1,267 research outputs found
Random projections and the optimization of an algorithm for phase retrieval
Iterative phase retrieval algorithms typically employ projections onto
constraint subspaces to recover the unknown phases in the Fourier transform of
an image, or, in the case of x-ray crystallography, the electron density of a
molecule. For a general class of algorithms, where the basic iteration is
specified by the difference map, solutions are associated with fixed points of
the map, the attractive character of which determines the effectiveness of the
algorithm. The behavior of the difference map near fixed points is controlled
by the relative orientation of the tangent spaces of the two constraint
subspaces employed by the map. Since the dimensionalities involved are always
large in practical applications, it is appropriate to use random matrix theory
ideas to analyze the average-case convergence at fixed points. Optimal values
of the gamma parameters of the difference map are found which differ somewhat
from the values previously obtained on the assumption of orthogonal tangent
spaces.Comment: 15 page
Interaction between static holes in a quantum dimer model on the kagome lattice
A quantum dimer model (QDM) on the kagome lattice with an extensive
ground-state entropy was recently introduced [Phys. Rev. B 67, 214413 (2003)].
The ground-state energy of this QDM in presence of one and two static holes is
investigated by means of exact diagonalizations on lattices containing up to
144 kagome sites. The interaction energy between the holes (at distances up to
7 lattice spacings) is evaluated and the results show no indication of
confinement at large hole separations.Comment: 6 pages, 3 figures. IOP style files included. To appear in J. Phys.:
Condens. Matter, Proceedings of the HFM2003 conference, Grenobl
Two-flavour Schwinger model with dynamical fermions in the L\"uscher formalism
We report preliminary results for 2D massive QED with two flavours of Wilson
fermions, using the Hermitean variant of L\"uscher's bosonization technique.
The chiral condensate and meson masses are obtained. The simplicity of the
model allows for high statistics simulations close to the chiral and continuum
limit, both in the quenched approximation and with dynamical fermions.Comment: Talk presented at LATTICE96(algorithms), 3 pages, 3 Postscript
figures, uses twoside, fleqn, espcrc2, epsf, revised version (details of
approx. polynomial
Magnetic Properties of Undoped
The Heisenberg antiferromagnet, which arises from the large Hubbard
model, is investigated on the molecule and other fullerenes. The
connectivity of leads to an exotic classical ground state with
nontrivial topology. We argue that there is no phase transition in the Hubbard
model as a function of , and thus the large solution is relevant for
the physical case of intermediate coupling. The system undergoes a first order
metamagnetic phase transition. We also consider the S=1/2 case using
perturbation theory. Experimental tests are suggested.Comment: 12 pages, 3 figures (included
Reduction of Guided Acoustic Wave Brillouin Scattering in Photonic Crystal Fibers
Guided Acoustic Wave Brillouin Scattering (GAWBS) generates phase and
polarization noise of light propagating in glass fibers. This excess noise
affects the performance of various experiments operating at the quantum noise
limit. We experimentally demonstrate the reduction of GAWBS noise in a photonic
crystal fiber in a broad frequency range using cavity sound dynamics. We
compare the noise spectrum to the one of a standard fiber and observe a 10-fold
noise reduction in the frequency range up to 200 MHz. Based on our measurement
results as well as on numerical simulations we establish a model for the
reduction of GAWBS noise in photonic crystal fibers.Comment: 4 pages, 7 figures; added numerical simulations, added reference
Ordering monomial factors of polynomials in the product representation
The numerical construction of polynomials in the product representation (as
used for instance in variants of the multiboson technique) can become
problematic if rounding errors induce an imprecise or even unstable evaluation
of the polynomial. We give criteria to quantify the effects of these rounding
errors on the computation of polynomials approximating the function . We
consider polynomials both in a real variable and in a Hermitian matrix. By
investigating several ordering schemes for the monomials of these polynomials,
we finally demonstrate that there exist orderings of the monomials that keep
rounding errors at a tolerable level.Comment: Latex2e file, 7 figures, 32 page
A method for dense packing discovery
The problem of packing a system of particles as densely as possible is
foundational in the field of discrete geometry and is a powerful model in the
material and biological sciences. As packing problems retreat from the reach of
solution by analytic constructions, the importance of an efficient numerical
method for conducting \textit{de novo} (from-scratch) searches for dense
packings becomes crucial. In this paper, we use the \textit{divide and concur}
framework to develop a general search method for the solution of periodic
constraint problems, and we apply it to the discovery of dense periodic
packings. An important feature of the method is the integration of the unit
cell parameters with the other packing variables in the definition of the
configuration space. The method we present led to improvements in the
densest-known tetrahedron packing which are reported in [arXiv:0910.5226].
Here, we use the method to reproduce the densest known lattice sphere packings
and the best known lattice kissing arrangements in up to 14 and 11 dimensions
respectively (the first such numerical evidence for their optimality in some of
these dimensions). For non-spherical particles, we report a new dense packing
of regular four-dimensional simplices with density
and with a similar structure to the densest known tetrahedron packing.Comment: 15 pages, 5 figure
Stability of the hard-sphere icosahedral quasilattice
The stability of the hard-sphere icosahedral quasilattice is analyzed using
the differential formulation of the generalized effective liquid approximation.
We find that the icosahedral quasilattice is metastable with respect to the
hard-sphere crystal structures. Our results agree with recent findings by
McCarley and Ashcroft [Phys. Rev. B {\bf 49}, 15600 (1994)] carried out using
the modified weighted density approximation.Comment: 15 pages, 2 figures available from authors upon request, (revtex),
submitted to Phys. Rev.
Recursion and Path-Integral Approaches to the Analytic Study of the Electronic Properties of
The recursion and path-integral methods are applied to analytically study the
electronic structure of a neutral molecule. We employ a tight-binding
Hamiltonian which considers both the and valence electrons of carbon.
From the recursion method, we obtain closed-form {\it analytic} expressions for
the and eigenvalues and eigenfunctions, including the highest
occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital
(LUMO) states, and the Green's functions. We also present the local densities
of states around several ring clusters, which can be probed experimentally by
using, for instance, a scanning tunneling microscope. {}From a path-integral
method, identical results for the energy spectrum are also derived. In
addition, the local density of states on one carbon atom is obtained; from this
we can derive the degree of degeneracy of the energy levels.Comment: 19 pages, RevTex, 6 figures upon reques
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