Coulomb potentials in two and three dimensions under periodic boundary conditions

A method to sum over logarithmic potential in 2D and Coulomb potential in 3D with periodic boundary conditions in all directions is given. We consider the most general form of unit cells, the rhombic cell in 2D and the triclinic cell in 3D. For the 3D case, this paper presents a generalization of Sperb's work [R. Sperb, Mol. Simulation, \textbf{22}, 199-212(1999)]. The expressions derived in this work converge extremely fast in all region of the simulation cell. We also obtain results for slab geometry. Furthermore, self-energies for both 2D as well as 3D cases are derived. Our general formulas can be employed to obtain Madelung constants for periodic structures.Comment: Generalization of the work done in cond-mat/0405574. To appear in J. Chem. Physics. A few typos have been correcte

Fast calculation of the electrostatic potential in ionic crystals by direct summation metho

An efficient real space method is derived for the evaluation of the Madelung's potential of ionic crystals. The proposed method is an extension of the Evjen's method. It takes advantage of a general analysis for the potential convergence in real space. Indeed, we show that the series convergence is exponential as a function of the number of annulled multipolar momenta in the unit cell. The method proposed in this work reaches such an exponential xconvergence rate. Its efficiency is comparable to the Ewald's method, however unlike the latter, it uses only simple algebraic functions

Effective way to sum over long range Coulomb potentials in two and three dimensions

I propose a method to calculate logarithmic interaction in two dimensions and coulomb interaction in three dimensions under periodic boundary conditions. This paper considers the case of a rectangular cell in two dimensions and an orthorhombic cell in three dimensions. Unlike the Ewald method, there is no parameter to be optimized, nor does it involve error functions, thus leading to the accuracy obtained. This method is similar in approach to that of Sperb [R. Sperb, Mol. Simulation, 22, 199 (1999).], but the derivation is considerably simpler and physically appealing. An important aspect of the proposed method is the faster convergence of the Green function for a particular case as compared to Sperb's work. The convergence of the sums for the most part of unit cell is exponential, and hence requires the calculation of only a few dozen terms. In a very simple way, we also obtain expressions for interaction for systems with slab geometries. Expressions for the Madelung constant of CsCl and NaCl are also obtained.Comment: To appear in Phy. Rev.

Saturn's aurora observed by the Cassini camera at visible wavelengths

The first observations of Saturn's visible-wavelength aurora were made by the Cassini camera. The aurora was observed between 2006 and 2013 in the northern and southern hemispheres. The color of the aurora changes from pink at a few hundred km above the horizon to purple at 1000-1500 km above the horizon. The spectrum observed in 9 filters spanning wavelengths from 250 nm to 1000 nm has a prominent H-alpha line and roughly agrees with laboratory simulated auroras. Auroras in both hemispheres vary dramatically with longitude. Auroras form bright arcs between 70 and 80 degree latitude north and between 65 and 80 degree latitude south, which sometimes spiral around the pole, and sometimes form double arcs. A large 10,000-km-scale longitudinal brightness structure persists for more than 100 hours. This structure rotates approximately together with Saturn. On top of the large steady structure, the auroras brighten suddenly on the timescales of a few minutes. These brightenings repeat with a period of about 1 hour. Smaller, 1000-km-scale structures may move faster or lag behind Saturn's rotation on timescales of tens of minutes. The persistence of nearly-corotating large bright longitudinal structure in the auroral oval seen in two movies spanning 8 and 11 rotations gives an estimate on the period of 10.65 $\pm$0.15 h for 2009 in the northern oval and 10.8$\pm$ 0.1 h for 2012 in the southern oval. The 2009 north aurora period is close to the north branch of Saturn Kilometric Radiation (SKR) detected at that time.Comment: 39 pages, 8 figures, 1 table, 6 supplementary movies, accepted to Icaru

Wavefront sensing of atmospheric phase distortions at the Palomar 200-in. telescope and implications for adaptive optics

