32 research outputs found
Time-dependent Internal DFT formalism and Kohn-Sham scheme
We generalize to the time-dependent case the stationary Internal DFT /
Kohn-Sham formalism presented in Ref. [14]. We prove that, in the
time-dependent case, the internal properties of a self-bound system (as an
atomic nuclei) are all defined by the internal one-body density and the initial
state. We set-up a time-dependent Internal Kohn-Sham scheme as a practical way
to compute the internal density. The main difference with the traditional DFT /
Kohn-Sham formalism is the inclusion of the center-of-mass correlations in the
functional.Comment: 13 pages. To be published in Phys. Rev.
Polarizibilities as a test of localized approximations to the self-interaction correction
We present applications of the recently introduced ``Generalized SIC-Slater''
scheme which provides a simple Self-Interaction Correction approximation in the
framework of the Optimized Effective Potential. We focus on the computation of
static polarizabilities which are known to constitute stringent tests for
Density Functional Theory. We apply the new method to model H chains, but also
to more realistic systems such as C4 (organic) chains, and less symmetrical
systems such as a Na5 (metallic) cluster. Comparison is made with other SIC
schemes, especially with the standard SIC-Slater one.Comment: 17 pages, 4 figures, 49 reference
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
Time-dependent density-functional theory with self-interaction correction
We discuss an extension of time-dependent density-functional theory by a
self-interaction correction (SIC). A strictly variational formulation is given
taking care of the necessary constraints. A manageable and transparent
propagation scheme using two sets of wavefunctions is proposed and applied to
laser excitation with subsequent ionization of a dimer molecule.Comment: 4 pages, 1 figur
Improved Slater approximation to SIC-OEP
We propose a simplification of the Optimized Effective Potential (OEP)
applied to the Self Interaction Correction (SIC) scheme of Density Functional
Theory (DFT). The new scheme fulfills several key formal properties and turns
out to be both simple and accurate. We show examples of applications on model
molecules in terms of observables known to be especially sensitive to details
of the SIC-OEP approach.Comment: 3 figure
The nuclear energy density functional formalism
The present document focuses on the theoretical foundations of the nuclear
energy density functional (EDF) method. As such, it does not aim at reviewing
the status of the field, at covering all possible ramifications of the approach
or at presenting recent achievements and applications. The objective is to
provide a modern account of the nuclear EDF formalism that is at variance with
traditional presentations that rely, at one point or another, on a {\it
Hamiltonian-based} picture. The latter is not general enough to encompass what
the nuclear EDF method represents as of today. Specifically, the traditional
Hamiltonian-based picture does not allow one to grasp the difficulties
associated with the fact that currently available parametrizations of the
energy kernel at play in the method do not derive from a genuine
Hamilton operator, would the latter be effective. The method is formulated from
the outset through the most general multi-reference, i.e. beyond mean-field,
implementation such that the single-reference, i.e. "mean-field", derives as a
particular case. As such, a key point of the presentation provided here is to
demonstrate that the multi-reference EDF method can indeed be formulated in a
{\it mathematically} meaningful fashion even if does {\it not} derive
from a genuine Hamilton operator. In particular, the restoration of symmetries
can be entirely formulated without making {\it any} reference to a projected
state, i.e. within a genuine EDF framework. However, and as is illustrated in
the present document, a mathematically meaningful formulation does not
guarantee that the formalism is sound from a {\it physical} standpoint. The
price at which the latter can be enforced as well in the future is eventually
alluded to.Comment: 64 pages, 8 figures, submitted to Euroschool Lecture Notes in Physics
Vol.IV, Christoph Scheidenberger and Marek Pfutzner editor