1,116 research outputs found
Energy Density Functionals From the Strong-Coupling Limit Applied to the Anions of the He Isoelectronic Series
Anions and radicals are important for many applications including
environmental chemistry, semiconductors, and charge transfer, but are poorly
described by the available approximate energy density functionals. Here we test
an approximate exchange-correlation functional based on the exact
strong-coupling limit of the Hohenberg-Kohn functional on the prototypical case
of the He isoelectronic series with varying nuclear charge , which
includes weakly bound negative ions and a quantum phase transition at a
critical value of , representing a big challenge for density functional
theory. We use accurate wavefunction calculations to validate our results,
comparing energies and Kohn-Sham potentials, thus also providing useful
reference data close to and at the quantum phase transition. We show that our
functional is able to bind H and to capture in general the physics of
loosely bound anions, with a tendency to strongly overbind that can be proven
mathematically. We also include corrections based on the uniform electron gas
which improve the results.Comment: Accepted for the JCP Special Topic Issue "Advances in DFT
Methodology
Jastrow correlation factor for atoms, molecules, and solids
A form of Jastrow factor is introduced for use in quantum Monte Carlo
simulations of finite and periodic systems. Test data are presented for atoms,
molecules, and solids, including both all-electron and pseudopotential atoms.
We demonstrate that our Jastrow factor is able to retrieve a large fraction of
the correlation energy
Low-energy general relativity with torsion: a systematic derivative expansion
We attempt to build systematically the low-energy effective Lagrangian for
the Einstein--Cartan formulation of gravity theory that generally includes the
torsion field. We list all invariant action terms in certain given order; some
of the invariants are new. We show that in the leading order the fermion action
with torsion possesses additional U(1)_L x U(1)_R gauge symmetry, with 4+4
components of the torsion (out of the general 24) playing the role of Abelian
gauge bosons. The bosonic action quadratic in torsion gives masses to those
gauge bosons. Integrating out torsion one obtains a point-like 4-fermion action
of a general form containing vector-vector, axial-vector and axial-axial
interactions. We present a quantum field-theoretic method to average the
4-fermion interaction over the fermion medium, and perform the explicit
averaging for free fermions with given chemical potential and temperature. The
result is different from that following from the "spin fluid" approach used
previously. On the whole, we arrive to rather pessimistic conclusions on the
possibility to observe effects of the torsion-induced 4-fermion interaction,
although under certain circumstances it may have cosmological consequences.Comment: 33 pages, 1 figure. A new section, discussion and references added.
Final (published) versio
On the relation between the Hartree-Fock and Kohn-Sham approaches
We show that the Hartree-Fock (HF) results cannot be reproduced within the
framework of Kohn-Sham (KS) theory because the single-particle densities of
finite systems obtained within the HF calculations are not -representable,
i.e., do not correspond to any ground state of a non-interacting electron
systems in a local external potential. For this reason, the KS theory, which
finds a minimum on a different subset of all densities, can overestimate the
ground state energy, as compared to the HF result. The discrepancy between the
two approaches provides no grounds to assume that either the KS theory or the
density functional theory suffers from internal contradictions.Comment: 7 pages, ReVtex, revised and accepted by Physics Letters
Proper time and path integral representations for the commutation function
On the example of the quantized spinor field, interacting with arbitrary
external electromagnetic field, the commutation function is studied. It is
shown that a proper time representation is available in any dimensions. Using
it, all the light cone singularities of the function are found explicitly,
generalizing the Fock formula in four dimensions, and a path integral
representation is constructed.Comment: 20 pages, LaTeX, uses pictex macro
Operational indistinguishably of varying speed of light theories
The varying speed of light theories have been recently proposed to solve the
standard model problems and anomalies in the ultra high energy cosmic rays.
These theories try to formulate a new relativity with no assumptions about the
constancy of the light speed. In this regard, we study two theories and want to
show that these theories are not the new theories of relativity, but only
re-descriptions of Einstein's special relativity.Comment: 5 pages, 2 figures, title changed, minor changes in notations and
formulae, a paragraph added, Int. J. Mod. Phys. D (in press) v
On the bound state of the antiproton-deuterium-tritium ion
The properties of the weakly-bound state in the ion
are investigated with the use of the results of highly accurate computations.
The hyperfine structure splitting of this ion is investigated. We also evaluate
the life-time of the ion against the nuclear fusion and
discuss a possibility to evaluate the corresponding annihilation rate(s)
Space-time in light of Karolyhazy uncertainty relation
General relativity and quantum mechanics provide a natural explanation for
the existence of dark energy with its observed value and predict its dynamics.
Dark energy proves to be necessary for the existence of space-time itself and
determines the rate of its stability.Comment: 5 pages, Two misprints are correcte
The two-dimensional hydrogen atom revisited
The bound state energy eigenvalues for the two-dimensional Kepler problem are
found to be degenerate. This "accidental" degeneracy is due to the existence of
a two-dimensional analogue of the quantum-mechanical Runge-Lenz vector.
Reformulating the problem in momentum space leads to an integral form of the
Schroedinger equation. This equation is solved by projecting the
two-dimensional momentum space onto the surface of a three-dimensional sphere.
The eigenfunctions are then expanded in terms of spherical harmonics, and this
leads to an integral relation in terms of special functions which has not
previously been tabulated. The dynamical symmetry of the problem is also
considered, and it is shown that the two components of the Runge-Lenz vector in
real space correspond to the generators of infinitesimal rotations about the
respective coordinate axes in momentum space.Comment: 10 pages, no figures, RevTex
Localization of Classical Waves in Weakly Scattering Two-Dimensional Media with Anisotropic Disorder
We study the localization of classical waves in weakly scattering 2D systems
with anisotropic disorder. The analysis is based on a perturbative
path-integral technique combined with a spectral filtering that accounts for
the first-order Bragg scattering only. It is shown that in the long-wavelength
limit the radiation is always localized, and the localization length is
independent of the direction of propagation, the latter in contrast to the
predictions based on an anisotropic tight-binding model. For shorter
wavelengths that are comparable to the correlation scales of the disorder, the
transport properties of disordered media are essentially different in the
directions along and across the correlation ellipse. There exists a
frequency-dependent critical value of the anisotropy parameter, below which
waves are localized at all angles of propagation. Above this critical value,
the radiation is localized only within some angular sectors centered at the
short axis of the correlation ellipse and is extended in other directions.Comment: 10 pages, 5 figure
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