11,562 research outputs found
Treatments of the exchange energy in density-functional theory
Following a recent work [Gal, Phys. Rev. A 64, 062503 (2001)], a simple
derivation of the density-functional correction of the Hartree-Fock equations,
the Hartree-Fock-Kohn-Sham equations, is presented, completing an integrated
view of quantum mechanical theories, in which the Kohn-Sham equations, the
Hartree-Fock-Kohn-Sham equations and the ground-state Schrodinger equation
formally stem from a common ground: density-functional theory, through its
Euler equation for the ground-state density. Along similar lines, the Kohn-Sham
formulation of the Hartree-Fock approach is also considered. Further, it is
pointed out that the exchange energy of density-functional theory built from
the Kohn-Sham orbitals can be given by degree-two homogeneous N-particle
density functionals (N=1,2,...), forming a sequence of degree-two homogeneous
exchange-energy density functionals, the first element of which is minus the
classical Coulomb-repulsion energy functional.Comment: 19 pages; original manuscript from 2001 (v1) revised for publication,
with presentation substantially improved, some errors corrected, plus an
additional summarizing figure (Appendix B) include
Two-Qubit Separabilities as Piecewise Continuous Functions of Maximal Concurrence
The generic real (b=1) and complex (b=2) two-qubit states are 9-dimensional
and 15-dimensional in nature, respectively. The total volumes of the spaces
they occupy with respect to the Hilbert-Schmidt and Bures metrics are
obtainable as special cases of formulas of Zyczkowski and Sommers. We claim
that if one could determine certain metric-independent 3-dimensional
"eigenvalue-parameterized separability functions" (EPSFs), then these formulas
could be readily modified so as to yield the Hilbert-Schmidt and Bures volumes
occupied by only the separable two-qubit states (and hence associated
separability probabilities). Motivated by analogous earlier analyses of
"diagonal-entry-parameterized separability functions", we further explore the
possibility that such 3-dimensional EPSFs might, in turn, be expressible as
univariate functions of some special relevant variable--which we hypothesize to
be the maximal concurrence (0 < C <1) over spectral orbits. Extensive numerical
results we obtain are rather closely supportive of this hypothesis. Both the
real and complex estimated EPSFs exhibit clearly pronounced jumps of magnitude
roughly 50% at C=1/2, as well as a number of additional matching
discontinuities.Comment: 12 pages, 7 figures, new abstract, revised for J. Phys.
Advances in delimiting the Hilbert-Schmidt separability probability of real two-qubit systems
We seek to derive the probability--expressed in terms of the Hilbert-Schmidt
(Euclidean or flat) metric--that a generic (nine-dimensional) real two-qubit
system is separable, by implementing the well-known Peres-Horodecki test on the
partial transposes (PT's) of the associated 4 x 4 density matrices). But the
full implementation of the test--requiring that the determinant of the PT be
nonnegative for separability to hold--appears to be, at least presently,
computationally intractable. So, we have previously implemented--using the
auxiliary concept of a diagonal-entry-parameterized separability function
(DESF)--the weaker implied test of nonnegativity of the six 2 x 2 principal
minors of the PT. This yielded an exact upper bound on the separability
probability of 1024/{135 pi^2} =0.76854$. Here, we piece together
(reflection-symmetric) results obtained by requiring that each of the four 3 x
3 principal minors of the PT, in turn, be nonnegative, giving an
improved/reduced upper bound of 22/35 = 0.628571. Then, we conclude that a
still further improved upper bound of 1129/2100 = 0.537619 can be found by
similarly piecing together the (reflection-symmetric) results of enforcing the
simultaneous nonnegativity of certain pairs of the four 3 x 3 principal minors.
