224,962 research outputs found
Momentum Space Integral Equations for Three Charged Particles: Diagonal Kernels
It has been a long-standing question whether momentum space integral
equations of the Faddeev type are applicable to reactions of three charged
particles, in particular above the three-body threshold. For, the presence of
long-range Coulomb forces has been thought to give rise to such severe
singularities in their kernels that the latter may lack the compactness
property known to exist in the case of purely short-range interactions.
Employing the rigorously equivalent formulation in terms of an
effective-two-body theory we have proved in a preceding paper [Phys. Rev. C
{\bf 61}, 064006 (2000)] that, for all energies, the nondiagonal kernels
occurring in the integral equations which determine the transition amplitudes
for all binary collision processes, possess on and off the energy shell only
integrable singularities, provided all three particles have charges of the same
sign, i.e., all Coulomb interactions are repulsive. In the present paper we
prove that, for particles with charges of equal sign, the diagonal kernels, in
contrast, possess one, but only one, nonintegrable singularity. The latter can,
however, be isolated explicitly and dealt with in a well-defined manner. Taken
together these results imply that modified integral equations can be
formulated, with kernels that become compact after a few iterations. This
concludes the proof that standard solution methods can be used for the
calculation of all binary (i.e., (in-)elastic and rearrangement) amplitudes by
means of momentum space integral equations of the effective-two-body type.Comment: 36 pages, 2 figures, accepted for publication in Phys. Rev.
Hydrodynamic chains and a classification of their Poisson brackets
Necessary and sufficient conditions for an existence of the Poisson brackets
significantly simplify in the Liouville coordinates. The corresponding
equations can be integrated. Thus, a description of local Hamiltonian
structures is a first step in a description of integrable hydrodynamic chains.
The concept of Poisson bracket is introduced. Several new Poisson brackets
are presented
The variation of the magnetic field of the Ap star HD~50169 over its 29 year rotation period
Context. The Ap stars that rotate extremely slowly, with periods of decades
to centuries, represent one of the keys to the understanding of the processes
leading to the differentiation of stellar rotation.
Aims. We characterise the variations of the magnetic field of the Ap star HD
50169 and derive constraints about its structure.
Methods. We combine published measurements of the mean longitudinal field
of HD 50169 with new determinations of this field moment from circular
spectropolarimetry obtained at the 6-m telescope BTA of the Special
Astrophysical Observatory of the Russian Academy of Sciences. For the mean
magnetic field modulus , literature data are complemented by the analysis of
ESO spectra, both newly acquired and from the archive. Radial velocities are
also obtained from these spectra.
Results. We present the first determination of the rotation period of HD
50169, Prot = (29.04+/-0.82) y. HD 50169 is currently the longest-period Ap
star for which magnetic field measurements have been obtained over more than a
full cycle. The variation curves of both and have a significant degree
of anharmonicity, and there is a definite phase shift between their respective
extrema. We confirm that HD 50169 is a wide spectroscopic binary, refine its
orbital elements, and suggest that the secondary is probably a dwarf star of
spectral type M.
Conclusions. The shapes and mutual phase shifts of the derived magnetic
variation curves unquestionably indicate that the magnetic field of HD 50169 is
not symmetric about an axis passing through its centre. Overall, HD 50169
appears similar to the bulk of the long-period Ap stars.Comment: 10 pages, 3 figures, accepted for publication in A&
Weak Turbulent Kolmogorov Spectrum for Surface Gravity Waves
We study the long-time evolution of gravity waves on deep water exited by the
stochastic external force concentrated in moderately small wave numbers. We
numerically implement the primitive Euler equations for the potential flow of
an ideal fluid with free surface written in canonical variables, using
expansion of the Hamiltonian in powers of nonlinearity of up to fourth order
terms.
