21 research outputs found
Exact first-order effect of interactions on the ground-state energy of harmonically-confined fermions
We consider a system of spinless fermions, interacting with each other
via a power-law interaction , and trapped in an external harmonic
potential , in dimensions. For any , we
obtain the ground-state energy of the system perturbatively in
, . We calculate
exactly, assuming that is such that the "outer
shell" is filled. For the case of a Coulomb interaction , we extract the
behavior of , focusing on the corrections to
the exchange term with respect to the leading-order term that is predicted from
the local density approximation applied to the Thomas-Fermi approximate density
distribution. The leading correction contains a logarithmic divergence, and is
of particular importance in the context of density functional theory. We also
study the effect of the interactions on the fermions' spatial density. Finally,
we find that our result for significantly simplifies
in the case where is even.Comment: 39 pages, 5 figure
Leading correction to the local density approximation for exchange in large- atoms
The large- asymptotic expansion of atomic exchange energies has been
useful in determining exact conditions for corrections to the local density
approximation in density functional theory. We find that the necessary
correction is fit well with a leading term, and find its coefficient
numerically. The gradient expansion approximation also displays such a term,
but with a substantially smaller coefficient. Analytic results in the limit of
vanishing interaction with hydrogenic orbitals (a Bohr atom) are given, leading
to the conjecture that the true coefficients for all atoms are precisely 2.7
times larger than their gradient expansion counterpart. Combined with the
hydrogen atom result, this yields an analytic expression for the
exchange-energy correction which is accurate to for all .Comment: 7 pages, 3 figure
Investigations of the exchange energy of neutral atoms in the large-Z limit
The non-relativistic large- expansion of the exchange energy of neutral
atoms provides an important input to modern non-empirical density functional
approximations. Recent works report results of fitting the terms beyond the
dominant term, given by the local density approximation (LDA), leading to an
anomalous ZlnZ term that can not be predicted from naive scaling arguments.
Here, we provide much more detailed data analysis of the mostly smooth
asymptotic trend describing the difference between exact and LDA exchange
energy, the nature of oscillations across rows of the periodic table, and the
behavior of the LDA contribution itself. Special emphasis is given to the
successes and difficulties in reproducing the exchange energy and its
asymptotics with existing density functional approximations.Comment: 15 pages 11 figures + 4 pages supplemental informatio
Thermodynamics as an alternative foundation for zero-temperature density functional theory and spin density functional theory
Thermodynamics provides a transparent definition of the free energy of
density functional theory (DFT), and of its derivatives - the potentials, at
finite temperatures T. By taking the T to 0 limit, it is shown here that both
DFT and spin-dependent DFT (for ground states) suffer from precisely the same
benign ambiguities: (a) charge and spin quantization lead to "up to a constant"
indeterminacies in the potential and the magnetic field respectively, and (b)
the potential in empty subspaces is undetermined but irrelevant. Surprisingly,
these simple facts were inaccessible within the standard formulation, leading
to recent discussions of apparent difficulties within spin-DFT.Comment: RevTeX, to appear in Phys. Rev.
Nonequilibrium Josephson-like effects in wide mesoscopic S-N-S junctions
Mesoscopic superconducting-normal-metal-superconducting (S-N-S) junctions
with a large separation between the superconducting electrodes (i.e. wide
junctions) exhibit nonequilibrium supercurrents, even at temperatures for which
the equilibrium Josephson effect is exponentially small. The second harmonic of
the Josephson frequency dominates these currents, as observed in recent
experiments. A simple description of these effects, in the spirit of the
Resistively-Shunted-Junction model, is suggested here. It is used to calculate
dc I-V characteristics, and to examine the effects of various types of noise
and of external microwave radiation (Shapiro steps). It is found that the
nonequilibrium supercurrents are excited when the junction is driven by a dc
bias or an ac bias, or even by external noise. In the case of junctions which
are also long in the direction perpendicular to the current flow, thermodynamic
phase fluctuations (thermal noise) alone can drive the quasiparticles out of
local equilibrium. Magnetic flux is then predicted to be trapped in units of
Phi_0 /2 = hc/4e.Comment: 10 pages, to appear in a special issue of Superlattices &
Microstructure