnetic traps created using a piece of periodically-magnetized
videotape mounted on an atom chip. The roughness of the confining potential is
studied with atomic clouds at temperatures of a few microKelvin and at
distances between 30 and 80 microns from the videotape-chip surface. The
inhomogeneities in the magnetic field created by the magnetized videotape close
to the central region of the chip are characterized in this way. In addition,
we demonstrate a novel transport mechanism whereby we convey cold atoms
confined in arrays of videotape magnetic micro-traps over distances as large as
~ 1 cm parallel to the chip surface. This conveying mechanism enables us to
survey the surface of the chip and observe potential-roughness effects across
different regions.Comment: 29 pages, 22 figures
Self-Similar Bootstrap of Divergent Series
A method is developed for calculating effective sums of divergent series.
This approach is a variant of the self-similar approximation theory. The
novelty here is in using an algebraic transformation with a power providing the
maximal stability of the self-similar renormalization procedure. The latter is
to be repeated as many times as it is necessary in order to convert into closed
self-similar expressions all sums from the series considered. This multiple and
complete renormalization is called self-similar bootstrap. The method is
illustrated by several examples from statistical physics.Comment: 1 file, 22 pages, RevTe
Comment on ``Indication, from Pioneer 10/11, Galileo and Ulysses Data, of an Apparent Anomalous, Weak, Long-Range Acceleration''
The reported anomalous acceleration may be explained as the recoil of
radiated waste RTG heat scattered by the back of the high gain antenna.Comment: 4pp, Revtex, recoil force now calculated numerically from Pioneer
engineering data, conclusions unchange
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