899 research outputs found
Increasing the Reliability of Adaptive Quadrature Using Explicit Interpolants
We present two new adaptive quadrature routines. Both routines differ from
previously published algorithms in many aspects, most significantly in how they
represent the integrand, how they treat non-numerical values of the integrand,
how they deal with improper divergent integrals and how they estimate the
integration error. The main focus of these improvements is to increase the
reliability of the algorithms without significantly impacting their efficiency.
Both algorithms are implemented in Matlab and tested using both the "families"
suggested by Lyness and Kaganove and the battery test used by Gander and
Gautschi and Kahaner. They are shown to be more reliable, albeit in some cases
less efficient, than other commonly-used adaptive integrators.Comment: 32 pages, submitted to ACM Transactions on Mathematical Softwar
Wave Mechanics of a Two Wire Atomic Beamsplitter
We consider the problem of an atomic beam propagating quantum mechanically
through an atom beam splitter. Casting the problem in an adiabatic
representation (in the spirit of the Born-Oppenheimer approximation in
molecular physics) sheds light on explicit effects due to non-adiabatic passage
of the atoms through the splitter region. We are thus able to probe the fully
three dimensional structure of the beam splitter, gathering quantitative
information about mode-mixing, splitting ratios,and reflection and transmission
probabilities
Adiabatic hyperspherical study of triatomic helium systems
The 4He3 system is studied using the adiabatic hyperspherical representation.
We adopt the current state-of-the-art helium interaction potential including
retardation and the nonadditive three-body term, to calculate all low-energy
properties of the triatomic 4He system. The bound state energies of the 4He
trimer are computed as well as the 4He+4He2 elastic scattering cross sections,
the three-body recombination and collision induced dissociation rates at finite
temperatures. We also treat the system that consists of two 4He and one 3He
atoms, and compute the spectrum of the isotopic trimer 4He2 3He, the 3He+4He2
elastic scattering cross sections, the rates for three-body recombination and
the collision induced dissociation rate at finite temperatures. The effects of
retardation and the nonadditive three-body term are investigated. Retardation
is found to be significant in some cases, while the three-body term plays only
a minor role for these systems.Comment: 24 pages 6 figures Submitted to Physical Review
An estimate for the average spectral measure of random band matrices
For a class of random band matrices of band width , we prove regularity of
the average spectral measure at scales , and find its
asymptotics at these scales.Comment: 19 pp., revised versio
Bivariate spline interpolation with optimal approximation order
Let be a triangulation of some polygonal domain f c R2 and let S9 (A) denote the space of all bivariate polynomial splines of smoothness r and degree q with respect to A. We develop the first Hermite-type interpolation scheme for S9 (A), q >_ 3r + 2, whose approximation error is bounded above by Kh4+i, where h is the maximal diameter of the triangles in A, and the constant K only depends on the smallest angle of the triangulation and is independent of near-degenerate edges and nearsingular vertices. Moreover, the fundamental functions of our scheme are minimally supported and form a locally linearly independent basis for a superspline subspace of Sr, (A). This shows that the optimal approximation order can be achieved by using minimally supported splines. Our method of proof is completely different from the quasi-interpolation techniques for the study of the approximation power of bivariate splines developed in [71 and [181
A combined R-matrix eigenstate basis set and finite-differences propagation method for the time-dependent Schr\"{od}dinger equation: the one-electron case
In this work we present the theoretical framework for the solution of the
time-dependent Schr\"{o}dinger equation (TDSE) of atomic and molecular systems
under strong electromagnetic fields with the configuration space of the
electron's coordinates separated over two regions, that is regions and
. In region the solution of the TDSE is obtained by an R-matrix basis
set representation of the time-dependent wavefunction. In region a grid
representation of the wavefunction is considered and propagation in space and
time is obtained through the finite-differences method. It appears this is the
first time a combination of basis set and grid methods has been put forward for
tackling multi-region time-dependent problems. In both regions, a high-order
explicit scheme is employed for the time propagation. While, in a purely
hydrogenic system no approximation is involved due to this separation, in
multi-electron systems the validity and the usefulness of the present method
relies on the basic assumption of R-matrix theory, namely that beyond a certain
distance (encompassing region ) a single ejected electron is distinguishable
from the other electrons of the multi-electron system and evolves there (region
II) effectively as a one-electron system. The method is developed in detail for
single active electron systems and applied to the exemplar case of the hydrogen
atom in an intense laser field.Comment: 13 pages, 6 figures, submitte
Diffusion Monte Carlo calculations for the ground states of atoms and ions in neutron star magnetic fields
The diffusion quantum Monte Carlo method is extended to solve the old
theoretical physics problem of many-electron atoms and ions in intense magnetic
fields. The feature of our approach is the use of adiabatic approximation wave
functions augmented by a Jastrow factor as guiding functions to initialize the
quantum Monte Carlo prodecure. We calcula te the ground state energies of atoms
and ions with nuclear charges from Z= 2, 3, 4, ..., 26 for magnetic field
strengths relevant for neutron stars.Comment: 6 pages, 1 figure, proceedings of the "9th International Conference
on Path Integrals - New Trends and Perspectives", Max-Planck-Institut fur
Physik komplexer Systeme, Dresden, Germany, September 23 - 28, 2007, to be
published as a book by World Scientific, Singapore (2008
Three-neutron resonance trajectories for realistic interaction models
Three-neutron resonances are investigated using realistic nucleon-nucleon
interaction models. The resonance pole trajectories are explored by first
adding an additional interaction to artificially bind the three-neutron system
and then gradually removing it. The pole positions for the three-neutron states
up to J=5/2 are localized in the third energy quadrant-Im (E)<=0, Re
(E)<=0-well before the additional interaction is removed. Our study shows that
realistic nucleon-nucleon interaction models exclude any possible experimental
signature of three-neutron resonances.Comment: 13 pages ; 8 figs ; 5 table
Three Bosons in One Dimension with Short Range Interactions I: Zero Range Potentials
We consider the three-boson problem with -function interactions in
one spatial dimension. Three different approaches are used to calculate the
phase shifts, which we interpret in the context of the effective range
expansion, for the scattering of one free particle a off of a bound pair. We
first follow a procedure outlined by McGuire in order to obtain an analytic
expression for the desired S-matrix element. This result is then compared to a
variational calculation in the adiabatic hyperspherical representation, and to
a numerical solution to the momentum space Faddeev equations. We find excellent
agreement with the exact phase shifts, and comment on some of the important
features in the scattering and bound-state sectors. In particular, we find that
the 1+2 scattering length is divergent, marking the presence of a zero-energy
resonance which appears as a feature when the pair-wise interactions are
short-range. Finally, we consider the introduction of a three-body interaction,
and comment on the cutoff dependence of the coupling.Comment: 9 figures, 2 table
One-way multigrid method in electronic structure calculations
We propose a simple and efficient one-way multigrid method for
self-consistent electronic structure calculations based on iterative
diagonalization. Total energy calculations are performed on several different
levels of grids starting from the coarsest grid, with wave functions
transferred to each finer level. The only changes compared to a single grid
calculation are interpolation and orthonormalization steps outside the original
total energy calculation and required only for transferring between grids. This
feature results in a minimal amount of code change, and enables us to employ a
sophisticated interpolation method and noninteger ratio of grid spacings.
Calculations employing a preconditioned conjugate gradient method are presented
for two examples, a quantum dot and a charged molecular system. Use of three
grid levels with grid spacings 2h, 1.5h, and h decreases the computer time by
about a factor of 5 compared to single level calculations.Comment: 10 pages, 2 figures, to appear in Phys. Rev. B, Rapid Communication
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