40 research outputs found
An analysis of the field theoretic approach to the quasi-continuum method
Using the orbital-free density functional theory as a model theory, we
present an analysis of the field theoretic approach to quasi-continuum method.
In particular, by perturbation method and multiple scale analysis, we provide a
formal justification for the validity of the coarse-graining of various fields,
which is central to the quasi-continuum reduction of field theories. Further,
we derive the homogenized equations that govern the behavior of electronic
fields in regions of smooth deformations. Using Fourier analysis, we determine
the far-field solutions for these fields in the presence of local defects, and
subsequently estimate cell-size effects in computed defect energies.Comment: 26 pages, 1 figur
Existence of global-in-time solutions to a generalized Dirac-Fock type evolution equation
We consider a generalized Dirac-Fock type evolution equation deduced from
no-photon Quantum Electrodynamics, which describes the self-consistent
time-evolution of relativistic electrons, the observable ones as well as those
filling up the Dirac sea. This equation has been originally introduced by Dirac
in 1934 in a simplified form. Since we work in a Hartree-Fock type
approximation, the elements describing the physical state of the electrons are
infinite rank projectors. Using the Bogoliubov-Dirac-Fock formalism, introduced
by Chaix-Iracane ({\it J. Phys. B.}, 22, 3791--3814, 1989), and recently
established by Hainzl-Lewin-Sere, we prove the existence of global-in-time
solutions of the considered evolution equation.Comment: 12 pages; more explanations added, some final (minor) corrections
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