Kinetic energy density functionals from the Airy gas, with an application to the atomization kinetic energies of molecules

We construct and study several semilocal density functional approximations for the positive Kohn-Sham kinetic energy density. These functionals fit the kinetic energy density of the Airy gas and they can be accurate for integrated kinetic energies of atoms, molecules, jellium clusters and jellium surfaces. We find that these functionals are the most accurate ones for atomization kinetic energies of molecules and for fragmentation of jellium clusters. We also report that local and semilocal kinetic energy functionals can show "binding" when the density of a spin unrestricted Kohn-Sham calculation is used.Comment: 7 pages, 7 figure

Laplacian-level density functionals for the kinetic energy density and exchange-correlation energy

We construct a Laplacian-level meta-generalized gradient approximation (meta-GGA) for the non-interacting (Kohn-Sham orbital) positive kinetic energy density $\tau$ of an electronic ground state of density $n$. This meta-GGA is designed to recover the fourth-order gradient expansion $\tau^{GE4}$ in the appropiate slowly-varying limit and the von Weizs\"{a}cker expression $\tau^{W}=|\nabla n|^2/(8n)$ in the rapidly-varying limit. It is constrained to satisfy the rigorous lower bound $\tau^{W}(\mathbf{r})\leq\tau(\mathbf{r})$. Our meta-GGA is typically a strong improvement over the gradient expansion of $\tau$ for atoms, spherical jellium clusters, jellium surfaces, the Airy gas, Hooke's atom, one-electron Gaussian density, quasi-two dimensional electron gas, and nonuniformly-scaled hydrogen atom. We also construct a Laplacian-level meta-GGA for exchange and correlation by employing our approximate $\tau$ in the Tao, Perdew, Staroverov and Scuseria (TPSS) meta-GGA density functional. The Laplacian-level TPSS gives almost the same exchange-correlation enhancement factors and energies as the full TPSS, suggesting that $\tau$ and $\nabla^2 n$ carry about the same information beyond that carried by $n$ and $\nabla n$. Our kinetic energy density integrates to an orbital-free kinetic energy functional that is about as accurate as the fourth-order gradient expansion for many real densities (with noticeable improvement in molecular atomization energies), but considerably more accurate for rapidly-varying ones.Comment: 9 pages, 16 figure

Influence of the Magnetic Field on the Fermion Scattering off Bubble and Kink Walls

We investigate the scattering of fermions off domain walls at the electroweak phase transition in presence of a magnetic field. We consider both the bubble wall and the kink domain wall. We derive and solve the Dirac equation for fermions with momentum perpendicular to the walls, and compute the transmission and reflection coefficients. In the case of kink domain wall, we briefly discuss the zero mode solutions localized on the wall. The possibile role of the magnetic field for the electroweak baryogenesis is also discussed.Comment: 11 pages and 3 eps figure

Nucleon distribution in nuclei beyond \beta-stability line

The radii of nucleon distribution, bulk density, and neutron skin in nuclei beyond the \beta-stability line are studied within the direct variational method. We evaluate the partial equation of state of finite nuclei and demonstrate that the bulk density decreases beyond the beta stability line. We show that the growth of the neutron skin in unstable nuclei does not obey the saturation condition because of the polarization effect. The value of the neutron-skin thickness \Delta r_{np}=\sqrt{}-\sqrt{} is caused by the different radii (skin effect) and only slightly by the different shapes (halo effect) of neutron and proton distributions. The relative contribution of both effects depends on the competition between the symmetry energy, and the spin-orbit and Coulomb interactions. The calculations of the isovector shift of the nuclear radius \Delta r_{np} show its primarily linear dependence on the asymmetry parameter X=(N-Z)/A.Comment: 20 pages, 9 figures, published in Phys. Rev. C. arXiv admin note: text overlap with arXiv:1010.510

Time-Dependent Density-Functional Theory for Trapped Strongly-Interacting Fermionic Atoms

The dynamics of strongly interacting trapped dilute Fermi gases (dilute in the sense that the range of interatomic potential is small compared with inter-particle spacing) is investigated in a single-equation approach to the time-dependent density-functional theory. Our results are in good agreement with recent experimental data in the BCS-BEC crossover regime. It is also shown that the calculated corrections to the hydrodynamic approximation may be important even for systems with a rather large number of atoms.Comment: Resubmitted to PRA in response to referee's comments. Abstract is changed. Added new figure

