14 research outputs found
Density functional theory in one-dimension for contact-interacting fermions
A density functional theory is developed for fermions in one dimension,
interacting via a delta-function. Such systems provide a natural testing ground
for questions of principle, as the local density approximation should work well
for short-ranged interactions. The exact-exchange contribution to the total
energy is a local functional of the density. A local density approximation for
correlation is obtained using perturbation theory and Bethe-Ansatz results for
the one-dimensional contact-interacting uniform Fermi gas. The ground-state
energies are calculated for two finite systems, the analogs of Helium and of
Hooke's atom. The local approximation is shown to be excellent, as expected.Comment: 10 pages, 7 Figure
Computational Nuclear Physics and Post Hartree-Fock Methods
We present a computational approach to infinite nuclear matter employing
Hartree-Fock theory, many-body perturbation theory and coupled cluster theory.
These lectures are closely linked with those of chapters 9, 10 and 11 and serve
as input for the correlation functions employed in Monte Carlo calculations in
chapter 9, the in-medium similarity renormalization group theory of dense
fermionic systems of chapter 10 and the Green's function approach in chapter
11. We provide extensive code examples and benchmark calculations, allowing
thereby an eventual reader to start writing her/his own codes. We start with an
object-oriented serial code and end with discussions on strategies for porting
the code to present and planned high-performance computing facilities.Comment: 82 pages, to appear in Lecture Notes in Physics (Springer), "An
advanced course in computational nuclear physics: Bridging the scales from
quarks to neutron stars", M. Hjorth-Jensen, M. P. Lombardo, U. van Kolck,
Editor
Self-consistent Green's function approaches
We present the fundamental techniques and working equations of many-body
Green's function theory for calculating ground state properties and the
spectral strength. Green's function methods closely relate to other polynomial
scaling approaches discussed in chapters 8 and 10. However, here we aim
directly at a global view of the many-fermion structure. We derive the working
equations for calculating many-body propagators, using both the Algebraic
Diagrammatic Construction technique and the self-consistent formalism at finite
temperature. Their implementation is discussed, as well as the inclusion of
three-nucleon interactions. The self-consistency feature is essential to
guarantee thermodynamic consistency. The pairing and neutron matter models
introduced in previous chapters are solved and compared with the other methods
in this book.Comment: 58 pages, 14 figures, Submitted to Lect. Notes Phys., "An advanced
course in computational nuclear physics: Bridging the scales from quarks to
neutron stars", M. Hjorth-Jensen, M. P. Lombardo, U. van Kolck, Editor
Quantum Vacuum Experiments Using High Intensity Lasers
The quantum vacuum constitutes a fascinating medium of study, in particular
since near-future laser facilities will be able to probe the nonlinear nature
of this vacuum. There has been a large number of proposed tests of the
low-energy, high intensity regime of quantum electrodynamics (QED) where the
nonlinear aspects of the electromagnetic vacuum comes into play, and we will
here give a short description of some of these. Such studies can shed light,
not only on the validity of QED, but also on certain aspects of nonperturbative
effects, and thus also give insights for quantum field theories in general.Comment: 9 pages, 8 figur