86 research outputs found
Non-perturbative embedding of local defects in crystalline materials
We present a new variational model for computing the electronic first-order
density matrix of a crystalline material in presence of a local defect. A
natural way to obtain variational discretizations of this model is to expand
the difference Q between the density matrix of the defective crystal and the
density matrix of the perfect crystal, in a basis of precomputed maximally
localized Wannier functions of the reference perfect crystal. This approach can
be used within any semi-empirical or Density Functional Theory framework.Comment: 13 pages, 4 figure
First report of Rice yellow mottle virus on rice in the Democratic Republic of Congo
International audienc
A Minimization Method for Relativistic Electrons in a Mean-Field Approximation of Quantum Electrodynamics
We study a mean-field relativistic model which is able to describe both the
behavior of finitely many spin-1/2 particles like electrons and of the Dirac
sea which is self-consistently polarized in the presence of the real particles.
The model is derived from the QED Hamiltonian in Coulomb gauge neglecting the
photon field. All our results are non-perturbative and mathematically rigorous.Comment: 18 pages, 3 figure
Renormalization and asymptotic expansion of Dirac's polarized vacuum
We perform rigorously the charge renormalization of the so-called reduced
Bogoliubov-Dirac-Fock (rBDF) model. This nonlinear theory, based on the Dirac
operator, describes atoms and molecules while taking into account vacuum
polarization effects. We consider the total physical density including both the
external density of a nucleus and the self-consistent polarization of the Dirac
sea, but no `real' electron. We show that it admits an asymptotic expansion to
any order in powers of the physical coupling constant \alphaph, provided that
the ultraviolet cut-off behaves as \Lambda\sim e^{3\pi(1-Z_3)/2\alphaph}\gg1.
The renormalization parameter $
Self-consistent solution for the polarized vacuum in a no-photon QED model
We study the Bogoliubov-Dirac-Fock model introduced by Chaix and Iracane
({\it J. Phys. B.}, 22, 3791--3814, 1989) which is a mean-field theory deduced
from no-photon QED. The associated functional is bounded from below. In the
presence of an external field, a minimizer, if it exists, is interpreted as the
polarized vacuum and it solves a self-consistent equation.
In a recent paper math-ph/0403005, we proved the convergence of the iterative
fixed-point scheme naturally associated with this equation to a global
minimizer of the BDF functional, under some restrictive conditions on the
external potential, the ultraviolet cut-off and the bare fine
structure constant . In the present work, we improve this result by
showing the existence of the minimizer by a variational method, for any cut-off
and without any constraint on the external field.
We also study the behaviour of the minimizer as goes to infinity
and show that the theory is "nullified" in that limit, as predicted first by
Landau: the vacuum totally kills the external potential. Therefore the limit
case of an infinite cut-off makes no sense both from a physical and
mathematical point of view.
Finally, we perform a charge and density renormalization scheme applying
simultaneously to all orders of the fine structure constant , on a
simplified model where the exchange term is neglected.Comment: Final version, to appear in J. Phys. A: Math. Ge
Construction of the Pauli-Villars-regulated Dirac vacuum in electromagnetic fields
Using the Pauli-Villars regularization and arguments from convex analysis, we
construct solutions to the classical time-independent Maxwell equations in
Dirac's vacuum, in the presence of small external electromagnetic sources. The
vacuum is not an empty space, but rather a quantum fluctuating medium which
behaves as a nonlinear polarizable material. Its behavior is described by a
Dirac equation involving infinitely many particles. The quantum corrections to
the usual Maxwell equations are nonlinear and nonlocal. Even if photons are
described by a purely classical electromagnetic field, the resulting vacuum
polarization coincides to first order with that of full Quantum
Electrodynamics.Comment: Final version to appear in Arch. Rat. Mech. Analysi
Exploiting Distance Technology to Foster Experimental Design as a Neglected Learning Objective in Labwork in Chemistry
This article deals with the design process of a remote laboratory for labwork in chemistry. In particular, it focuses on the mutual dependency of theoretical conjectures about learning in the experimental sciences and technological opportunities in creating learning environments. The design process involves a detailed analysis of the expert task and knowledge, e.g., spectrophotometry as a method for the determination of the concentration of a compound in a solution. In so doing, modifications in transposing tasks and knowledge to the learning situation can be monitored. The remote laboratory is described, as well as the specific features that alter the degree of fidelity of the learning situation in comparison to the expert one. It is conjectured that these alterations might represent actual benefits for learning
The relationship between students' views of the nature of science and their views of the nature of scientific measurement
The present study explores the relationship between studentsâ views on the nature of science (NOS) and their views of the nature of scientific measurement. A questionnaire with two-tier diagnostic multiple choice items on both the NOS and measurement was administered to 179 first year physics students with diverse school experiences. Studentsâ views on the NOS were classified into four âNOS profilesâ and views on measurement were classified according to either the point or set paradigms. The findings show that students with a NOS profile which is dominated by a belief that the laws of nature are to be discovered by scientists, are more likely to have a view of the nature of scientific measurement characterised by a belief in âtrueâ values. On the other hand, students who believe that scientific theories are inventions of scientists, constructed from observations which are then validated through further experimentation, are more likely to have a view of the nature of scientific measurement which is underpinned by the uncertain nature of scientific evidence. The implications for teaching scientific measurement at tertiary level are discussed
Ground State and Charge Renormalization in a Nonlinear Model of Relativistic Atoms
We study the reduced Bogoliubov-Dirac-Fock (BDF) energy which allows to
describe relativistic electrons interacting with the Dirac sea, in an external
electrostatic potential. The model can be seen as a mean-field approximation of
Quantum Electrodynamics (QED) where photons and the so-called exchange term are
neglected. A state of the system is described by its one-body density matrix,
an infinite rank self-adjoint operator which is a compact perturbation of the
negative spectral projector of the free Dirac operator (the Dirac sea).
We study the minimization of the reduced BDF energy under a charge
constraint. We prove the existence of minimizers for a large range of values of
the charge, and any positive value of the coupling constant . Our
result covers neutral and positively charged molecules, provided that the
positive charge is not large enough to create electron-positron pairs. We also
prove that the density of any minimizer is an function and compute the
effective charge of the system, recovering the usual renormalization of charge:
the physical coupling constant is related to by the formula
, where
is the ultraviolet cut-off. We eventually prove an estimate on the
highest number of electrons which can be bound by a nucleus of charge . In
the nonrelativistic limit, we obtain that this number is , recovering
a result of Lieb.
This work is based on a series of papers by Hainzl, Lewin, Sere and Solovej
on the mean-field approximation of no-photon QED.Comment: 37 pages, 1 figur
The Relationship between Studentsâ Views of the Nature of Science and their Views of the Nature of Scientific Measurement
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