21,598 research outputs found
Anatomy of three-body decay III. Energy distributions
We address the problem of calculating momentum distributions of particles
emerging from the three-body decay of a many-body resonance. We show that these
distributions are determined by the asymptotics of the coordinate-space
complex-energy wave-function of the resonance. We use the hyperspherical
adiabatic expansion method where all lengths are proportional to the
hyperradius. The structures of the resonances are related to different decay
mechanisms. For direct decay all inter-particle distances increase proportional
to the hyperradius at intermediate and large distances. Sequential three-body
decay proceeds via spatially confined quasi-stationary two-body configurations.
Then two particles remain close while the third moves away. The wave function
may contain mixtures which produce coherence effects at small distances, but
the energy distributions can still be added incoherently. Two-neutron halos are
discussed in details and illustrated by the resonance in He. The
dynamic evolution of the decay process is discussed.Comment: 30 pages, 8 figures, to be published in Nuclear Physics
Structure of boson systems beyond the mean-field
We investigate systems of identical bosons with the focus on two-body
correlations. We use the hyperspherical adiabatic method and a decomposition of
the wave function in two-body amplitudes. An analytic parametrization is used
for the adiabatic effective radial potential. We discuss the structure of a
condensate for arbitrary scattering length. Stability and time scales for
various decay processes are estimated. The previously predicted Efimov-like
states are found to be very narrow. We discuss the validity conditions and
formal connections between the zero- and finite-range mean-field
approximations, Faddeev-Yakubovskii formulation, Jastrow ansatz, and the
present method. We compare numerical results from present work with mean-field
calculations and discuss qualitatively the connection with measurements.Comment: 26 pages, 6 figures, submitted to J. Phys. B. Ver. 2 is 28 pages with
modified figures and discussion
Convergence and round-off errors in a two-dimensional eigenvalue problem using spectral methods and Arnoldi-Chebyshev algorithm
An efficient way of solving 2D stability problems in fluid mechanics is to
use, after discretization of the equations that cast the problem in the form of
a generalized eigenvalue problem, the incomplete Arnoldi-Chebyshev method. This
method preserves the banded structure sparsity of matrices of the algebraic
eigenvalue problem and thus decreases memory use and CPU-time consumption.
The errors that affect computed eigenvalues and eigenvectors are due to the
truncation in the discretization and to finite precision in the computation of
the discretized problem. In this paper we analyze those two errors and the
interplay between them. We use as a test case the two-dimensional eigenvalue
problem yielded by the computation of inertial modes in a spherical shell. This
problem contains many difficulties that make it a very good test case. It turns
out that that single modes (especially most-damped modes i.e. with high spatial
frequency) can be very sensitive to round-off errors, even when apparently good
spectral convergence is achieved. The influence of round-off errors is analyzed
using the spectral portrait technique and by comparison of double precision and
extended precision computations. Through the analysis we give practical recipes
to control the truncation and round-off errors on eigenvalues and eigenvectors.Comment: 15 pages, 9 figure
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