5,051 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.
Tangential Touch between the Free and the Fixed Boundary in a Semilinear Free Boundary Problem in Two Dimensions
The main result of this paper concerns the behavior of a free boundary
arising from a minimization problem, close to the fixed boundary in two
dimensions
Geometric approach to nonvariational singular elliptic equations
In this work we develop a systematic geometric approach to study fully
nonlinear elliptic equations with singular absorption terms as well as their
related free boundary problems. The magnitude of the singularity is measured by
a negative parameter , for , which reflects on
lack of smoothness for an existing solution along the singular interface
between its positive and zero phases. We establish existence as well sharp
regularity properties of solutions. We further prove that minimal solutions are
non-degenerate and obtain fine geometric-measure properties of the free
boundary . In particular we show sharp
Hausdorff estimates which imply local finiteness of the perimeter of the region
and a.e. weak differentiability property of
.Comment: Paper from D. Araujo's Ph.D. thesis, distinguished at the 2013 Carlos
Gutierrez prize for best thesis, Archive for Rational Mechanics and Analysis
201
Bose Einstein Condensate in a Box
Bose-Einstein condensates have been produced in an optical box trap. This
novel optical trap type has strong confinement in two directions comparable to
that which is possible in an optical lattice, yet produces individual
condensates rather than the thousands typical of a lattice. The box trap is
integrated with single atom detection capability, paving the way for studies of
quantum atom statistics.Comment: 4 pages, 5 figure
The Balian-Br\'ezin Method in Relativistic Quantum Mechanics
The method suggested by Balian and Br\'ezin for treating angular momentum
reduction in the Faddeev equations is shown to be applicable to the
relativistic three-body problem.Comment: 14 pages in LaTe
N-d scattering above the deuteron breakup threshold
The complex Kohn variational principle and the (correlated) Hyperspherical
Harmonics technique are applied to study the N--d scattering above the deuteron
breakup threshold. The configuration with three outgoing nucleons is explicitly
taken into account by solving a set of differential equations with outgoing
boundary conditions. A convenient procedure is used to obtain the correct
boundary conditions at values of the hyperradius fm. The
inclusion of the Coulomb potential is straightforward and does not give
additional difficulties. Numerical results have been obtained for a simple
s-wave central potential. They are in nice agreement with the benchmarks
produced by different groups using the Faddeev technique. Comparisons are also
done with experimental elastic N--d cross section at several energies.Comment: LaTeX, 13 pages, 3 figure
proton-deuteron elastic scattering above the deuteron breakup
The complex Kohn variational principle and the (correlated) hyperspherical
harmonics method are applied to study the proton-deuteron elastic scattering at
energies above the deuteron breakup threshold. Results for the elastic cross
section and various elastic polarization observables have been obtained by
fully taking into account the long-range effect of the Coulomb interaction and
using a realistic nucleon-nucleon interaction model. Detailed comparison
between the theoretical predictions and the accurate and abundant
proton-deuteron experimental data can now be performed.Comment: 6 pages, 2 figure
Analyzing symmetry breaking within a chaotic quantum system via Bayesian inference
Bayesian inference is applied to the level fluctuations of two coupled
microwave billiards in order to extract the coupling strength. The coupled
resonators provide a model of a chaotic quantum system containing two coupled
symmetry classes of levels. The number variance is used to quantify the level
fluctuations as a function of the coupling and to construct the conditional
probability distribution of the data. The prior distribution of the coupling
parameter is obtained from an invariance argument on the entropy of the
posterior distribution.Comment: Example from chaotic dynamics. 8 pages, 7 figures. Submitted to PR
Enforcing Termination of Interprocedural Analysis
Interprocedural analysis by means of partial tabulation of summary functions
may not terminate when the same procedure is analyzed for infinitely many
abstract calling contexts or when the abstract domain has infinite strictly
ascending chains. As a remedy, we present a novel local solver for general
abstract equation systems, be they monotonic or not, and prove that this solver
fails to terminate only when infinitely many variables are encountered. We
clarify in which sense the computed results are sound. Moreover, we show that
interprocedural analysis performed by this novel local solver, is guaranteed to
terminate for all non-recursive programs --- irrespective of whether the
complete lattice is infinite or has infinite strictly ascending or descending
chains
Scaling law in target-hunting processes
We study the hunting process for a target, in which the hunter tracks the
goal by smelling odors it emits. The odor intensity is supposed to decrease
with the distance it diffuses. The Monte Carlo experiment is carried out on a
2-dimensional square lattice. Having no idea of the location of the target, the
hunter determines its moves only by random attempts in each direction. By
sorting the searching time in each simulation and introducing a variable to
reflect the sequence of searching time, we obtain a curve with a wide plateau,
indicating a most probable time of successfully finding out the target. The
simulations reveal a scaling law for the searching time versus the distance to
the position of the target. The scaling exponent depends on the sensitivity of
the hunter. Our model may be a prototype in studying such the searching
processes as various foods-foraging behavior of the wild animals.Comment: 7 figure
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