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.

Explicit characterization of the identity configuration in an Abelian Sandpile Model

Since the work of Creutz, identifying the group identities for the Abelian Sandpile Model (ASM) on a given lattice is a puzzling issue: on rectangular portions of Z^2 complex quasi-self-similar structures arise. We study the ASM on the square lattice, in different geometries, and a variant with directed edges. Cylinders, through their extra symmetry, allow an easy determination of the identity, which is a homogeneous function. The directed variant on square geometry shows a remarkable exact structure, asymptotically self-similar.Comment: 11 pages, 8 figure

Aharonov-Bohm Oscillations with Spin: Evidence for Berry's Phase

We report a study of the Aharonov-Bohm effect, the oscillations of the resistance of a mesoscopic ring as a function of a perpendicular magnetic field, in a GaAs two-dimensional hole system with a strong spin-orbit interaction. The Fourier spectra of the oscillations reveal extra structure near the main peak whose frequency corresponds to the magnetic flux enclosed by the ring. A comparison of the experimental data with results of simulations demonstrates that the origin of the extra structure is the geometric (Berry) phase acquired by the carrier spin as it travels around the ring.Comment: To be published in Physical Review Letter

Three-leg correlations in the two component spanning tree on the upper half-plane

We present a detailed asymptotic analysis of correlation functions for the two component spanning tree on the two-dimensional lattice when one component contains three paths connecting vicinities of two fixed lattice sites at large distance $s$ apart. We extend the known result for correlations on the plane to the case of the upper half-plane with closed and open boundary conditions. We found asymptotics of correlations for distance $r$ from the boundary to one of the fixed lattice sites for the cases $r\gg s \gg 1$ and $s \gg r \gg 1$.Comment: 16 pages, 5 figure

Abelian Sandpile Model on the Honeycomb Lattice

We check the universality properties of the two-dimensional Abelian sandpile model by computing some of its properties on the honeycomb lattice. Exact expressions for unit height correlation functions in presence of boundaries and for different boundary conditions are derived. Also, we study the statistics of the boundaries of avalanche waves by using the theory of SLE and suggest that these curves are conformally invariant and described by SLE2.Comment: 24 pages, 5 figure

Logarithmic two-point correlators in the Abelian sandpile model

We present the detailed calculations of the asymptotics of two-site correlation functions for height variables in the two-dimensional Abelian sandpile model. By using combinatorial methods for the enumeration of spanning trees, we extend the well-known result for the correlation $\sigma_{1,1} \simeq 1/r^4$ of minimal heights $h_1=h_2=1$ to $\sigma_{1,h} = P_{1,h}-P_1P_h$ for height values $h=2,3,4$. These results confirm the dominant logarithmic behaviour $\sigma_{1,h} \simeq (c_h\log r + d_h)/r^4 + {\cal O}(r^{-5})$ for large $r$, predicted by logarithmic conformal field theory based on field identifications obtained previously. We obtain, from our lattice calculations, the explicit values for the coefficients $c_h$ and $d_h$ (the latter are new).Comment: 28 page

Complex-Orbital Order in Fe_3O_4 and Mechanism of the Verwey Transition

Electronic state and the Verwey transition in magnetite (Fe_3O_4) are studied using a spinless three-band Hubbard model for 3d electrons on the B sites with the Hartree-Fock approximation and the exact diagonalisation method. Complex-orbital, e.g., 1/sqrt(2)[|zx> + i |yz>], ordered (COO) states having noncollinear orbital moments ~ 0.4 mu_B on the B sites are obtained with the cubic lattice structure of the high-temperature phase. The COO state is a novel form of magnetic ordering within the orbital degree of freedom. It arises from the formation of Hund's second rule states of spinless pseudo-d molecular orbitals in the Fe_4 tetrahedral units of the B sites and ferromagnetic alignment of their fictitious orbital moments. A COO state with longer periodicity is obtained with pseudo-orthorhombic Pmca and Pmc2_1 structures for the low-temperature phase. The state spontaneously lowers the crystal symmetry to the monoclinic and explains experimentally observed rhombohedral cell deformation and Jahn-Teller like distortion. From these findings, we consider that at the Verwey transition temperature, the COO state remaining to be short-range order impeded by dynamical lattice distortion in high temperature is developed into that with long-range order coupled with the monoclinic lattice distortion.Comment: 16 pages, 13 figures, 6 tables, accepted for publication in J. Phys. Soc. Jp

When Models Interact with their Subjects: The Dynamics of Model Aware Systems

A scientific model need not be a passive and static descriptor of its subject. If the subject is affected by the model, the model must be updated to explain its affected subject. In this study, two models regarding the dynamics of model aware systems are presented. The first explores the behavior of "prediction seeking" (PSP) and "prediction avoiding" (PAP) populations under the influence of a model that describes them. The second explores the publishing behavior of a group of experimentalists coupled to a model by means of confirmation bias. It is found that model aware systems can exhibit convergent random or oscillatory behavior and display universal 1/f noise. A numerical simulation of the physical experimentalists is compared with actual publications of neutron life time and {\Lambda} mass measurements and is in good quantitative agreement.Comment: Accepted for publication in PLoS-ON