Systematic {\it ab initio} study of the magnetic and electronic properties of all 3d transition metal linear and zigzag nanowires

It is found that all the zigzag chains except the nonmagnetic (NM) Ni and antiferromagnetic (AF) Fe chains which form a twisted two-legger ladder, look like a corner-sharing triangle ribbon, and have a lower total energy than the corresponding linear chains. All the 3d transition metals in both linear and zigzag structures have a stable or metastable ferromagnetic (FM) state. The electronic spin-polarization at the Fermi level in the FM Sc, V, Mn, Fe, Co and Ni linear chains is close to 90% or above. In the zigzag structure, the AF state is more stable than the FM state only in the Cr chain. It is found that the shape anisotropy energy may be comparable to the electronic one and always prefers the axial magnetization in both the linear and zigzag structures. In the zigzag chains, there is also a pronounced shape anisotropy in the plane perpendicular to the chain axis. Remarkably, the axial magnetic anisotropy in the FM Ni linear chain is gigantic, being ~12 meV/atom. Interestingly, there is a spin-reorientation transition in the FM Fe and Co linear chains when the chains are compressed or elongated. Large orbital magnetic moment is found in the FM Fe, Co and Ni linear chains

Two-Dimensional Wigner Crystal in Anisotropic Semiconductor

We investigate the effect of mass anisotropy on the Wigner crystallization transition in a two-dimensional (2D) electron gas. The static and dynamical properties of a 2D Wigner crystal have been calculated for arbitrary 2D Bravais lattices in the presence of anisotropic mass, as may be obtainable in Si MOSFETs with (110) surface. By studying the stability of all possible lattices, we find significant change in the crystal structure and melting density of the electron lattice with the lowest ground state energy.Comment: 4 pages, revtex, 4 figure

Stochastic Simulation of Process Calculi for Biology

Biological systems typically involve large numbers of components with complex, highly parallel interactions and intrinsic stochasticity. To model this complexity, numerous programming languages based on process calculi have been developed, many of which are expressive enough to generate unbounded numbers of molecular species and reactions. As a result of this expressiveness, such calculi cannot rely on standard reaction-based simulation methods, which require fixed numbers of species and reactions. Rather than implementing custom stochastic simulation algorithms for each process calculus, we propose to use a generic abstract machine that can be instantiated to a range of process calculi and a range of reaction-based simulation algorithms. The abstract machine functions as a just-in-time compiler, which dynamically updates the set of possible reactions and chooses the next reaction in an iterative cycle. In this short paper we give a brief summary of the generic abstract machine, and show how it can be instantiated with the stochastic simulation algorithm known as Gillespie's Direct Method. We also discuss the wider implications of such an abstract machine, and outline how it can be used to simulate multiple calculi simultaneously within a common framework.Comment: In Proceedings MeCBIC 2010, arXiv:1011.005

Reverberation Mapping Measurements of Black Hole Masses in Six Local Seyfert Galaxies

We present the final results from a high sampling rate, multi-month, spectrophotometric reverberation mapping campaign undertaken to obtain either new or improved Hbeta reverberation lag measurements for several relatively low-luminosity AGNs. We have reliably measured thetime delay between variations in the continuum and Hbeta emission line in six local Seyfert 1 galaxies. These measurements are used to calculate the mass of the supermassive black hole at the center of each of these AGNs. We place our results in context to the most current calibration of the broad-line region (BLR) R-L relationship, where our results remove outliers and reduce the scatter at the low-luminosity end of this relationship. We also present velocity-resolved Hbeta time delay measurements for our complete sample, though the clearest velocity-resolved kinematic signatures have already been published.Comment: 52 pages (AASTeX: 29 pages of text, 8 tables, 7 figures), accepted for publication in the Astrophysical Journa

Universality in the Screening Cloud of Dislocations Surrounding a Disclination

A detailed analytical and numerical analysis for the dislocation cloud surrounding a disclination is presented. The analytical results show that the combined system behaves as a single disclination with an effective fractional charge which can be computed from the properties of the grain boundaries forming the dislocation cloud. Expressions are also given when the crystal is subjected to an external two-dimensional pressure. The analytical results are generalized to a scaling form for the energy which up to core energies is given by the Young modulus of the crystal times a universal function. The accuracy of the universality hypothesis is numerically checked to high accuracy. The numerical approach, based on a generalization from previous work by S. Seung and D.R. Nelson ({\em Phys. Rev A 38:1005 (1988)}), is interesting on its own and allows to compute the energy for an {\em arbitrary} distribution of defects, on an {\em arbitrary geometry} with an arbitrary elastic {\em energy} with very minor additional computational effort. Some implications for recent experimental, computational and theoretical work are also discussed.Comment: 35 pages, 21 eps file

