3,174 research outputs found
Solving the inhomogeneous Bethe-Salpeter equation
We develop an advanced method of solving homogeneous and inhomogeneous
Bethe-Salpeter equations by using the expansion over the complete set of
4-dimensional spherical harmonics. We solve Bethe-Salpeter equations for bound
and scattering states of scalar and spinor particles for the case of one meson
exchange kernels. Phase shifts calculated for the scalar model are in agreement
with the previously published results. We discuss possible manifestations of
separability for one meson exchange interaction kernels.Comment: 9 pages, 11 eps-figures. Talk presented by S. S. Semikh at XVII
International Baldin Seminar on High Energy Physics Problems "Relativistic
Nuclear Physics and Quantum Chromodynamics", September 27 - October 2, 2004,
Dubna, Russia; to appear in the proceedings of this conferenc
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
Symmetries of Three Harmonically-Trapped Particles in One Dimension
We present a method for solving trapped few-body problems and apply it to
three equal-mass particles in a one-dimensional harmonic trap, interacting via
a contact potential. By expressing the relative Hamiltonian in Jacobi
cylindrical coordinates, i.e. the two-dimensional version of three-body
hyperspherical coordinates, we discover an underlying symmetry.
This symmetry simplifies the calculation of energy eigenstates of the full
Hamiltonian in a truncated Hilbert space constructed from the trap Hamiltonian
eigenstates. Particle superselection rules are implemented by choosing the
relevant representations of . We find that the one-dimensional
system shows nearly the full richness of the three-dimensional system, and can
be used to understand separability and reducibility in this system and in
standard few-body approximation techniques.Comment: 27 pages, 5 figures, 6 tables, 37 references, 4 footnotes, 1 article;
v2 has revised introduction and results sections as well as typos correcte
Analytical derivation of the radial distribution function in spherical dark matter halos
The velocity distribution of dark matter near the Earth is important for an
accurate analysis of the signals in terrestrial detectors. This distribution is
typically extracted from numerical simulations. Here we address the possibility
of deriving the velocity distribution function analytically. We derive a
differential equation which is a function of radius and the radial component of
the velocity. Under various assumptions this can be solved, and we compare the
solution with the results from controlled numerical simulations. Our findings
complement the previously derived tangential velocity distribution. We hereby
demonstrate that the entire distribution function, below 0.7 v_esc, can be
derived analytically for spherical and equilibrated dark matter structures.Comment: 6 pages, 5 figures, submitted to MNRA
Coalescence of Two Spinning Black Holes: An Effective One-Body Approach
We generalize to the case of spinning black holes a recently introduced
``effective one-body'' approach to the general relativistic dynamics of binary
systems. The combination of the effective one-body approach, and of a Pad\'e
definition of some crucial effective radial functions, is shown to define a
dynamics with much improved post-Newtonian convergence properties, even for
black hole separations of the order of . We discuss the approximate
existence of a two-parameter family of ``spherical orbits'' (with constant
radius), and, of a corresponding one-parameter family of ``last stable
spherical orbits'' (LSSO). These orbits are of special interest for forthcoming
LIGO/VIRGO/GEO gravitational wave observations. It is argued that for most (but
not all) of the parameter space of two spinning holes the effective one-body
approach gives a reliable analytical tool for describing the dynamics of the
last orbits before coalescence. This tool predicts, in a quantitative way, how
certain spin orientations increase the binding energy of the LSSO. This leads
to a detection bias, in LIGO/VIRGO/GEO observations, favouring spinning black
hole systems, and makes it urgent to complete the conservative effective
one-body dynamics given here by adding (resummed) radiation reaction effects,
and by constructing gravitational waveform templates that include spin effects.
Finally, our approach predicts that the spin of the final hole formed by the
coalescence of two arbitrarily spinning holes never approaches extremality.Comment: 26 pages, two eps figures, accepted in Phys. Rev. D, minor updating
of the text, clarifications added and inclusion of a few new reference
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