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 $Z<2$, which includes weakly bound negative ions and a quantum phase transition at a critical value of $Z$, 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 $v$-representable, i.e., do not correspond to any ground state of a $N$ 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 $S(L = 0)-$state in the $\bar{p}dt$ 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 $\bar{p}dt$ ion against the nuclear $(d,t)-$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