4,762 research outputs found
Two electrons on a hypersphere: a quasi-exactly solvable model
We show that the exact wave function for two electrons, interacting through a
Coulomb potential but constrained to remain on the surface of a
-sphere (), is a polynomial in the
interelectronic distance for a countably infinite set of values of the
radius . A selection of these radii, and the associated energies, are
reported for ground and excited states on the singlet and triplet manifolds. We
conclude that the model bears the greatest similarity to normal
physical systems.Comment: 4 pages, 0 figur
A Multiobjective G.A./Fuzzy Logic augmented flight controller for an F16 aircraft.
An investigation is made in this paper of the pos- sibility of enhancing the performance of controllers of unstable systems while retaining safety critical function. In this case, a General Dynamics F16 fighter is considered in simulation. A fuzzy logic controller is designed and its membership functions tuned by Multiobjective Genetic Algorithms in order to design an augmented flight controller with enhanced manouverability which still retains safety critical operation. The controller is assessed in terms of pilot effort and thus reduction of pilot fatigue. The controller is incorporated into a six degree of freedom real-time flight simulator, and flight tested by a qualified pilot instructor
Thermodynamic Limit and Decoherence: Rigorous Results
Time evolution operator in quantum mechanics can be changed into a
statistical operator by a Wick rotation. This strict relation between
statistical mechanics and quantum evolution can reveal deep results when the
thermodynamic limit is considered. These results translate in a set of theorems
proving that these effects can be effectively at work producing an emerging
classical world without recurring to any external entity that in some cases
cannot be properly defined. In a many-body system has been recently shown that
Gaussian decay of the coherence is the rule with a duration of recurrence more
and more small as the number of particles increases. This effect has been
observed experimentally. More generally, a theorem about coherence of bulk
matter can be proved. All this takes us to the conclusion that a well definite
boundary for the quantum to classical world does exist and that can be drawn by
the thermodynamic limit, extending in this way the deep link between
statistical mechanics and quantum evolution to a high degree.Comment: 5 pages, no figures. Contribution to proceedings of DICE 2006
(Piombino, Italy, September 11-15, 2006
Invariance of the correlation energy at high density and large dimension in two-electron systems
We prove that, in the large-dimension limit, the high-density correlation
energy \Ec of two opposite-spin electrons confined in a -dimensional space
and interacting {\em via} a Coulomb potential is given by \Ec \sim -1/(8D^2)
for any radial confining potential . This result explains the observed
similarity of \Ec in a variety of two-electron systems in three-dimensional
space.Comment: 4 pages, 1 figure, to appear in Phys. Rev. Let
Hole polaron formation and migration in olivine phosphate materials
By combining first principles calculations and experimental XPS measurements,
we investigate the electronic structure of potential Li-ion battery cathode
materials LiMPO4 (M=Mn,Fe,Co,Ni) to uncover the underlying mechanisms that
determine small hole polaron formation and migration. We show that small hole
polaron formation depends on features in the electronic structure near the
valence-band maximum and that, calculationally, these features depend on the
methodology chosen for dealing with the correlated nature of the
transition-metal d-derived states in these systems. Comparison with experiment
reveals that a hybrid functional approach is superior to GGA+U in correctly
reproducing the XPS spectra. Using this approach we find that LiNiPO4 cannot
support small hole polarons, but that the other three compounds can. The
migration barrier is determined mainly by the strong or weak bonding nature of
the states at the top of the valence band, resulting in a substantially higher
barrier for LiMnPO4 than for LiCoPO4 or LiFePO4
Orbital-Free Density Functional Theory: Kinetic Potentials and Ab-Initio Local Pseudopotentials
In the density functional (DF) theory of Kohn and Sham, the kinetic energy of
the ground state of a system of noninteracting electrons in a general external
field is calculated using a set of orbitals. Orbital free methods attempt to
calculate this directly from the electron density by approximating the
universal but unknown kinetic energy density functional. However simple local
approximations are inaccurate and it has proved very difficult to devise
generally accurate nonlocal approximations. We focus instead on the kinetic
potential, the functional derivative of the kinetic energy DF, which appears in
the Euler equation for the electron density. We argue that the kinetic
potential is more local and more amenable to simple physically motivated
approximations in many relevant cases, and describe two pathways by which the
value of the kinetic energy can be efficiently calculated. We propose two
nonlocal orbital free kinetic potentials that reduce to known exact forms for
both slowly varying and rapidly varying perturbations and also reproduce exact
results for the linear response of the density of the homogeneous system to
small perturbations. A simple and systematic approach for generating accurate
and weak ab-initio local pseudopotentials which produce a smooth slowly varying
valence component of the electron density is proposed for use in orbital free
DF calculations of molecules and solids. The use of these local
pseudopotentials further minimizes the possible errors from the kinetic
potentials. Our theory yields results for the total energies and ionization
energies of atoms, and for the shell structure in the atomic radial density
profiles that are in very good agreement with calculations using the full
Kohn-Sham theory.Comment: To be published in Phys. Rev.
Quantum number projection at finite temperature via thermofield dynamics
Applying the thermo field dynamics, we reformulate exact quantum number
projection in the finite-temperature Hartree-Fock-Bogoliubov theory. Explicit
formulae are derived for the simultaneous projection of particle number and
angular momentum, in parallel to the zero-temperature case. We also propose a
practical method for the variation-after-projection calculation, by
approximating entropy without conflict with the Peierls inequality. The quantum
number projection in the finite-temperature mean-field theory will be useful to
study effects of quantum fluctuations associated with the conservation laws on
thermal properties of nuclei.Comment: 27 pages, using revtex4, to be published in PR
Exchange and correlation near the nucleus in density functional theory
The near nucleus behavior of the exchange-correlation potential in Hohenberg-Kohn-Sham density functional theory is investigated. It is
shown that near the nucleus the linear term of of the spherically
averaged exchange-correlation potential is nonzero, and that
it arises purely from the difference between the kinetic energy density at the
nucleus of the interacting system and the noninteracting Kohn-Sham system. An
analytical expression for the linear term is derived. Similar results for the
exchange and correlation potentials are also
obtained separately. It is further pointed out that the linear term in
arising mainly from is rather small, and
therefore has a nearly quadratic structure near the nucleus.
Implications of the results for the construction of the Kohn-Sham system are
discussed with examples.Comment: 10 page
Calculation of the energy spectrum of a two-electron spherical quantum dot
We study the energy spectrum of the two-electron spherical parabolic quantum
dot using the exact Schroedinger, the Hartree-Fock, and the Kohn-Sham
equations. The results obtained by applying the shifted-1/N method are compared
with those obtained by using an accurate numerical technique, showing that the
relative error is reasonably small, although the first method consistently
underestimates the correct values. The approximate ground-state Hartree-Fock
and local-density Kohn-Sham energies, estimated using the shifted-1/N method,
are compared with accurate numerical self-consistent solutions. We make some
perturbative analyses of the exact energy in terms of the confinement strength,
and we propose some interpolation formulae. Similar analysis is made for both
mean-field approximations and interpolation formulae are also proposed for
these exchange-only ground-state cases.Comment: 18 pages, LaTeX, 2 figures-ep
On the effect of Ti on Oxidation Behaviour of a Polycrystalline Nickel-based Superalloy
Titanium is commonly added to nickel superalloys but has a well-documented
detrimental effect on oxidation resistance. The present work constitutes the
first atomistic-scale quantitative measurements of grain boundary and bulk
compositions in the oxide scale of a current generation polycrystalline nickel
superalloy performed through atom probe tomography. Titanium was found to be
particularly detrimental to oxide scale growth through grain boundary
diffusion
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