7,024 research outputs found
Constrained Orthogonal Polynomials
We define sets of orthogonal polynomials satisfying the additional constraint
of a vanishing average. These are of interest, for example, for the study of
the Hohenberg-Kohn functional for electronic or nucleonic densities and for the
study of density fluctuations in centrifuges. We give explicit properties of
such polynomial sets, generalizing Laguerre and Legendre polynomials. The
nature of the dimension 1 subspace completing such sets is described. A
numerical example illustrates the use of such polynomials.Comment: 11 pages, 10 figure
Existence of a Density Functional for an Intrinsic State
A generalization of the Hohenberg-Kohn theorem proves the existence of a
density functional for an intrinsic state, symmetry violating, out of which a
physical state with good quantum numbers can be projected.Comment: 6 page
Antisymmetrization of a Mean Field Calculation of the T-Matrix
The usual definition of the prior(post) interaction between
projectile and target (resp. ejectile and residual target) being contradictory
with full antisymmetrization between nucleons, an explicit antisymmetrization
projector must be included in the definition of the transition
operator, We derive the
suitably antisymmetrized mean field equations leading to a non perturbative
estimate of . The theory is illustrated by a calculation of forward
- scattering, making use of self consistent symmetries.Comment: 30 pages, no figures, plain TeX, SPHT/93/14
Open problems in nuclear density functional theory
This note describes five subjects of some interest for the density functional
theory in nuclear physics. These are, respectively, i) the need for concave
functionals, ii) the nature of the Kohn-Sham potential for the radial density
theory, iii) a proper implementation of a density functional for an "intrinsic"
rotational density, iv) the possible existence of a potential driving the
square root of the density, and v) the existence of many models where a density
functional can be explicitly constructed.Comment: 10 page
Entanglement and localization of wavefunctions
We review recent works that relate entanglement of random vectors to their
localization properties. In particular, the linear entropy is related by a
simple expression to the inverse participation ratio, while next orders of the
entropy of entanglement contain information about e.g. the multifractal
exponents. Numerical simulations show that these results can account for the
entanglement present in wavefunctions of physical systems.Comment: 6 pages, 4 figures, to appear in the proceedings of the NATO Advanced
Research Workshop 'Recent Advances in Nonlinear Dynamics and Complex System
Physics', Tashkent, Uzbekistan, 200
Finite geometries and diffractive orbits in isospectral billiards
Several examples of pairs of isospectral planar domains have been produced in
the two-dimensional Euclidean space by various methods. We show that all these
examples rely on the symmetry between points and blocks in finite projective
spaces; from the properties of these spaces, one can derive a relation between
Green functions as well as a relation between diffractive orbits in isospectral
billiards.Comment: 10 page
MRI/TRUS data fusion for brachytherapy
BACKGROUND: Prostate brachytherapy consists in placing radioactive seeds for
tumour destruction under transrectal ultrasound imaging (TRUS) control. It
requires prostate delineation from the images for dose planning. Because
ultrasound imaging is patient- and operator-dependent, we have proposed to fuse
MRI data to TRUS data to make image processing more reliable. The technical
accuracy of this approach has already been evaluated. METHODS: We present work
in progress concerning the evaluation of the approach from the dosimetry
viewpoint. The objective is to determine what impact this system may have on
the treatment of the patient. Dose planning is performed from initial TRUS
prostate contours and evaluated on contours modified by data fusion. RESULTS:
For the eight patients included, we demonstrate that TRUS prostate volume is
most often underestimated and that dose is overestimated in a correlated way.
However, dose constraints are still verified for those eight patients.
CONCLUSIONS: This confirms our initial hypothesis
Crossed Module Bundle Gerbes; Classification, String Group and Differential Geometry
We discuss nonabelian bundle gerbes and their differential geometry using
simplicial methods. Associated to any crossed module there is a simplicial
group NC, the nerve of the 1-category defined by the crossed module and its
geometric realization |NC|. Equivalence classes of principal bundles with
structure group |NC| are shown to be one-to-one with stable equivalence classes
of what we call crossed module gerbes bundle gerbes. We can also associate to a
crossed module a 2-category C'. Then there are two equivalent ways how to view
classifying spaces of NC-bundles and hence of |NC|-bundles and crossed module
bundle gerbes. We can either apply the W-construction to NC or take the nerve
of the 2-category C'. We discuss the string group and string structures from
this point of view. Also a simplicial principal bundle can be equipped with a
simplicial connection and a B-field. It is shown how in the case of a
simplicial principal NC-bundle these simplicial objects give the bundle gerbe
connection and the bundle gerbe B-field
Dielectric resonances of lattice animals and other fractal structures
Electrical and optical properties of binary inhomogeneous media are currently
modelled by a random network of metallic bonds (conductance ,
concentration ) and dielectric bonds (conductance , concentration
). The macroscopic conductivity of this model is analytic in the complex
plane of the dimensionless ratio of the conductances of
both phases, cut along the negative real axis. This cut originates in the
accumulation of the resonances of clusters with any size and shape. We
demonstrate that the dielectric response of an isolated cluster, or a finite
set of clusters, is characterised by a finite spectrum of resonances, occurring
at well-defined negative real values of , and we define the cross-section
which gives a measure of the strength of each resonance. These resonances show
up as narrow peaks with Lorentzian line shapes, e.g. in the weak-dissipation
regime of the model. The resonance frequencies and the corresponding
cross-sections only depend on the underlying lattice, on the geometry of the
clusters, and on their relative positions. Our approach allows an exact
determination of these characteristics. It is applied to several examples of
clusters drawn on the square lattice. Scaling laws are derived analytically,
and checked numerically, for the resonance spectra of linear clusters, of
lattice animals, and of several examples of self-similar fractals.Comment: 25 pages, plain TeX. Figures (hard copies) available upon request, to
appear in the Journal of Physics
AGAPE, an experiment to detect MACHO's in the direction of the Andromeda galaxy
The status of the Agape experiment to detect Machos in the direction of the
andromeda galaxy is presented.Comment: 4 pages, 1 figure in a separate compressed, tarred, uuencoded uufile.
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