In deriving our improved upper bounds, we rely repeatedly upon the use of
certain integrals over cubes that arise. Finally, we apply an independence
assumption to a pair of DESF's that comes close to reproducing our numerical
estimate of the true separability function.Comment: 16 pages, 9 figures, a few inadvertent misstatements made near the
end are correcte
A priori probability that a qubit-qutrit pair is separable
We extend to arbitrarily coupled pairs of qubits (two-state quantum systems)
and qutrits (three-state quantum systems) our earlier study (quant-ph/0207181),
which was concerned with the simplest instance of entangled quantum systems,
pairs of qubits. As in that analysis -- again on the basis of numerical
(quasi-Monte Carlo) integration results, but now in a still higher-dimensional
space (35-d vs. 15-d) -- we examine a conjecture that the Bures/SD (statistical
distinguishability) probability that arbitrarily paired qubits and qutrits are
separable (unentangled) has a simple exact value, u/(v Pi^3)= >.00124706, where
u = 2^20 3^3 5 7 and v = 19 23 29 31 37 41 43 (the product of consecutive
primes). This is considerably less than the conjectured value of the Bures/SD
probability, 8/(11 Pi^2) = 0736881, in the qubit-qubit case. Both of these
conjectures, in turn, rely upon ones to the effect that the SD volumes of
separable states assume certain remarkable forms, involving "primorial"
numbers. We also estimate the SD area of the boundary of separable qubit-qutrit
states, and provide preliminary calculations of the Bures/SD probability of
separability in the general qubit-qubit-qubit and qutrit-qutrit cases.Comment: 9 pages, 3 figures, 2 tables, LaTeX, we utilize recent exact
computations of Sommers and Zyczkowski (quant-ph/0304041) of "the Bures
volume of mixed quantum states" to refine our conjecture
On the structure of the body of states with positive partial transpose
We show that the convex set of separable mixed states of the 2 x 2 system is
a body of constant height. This fact is used to prove that the probability to
find a random state to be separable equals 2 times the probability to find a
random boundary state to be separable, provided the random states are generated
uniformly with respect to the Hilbert-Schmidt (Euclidean) distance. An
analogous property holds for the set of positive-partial-transpose states for
an arbitrary bipartite system.Comment: 10 pages, 1 figure; ver. 2 - minor changes, new proof of lemma
On the nucleon-nucleon interaction leading to a standing wave instability in symmetric nuclear matter
We examine a recently proposed nucleon-nucleon interaction, claimed by its
authors both realistic and leading to a standing wave instability in symmetric
nuclear matter. Contrary to these claims, we find that this interaction leads
to a serious overbinding of 4He, 16O and 40Ca nuclei when the Hartree-Fock
method is properly applied. The resulting nuclear densities contradict the
experimental data and all realistic Hartree-Fock results.Comment: 4 pages, 1 figur
Electron corrected Lorentz forces in solids and molecules in magnetic field
We describe the effective Lorentz forces on the ions of a generic insulating
system in an magnetic field, in the context of Born-Oppenheimer ab-initio
molecular dynamics. The force on each ion includes an important contribution of
electronic origin, which depends explicitly on the velocity of all other ions.
It is formulated in terms of a Berry curvature, in a form directly suitable for
future first principles classical dynamics simulations based {\it e.g.,} on
density functional methods. As a preliminary analytical demonstration we
present the dynamics of an H molecule in a field of intermediate strength,
approximately describing the electrons through Slater's variational
wavefunction.Comment: 5 pages, 2 figures; to appear in Phys. Rev.
Hilbert-Schmidt Separability Probabilities and Noninformativity of Priors
The Horodecki family employed the Jaynes maximum-entropy principle, fitting
the mean (b_{1}) of the Bell-CHSH observable (B). This model was extended by
Rajagopal by incorporating the dispersion (\sigma_{1}^2) of the observable, and
by Canosa and Rossignoli, by generalizing the observable (B_{\alpha}). We
further extend the Horodecki one-parameter model in both these manners,
obtaining a three-parameter (b_{1},\sigma_{1}^2,\alpha) two-qubit model, for
which we find a highly interesting/intricate continuum (-\infty < \alpha <
\infty) of Hilbert-Schmidt (HS) separability probabilities -- in which, the
golden ratio is featured. Our model can be contrasted with the three-parameter
(b_{q}, \sigma_{q}^2,q) one of Abe and Rajagopal, which employs a
q(Tsallis)-parameter rather than , and has simply q-invariant HS
separability probabilities of 1/2. Our results emerge in a study initially
focused on embedding certain information metrics over the two-level quantum
systems into a q-framework. We find evidence that Srednicki's recently-stated
biasedness criterion for noninformative priors yields rankings of priors fully
consistent with an information-theoretic test of Clarke, previously applied to
quantum systems by Slater.Comment: 26 pages, 12 figure
On Metric Dimension of Functigraphs
The \emph{metric dimension} of a graph , denoted by , is the
minimum number of vertices such that each vertex is uniquely determined by its
distances to the chosen vertices. Let and be disjoint copies of a
graph and let be a function. Then a
\emph{functigraph} has the vertex set
and the edge set . We study how
metric dimension behaves in passing from to by first showing that
, if is a connected graph of order
and is any function. We further investigate the metric dimension of
functigraphs on complete graphs and on cycles.Comment: 10 pages, 7 figure
Spin-dependent transport in molecular tunnel junctions
We present measurements of magnetic tunnel junctions made using a
self-assembled-monolayer molecular barrier. Ni/octanethiol/Ni samples were
fabricated in a nanopore geometry. The devices exhibit significant changes in
resistance as the angle between the magnetic moments in the two electrodes is
varied, demonstrating that low-energy electrons can traverse the molecular
barrier while maintaining spin coherence. An analysis of the voltage and
temperature dependence of the data suggests that the spin-coherent transport
signals can be degraded by localized states in the molecular barriers.Comment: 4 pages, 5 color figure
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