We show that due to nonlinear interaction processes a stationary energy
spectrum close to is formed. The observed spectrum can be
interpreted as a weak-turbulent Kolmogorov spectrum for a direct cascade of
energy.Comment: 4 pages, 5 figure
The evolution with temperature of magnetic polaron state in an antiferromagnetic chain with impurities
The thermal behavior of a one-dimensional antiferromagnetic chain doped by
donor impurities was analyzed. The ground state of such a chain corresponds to
the formation of a set of ferromagnetically correlated regions localized near
impurities (bound magnetic polarons). At finite temperatures, the magnetic
structure of the chain was calculated simultaneously with the wave function of
a conduction electron bound by an impurity. The calculations were performed
using an approximate variational method and a Monte Carlo simulation. Both
these methods give similar results. The analysis of the temperature dependence
of correlation functions for neighboring local spins demonstrated that the
ferromagnetic correlations inside a magnetic polaron remain significant even
above the N\'eel temperature implying rather high stability of the
magnetic polaron state. In the case when the electron-impurity coupling energy
is not too high (for lower that the electron hopping integral ), the
magnetic polaron could be depinned from impurity retaining its magnetic
structure. Such a depinning occurs at temperatures of the order of . At
even higher temperatures () magnetic polarons disappear and the chain
becomes completely disordered.Comment: 17 pages, 5 figures, RevTe
Long-range behavior of the optical potential for the elastic scattering of charged composite particles
The asymptotic behavior of the optical potential, describing elastic
scattering of a charged particle off a bound state of two charged, or
one charged and one neutral, particles at small momentum transfer
or equivalently at large intercluster distance
, is investigated within the framework of the exact three-body
theory. For the three-charged-particle Green function that occurs in the exact
expression for the optical potential, a recently derived expression, which is
appropriate for the asymptotic region under consideration, is used. We find
that for arbitrary values of the energy parameter the non-static part of the
optical potential behaves for as
. From this we derive for the
Fourier transform of its on-shell restriction for the behavior , i.e.,
dipole or quadrupole terms do not occur in the coordinate-space asymptotics.
This result corroborates the standard one, which is obtained by perturbative
methods. The general, energy-dependent expression for the dynamic
polarisability is derived; on the energy shell it reduces to the
conventional polarisability which is independent of the energy. We
emphasize that the present derivation is {\em non-perturbative}, i.e., it does
not make use of adiabatic or similar approximations, and is valid for energies
{\em below as well as above the three-body dissociation threshold}.Comment: 35 pages, no figures, revte
Nonlinear lattice model of viscoelastic Mode III fracture
We study the effect of general nonlinear force laws in viscoelastic lattice
models of fracture, focusing on the existence and stability of steady-state
Mode III cracks. We show that the hysteretic behavior at small driving is very
sensitive to the smoothness of the force law. At large driving, we find a Hopf
bifurcation to a straight crack whose velocity is periodic in time. The
frequency of the unstable bifurcating mode depends on the smoothness of the
potential, but is very close to an exact period-doubling instability. Slightly
above the onset of the instability, the system settles into a exactly
period-doubled state, presumably connected to the aforementioned bifurcation
structure. We explicitly solve for this new state and map out its
velocity-driving relation
Dependences of the Casimir-Polder interaction between an atom and a cavity wall on atomic and material properties
The Casimir-Polder and van der Waals interactions between an atom and a flat
cavity wall are investigated under the influence of real conditions including
the dynamic polarizability of the atom, actual conductivity of the wall
material and nonzero temperature of the wall. The cases of different atoms near
metal and dielectric walls are considered. It is shown that to obtain accurate
results for the atom-wall interaction at short separations, one should use the
complete tabulated optical data for the complex refractive index of the wall
material and the accurate dynamic polarizability of an atom. At relatively
large separations in the case of a metal wall, one may use the plasma model
dielectric function to describe the dielectric properties of wall material. The
obtained results are important for the theoretical interpretation of
experiments on quantum reflection and Bose-Einstein condensation.Comment: 5 pages, 1 figure, iopart.cls is used, to appear in J. Phys. A
(special issue: Proceedings of QFEXT05, Barcelona, Sept. 5-9, 2005
Closed form solution for a double quantum well using Gr\"obner basis
Analytical expressions for spectrum, eigenfunctions and dipole matrix
elements of a square double quantum well (DQW) are presented for a general case
when the potential in different regions of the DQW has different heights and
effective masses are different. This was achieved by Gr\"obner basis algorithm
which allows to disentangle the resulting coupled polynomials without
explicitly solving the transcendental eigenvalue equation.Comment: 4 figures, Mathematica full calculation noteboo
An outburst from a massive star 40 days before a supernova explosion
Various lines of evidence suggest that very massive stars experience extreme
mass-loss episodes shortly before they explode as a supernova. Interestingly,
several models predict such pre-explosion outbursts. Establishing a causal
connection between these mass-loss episodes and the final supernova explosion
will provide a novel way to study pre-supernova massive-star evolution. Here we
report on observations of a remarkable mass-loss event detected 40 days prior
to the explosion of the Type IIn supernova SN 2010mc (PTF 10tel). Our
photometric and spectroscopic data suggest that this event is a result of an
energetic outburst, radiating at least 6x10^47 erg of energy, and releasing
about 0.01 Solar mass at typical velocities of 2000 km/s. We show that the
temporal proximity of the mass-loss outburst and the supernova explosion
implies a causal connection between them. Moreover, we find that the outburst
luminosity and velocity are consistent with the predictions of the wave-driven
pulsation model and disfavor alternative suggestions.Comment: Nature 494, 65, including supplementary informatio
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