Major efforts in astronomical instrumentation are now being made to apply the techniques of adaptive optics to the correction of phase distortions induced by the turbulent atmosphere and by quasi-static aberrations in telescopes themselves. Despite decades of study, the problem of atmospheric turbulence is still only partially understood. We have obtained video-rate (30 Hz) imaging of stellar clusters and of single-star phase distortions over the pupil of the 200" Hale telescope on Palomar Mountain. These data show complex temporal and spatial behavior, with multiple components arising at a number of scale heights in the atmosphere; we hope to quantify this behavior to ensure the feasibility of adaptive optics at the Observatory. We have implemented different wavefront sensing techniques to measure aperture phase in wavefronts from single stars, including the classical Foucault test, which measures the local gradient of phase, and the recently-devised curvature sensing technique, which measures the second derivative of pupil phase and has formed the real-time wavefront sensor for some very productive astronomical adaptive optics. Our data, though not fast enough to capture all details of atmospheric phase fluctuations, provide important information regarding the capabilities that must be met by the adaptive optics system now being built for the 200" telescope by a team at the Jet Propulsion Lab. We describe our data acquisition techniques, initial results from efforts to characterize the properties of the turbulent atmosphere at Palomar Mountain, and future plans to extract additional quantitative parameters of use for adaptive optics performance predictions

Dynamical Diffraction Theory for Wave Packet Propagation in Deformed Crystals

We develop a theory for the trajectory of an x ray in the presence of a crystal deformation. A set of equations of motion for an x-ray wave packet including the dynamical diffraction is derived, taking into account the Berry phase as a correction to geometrical optics. The trajectory of the wave packet has a shift of the center position due to a crystal deformation. Remarkably, in the vicinity of the Bragg condition, the shift is enhanced by a factor $\omega /\Delta \omega$ ($\omega$: frequency of an x ray, $\Delta\omega$: gap frequency induced by the Bragg reflection). Comparison with the conventional dynamical diffraction theory is also made.Comment: 4 pages, 2 figures. Title change

Absence of Domain Wall Roughening in a Transverse Field Ising Model with Long-Range Interactions

We investigate roughening transitions in the context of transverse-field Ising models. As a modification of the transverse Ising model with short range interactions, which has been shown to exhibit domain wall roughening, we have looked into the possibility of a roughening transition for the case of long-range interactions, since such a system is physically realized in the insulator LiHoF4. The combination of strong Ising anisotropy and long-range forces lead naturally to the formation of domain walls but we find that the long-range forces destroy the roughening transition.Comment: 7 pages, 5 figures, revtex

From bcc to fcc: interplay between oscillating long-range and repulsive short-range forces

This paper supplements and partly extends an earlier publication, Phys. Rev. Lett. 95, 265501 (2005). In $d$-dimensional continuous space we describe the infinite volume ground state configurations (GSCs) of pair interactions \vfi and \vfi+\psi, where \vfi is the inverse Fourier transform of a nonnegative function vanishing outside the sphere of radius $K_0$, and $\psi$ is any nonnegative finite-range interaction of range $r_0\leq\gamma_d/K_0$, where $\gamma_3=\sqrt{6}\pi$. In three dimensions the decay of \vfi can be as slow as $\sim r^{-2}$, and an interaction of asymptotic form $\sim\cos(K_0r+\pi/2)/r^3$ is among the examples. At a dimension-dependent density $\rho_d$ the ground state of \vfi is a unique Bravais lattice, and for higher densities it is continuously degenerate: any union of Bravais lattices whose reciprocal lattice vectors are not shorter than $K_0$ is a GSC. Adding $\psi$ decreases the ground state degeneracy which, nonetheless, remains continuous in the open interval $(\rho_d,\rho_d')$, where $\rho_d'$ is the close-packing density of hard balls of diameter $r_0$. The ground state is unique at both ends of the interval. In three dimensions this unique GSC is the bcc lattice at $\rho_3$ and the fcc lattice at $\rho_3'=\sqrt{2}/r_0^3$.Comment: Published versio