Phase Structure and Nonperturbative States in Three-Dimensional Adjoint Higgs Model

The thermodynamics of 3d adjoint Higgs model is considered. We study the properties of the Polyakov loop correlators and the critical behavior at the deconfinement phase transition. Our main tool is a reduction to the 2d sine-Gordon model. The Polyakov loops appear to be connected with the soliton operators in it. The known exact results in the sine-Gordon theory allow us to study in detail the temperature dependence of the string tension, as well as to get some information about a nonperturbative dynamics in the confinement phase. We also consider the symmetry restoration at high temperature which makes it possible to construct the phase diagram of the model completely.Comment: 15pp., Revtex; 4 figures; replaced by a version to be published in Phys. Rev.

Testing White Dwarf Crystallization Theory with Asteroseismology of the Massive Pulsating DA Star BPM 37093

It was predicted more than 40 years ago that the cores of the coolest white dwarf stars should eventually crystallize. This effect is one of the largest sources of uncertainty in white dwarf cooling models, which are now routinely used to estimate the ages of stellar populations in both the Galactic disk and the halo. We are attempting to minimize this source of uncertainty by calibrating the models, using observations of pulsating white dwarfs. In a typical mass white dwarf model, crystallization does not begin until the surface temperature reaches 6000-8000 K. In more massive white dwarf models the effect begins at higher surface temperatures, where pulsations are observed in the ZZ Ceti (DAV) stars. We use the observed pulsation periods of BPM 37093, the most massive DAV white dwarf presently known, to probe the interior and determine the size of the crystallized core empirically. Our initial exploration of the models strongly suggests the presence of a solid core containing about 90% of the stellar mass, which is consistent with our theoretical expectations.Comment: minor changes for length, accepted for ApJ Letter

Astroparticle Physics: Puzzles and Discoveries

Puzzles often give birth to the great discoveries, the false discoveries sometimes stimulate the exiting ideas in theoretical physics. The historical examples of both are described in Introduction and in section ``Cosmological Puzzles''. From existing puzzles most attention is given to Ultra High Energy Cosmic Ray (UHECR) puzzle and to cosmological constant problem. The 40-years old UHECR problem consisted in absence of the sharp steepening in spectrum of extragalactic cosmic rays caused by interaction with CMB radiation. This steepening is known as Greisen-Zatsepin-Kuzmin (GZK) cutoff. It is demonstrated here that the features of interaction of cosmic ray protons with CMB are seen now in the spectrum in the form of the dip and beginning of the GZK cutoff. The most serious cosmological problem is caused by large vacuum energy of the known elementary-particle fields which exceeds at least by 45 orders of magnitude the cosmological vacuum energy. The various ideas put forward to solve this problem during last 40 years, have weaknesses and cannot be accepted as the final solution of this puzzle. The anthropic approach is discussed.Comment: Invited talk at TAUP 2007 conference, September 2007, Sendai, Japa

On the Need for Phenomenological Theory of P-Vortices or Does Spaghetti Confinement Pattern Admit Condensed-Matter Analogies?

Usually the intuition from condensed-matter physics is used to provide ideas for possible confinement mechanisms in gauge theories. Today, with a clear but puzzling ``spaghetti'' confinement pattern, arising after a decade of lattice computer experiments, which implies formation of a fluctuating net of peculiar magnetic vortices rather than condensation of the homogeneously distributed magnetic monopoles, the time is coming to reverse the logic and search for similar patterns in condensed matter systems. The main thing to look for in a condensed matter setup is the simultaneous existence of narrow tubes ($P$-vortices or 1-branes) of direction-changing electric field and broader tubes (Abrikosov lines) of magnetic field, a pattern dual to the one, presumably underlying confinement in gluodynamics. As a possible place for this search we suggest systems with coexisting charge-density waves and superconductivity.Comment: 20 pages, 7 figures; to be published in ZhET

Fermion sea along the sphaleron barrier

In this revised version we have improved the treatment of the top and bottom quark mass. This leads to slight changes of the numerical results, especially of those presented in Fig.4. The discussion of the numerical procedure and accuracy has been extended.Comment: 39 pages (LaTex) plus 5 figures (uuencoded postscript files); RUB-TPII-62/93, to appear in Phys.Rev.