6,723 research outputs found
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
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
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
Two scenarios for quantum multifractality breakdown
We expose two scenarios for the breakdown of quantum multifractality under
the effect of perturbations. In the first scenario, multifractality survives
below a certain scale of the quantum fluctuations. In the other one, the
fluctuations of the wave functions are changed at every scale and each
multifractal dimension smoothly goes to the ergodic value. We use as generic
examples a one-dimensional dynamical system and the three-dimensional Anderson
model at the metal-insulator transition. Based on our results, we conjecture
that the sensitivity of quantum multifractality to perturbation is universal in
the sense that it follows one of these two scenarios depending on the
perturbation. We also discuss the experimental implications.Comment: 5 pages, 4 figures, minor modifications, published versio
Multifractality of quantum wave functions in the presence of perturbations
We present a comprehensive study of the destruction of quantum
multifractality in the presence of perturbations. We study diverse
representative models displaying multifractality, including a pseudointegrable
system, the Anderson model and a random matrix model. We apply several types of
natural perturbations which can be relevant for experimental implementations.
We construct an analytical theory for certain cases, and perform extensive
large-scale numerical simulations in other cases. The data are analyzed through
refined methods including double scaling analysis. Our results confirm the
recent conjecture that multifractality breaks down following two scenarios. In
the first one, multifractality is preserved unchanged below a certain
characteristic length which decreases with perturbation strength. In the second
one, multifractality is affected at all scales and disappears uniformly for a
strong enough perturbation. Our refined analysis shows that subtle variants of
these scenarios can be present in certain cases. This study could guide
experimental implementations in order to observe quantum multifractality in
real systems.Comment: 20 pages, 27 figure
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
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
Retrieving Nuclear Information from Protons Propagating through A Thick Target
The multiple scattering of high-energy particles in a thick target is
fromulated in an impact parameter representation. A formalism similar but not
identical to that of Moliere is obtained. We show that calculations of particle
beam broadening due to multiple Coulomb scattering alone can be given in closed
form. The focus of this study is on whether or not the broadening of the
Coulomb angular distribution prevents the retrieval of nuclear-interaction
information from mesauring the angular distributions of charged partiles
scattered from a thick target. For this purpose, we study multiple scatterings
with both the nuclear and Coulomb interactions included and we do not make a
small-angle expansion. Condition for retrieving nuclear infomration from
high-energy protons propagating through a block of material are obtained.Comment: 29 pages, 13 figure
Ferromagnetic (Ga,Mn)N epilayers versus antiferromagnetic GaMnN clusters
Mn-doped wurtzite GaN epilayers have been grown by nitrogen plasma-assisted
molecular beam epitaxy. Correlated SIMS, structural and magnetic measurements
show that the incorporation of Mn strongly depends on the conditions of the
growth. Hysteresis loops which persist at high temperature do not appear to be
correlated to the presence of Mn. Samples with up to 2% Mn are purely
substitutional GaMnN epilayers, and exhibit paramagnetic
properties. At higher Mn contents, precipitates are formed which are identified
as GaMnN clusters by x-ray diffraction and absorption: this induces a
decrease of the paramagnetic magnetisation. Samples co-doped with enough Mg
exhibit a new feature: a ferromagnetic component is observed up to
K, which cannot be related to superparamagnetism of unresolved magnetic
precipitates.Comment: Revised versio
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