1,225 research outputs found
Theoretical description of two ultracold atoms in finite 3D optical lattices using realistic interatomic interaction potentials
A theoretical approach is described for an exact numerical treatment of a
pair of ultracold atoms interacting via a central potential that are trapped in
a finite three-dimensional optical lattice. The coupling of center-of-mass and
relative-motion coordinates is treated using an exact diagonalization
(configuration-interaction) approach. The orthorhombic symmetry of an optical
lattice with three different but orthogonal lattice vectors is explicitly
considered as is the Fermionic or Bosonic symmetry in the case of
indistinguishable particles.Comment: 19 pages, 5 figure
B-splines, Pólya curves, and duality
AbstractLocal duality between B-splines and Pólya curves is examined, mostly from the viewpoint of computer-aided geometric design. Certain known results for the two curve types are shown to be related. A few new results for Pólya curves and a curve scheme related to B-splines also follow from these investigations
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
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
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
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
Multivariate Anisotropic Interpolation on the Torus
We investigate the error of periodic interpolation, when sampling a function
on an arbitrary pattern on the torus. We generalize the periodic Strang-Fix
conditions to an anisotropic setting and provide an upper bound for the error
of interpolation. These conditions and the investigation of the error
especially take different levels of smoothness along certain directions into
account
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
Overlap of QRPA states based on ground states of different nuclei --mathematical properties and test calculations--
The overlap of the excited states in quasiparticle random-phase approximation
(QRPA) is calculated in order to simulate the overlap of the intermediate
nuclear states of the double-beta decay. Our basic idea is to use the
like-particle QRPA with the aid of the closure approximation and calculate the
overlap as rigorously as possible by making use of the explicit equation of the
QRPA ground state. The formulation is shown in detail, and the mathematical
properties of the overlap matrix are investigated. Two test calculations are
performed for relatively light nuclei with the Skyrme and volume delta-pairing
energy functionals. The validity of the truncations used in the calculation is
examined and confirmed.Comment: 17 pages, 15 figures, full paper following arXiv:1205.5354 and Phys.
Rev. C 86 (2012) 021301(R
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
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