Quantum spin fluctuations in the dipolar Heisenberg-like rare earth pyrochlores

The magnetic pyrochlore oxide materials of general chemical formula R2Ti2O7 and R2Sn2O7 (R = rare earth) display a host of interesting physical behaviours depending on the flavour of rare earth ion. These properties depend on the value of the total magnetic moment, the crystal field interactions at each rare earth site and the complex interplay between magnetic exchange and long-range dipole-dipole interactions. This work focuses on the low temperature physics of the dipolar isotropic frustrated antiferromagnetic pyrochlore materials. Candidate magnetic ground states are numerically determined at zero temperature and the role of quantum spin fluctuations around these states are studied using a Holstein-Primakoff spin wave expansion to order 1/S. The results indicate the strong stability of the proposed classical ground states against quantum fluctuations. The inclusion of long range dipole interactions causes a restoration of symmetry and a suppression of the observed anisotropy gap leading to an increase in quantum fluctuations in the ground state when compared to a model with truncated dipole interactions. The system retains most of its classical character and there is little deviation from the fully ordered moment at zero temperature.Comment: Latex2e, 18 pages, 4 figures, IOP forma

Effects of Backflow Correlation in the Three-Dimensional Electron Gas: Quantum Monte Carlo Study

The correlation energy of the homogeneous three-dimensional interacting electron gas is calculated using the variational and fixed-node diffusion Monte Carlo methods, with trial functions that include backflow and three-body correlations. In the high density regime the effects of backflow dominate over those due to three-body correlations, but the relative importance of the latter increases as the density decreases. Since the backflow correlations vary the nodes of the trial function, this leads to improved energies in the fixed-node diffusion Monte Carlo calculations. The effects are comparable to those found for the two-dimensional electron gas, leading to much improved variational energies and fixed-node diffusion energies equal to the release-node energies of Ceperley and Alder within statistical and systematic errors.Comment: 14 pages, 5 figures, submitted to Physical Review

Graphite and Hexagonal Boron-Nitride Possess the Same Interlayer Distance. Why?

Graphite and hexagonal boron nitride (h-BN) are two prominent members of the family of layered materials possessing a hexagonal lattice. While graphite has non-polar homo-nuclear C-C intra-layer bonds, h-BN presents highly polar B-N bonds resulting in different optimal stacking modes of the two materials in bulk form. Furthermore, the static polarizabilities of the constituent atoms considerably differ from each other suggesting large differences in the dispersive component of the interlayer bonding. Despite these major differences both materials present practically identical interlayer distances. To understand this finding, a comparative study of the nature of the interlayer bonding in both materials is presented. A full lattice sum of the interactions between the partially charged atomic centers in h-BN results in vanishingly small monopolar electrostatic contributions to the interlayer binding energy. Higher order electrostatic multipoles, exchange, and short-range correlation contributions are found to be very similar in both materials and to almost completely cancel out by the Pauli repulsions at physically relevant interlayer distances resulting in a marginal effective contribution to the interlayer binding. Further analysis of the dispersive energy term reveals that despite the large differences in the individual atomic polarizabilities the hetero-atomic B-N C6 coefficient is very similar to the homo-atomic C-C coefficient in the hexagonal bulk form resulting in very similar dispersive contribution to the interlayer binding. The overall binding energy curves of both materials are thus very similar predicting practically the same interlayer distance and very similar binding energies.Comment: 18 pages, 5 figures, 2 table

Finite size errors in quantum many-body simulations of extended systems

Further developments are introduced in the theory of finite size errors in quantum many-body simulations of extended systems using periodic boundary conditions. We show that our recently introduced Model Periodic Coulomb interaction [A. J. Williamson et al., Phys. Rev. B 55, R4851 (1997)] can be applied consistently to all Coulomb interactions in the system. The Model Periodic Coulomb interaction greatly reduces the finite size errors in quantum many-body simulations. We illustrate the practical application of our techniques with Hartree-Fock and variational and diffusion quantum Monte Carlo calculations for ground and excited state calculations. We demonstrate that the finite size effects in electron promotion and electron addition/subtraction excitation energy calculations are very similar.Comment: 15 pages, 6 figures. To appear in Phys. Rev.