Small Lattice Spacing Research Articles

Perturbative study of anisotropic lattice actions for heavy quarks

Anisotropic lattice fermion actions are investigated with one-loop perturbative calculations aiming at constructing a formulation for a heavy quark with controlled systematic uncertainties. For heavy-light systems at rest an anisotropic lattice with small temporal lattice spacing ${a}_{t}$ suppresses the discretization error by a power of ${a}_{t}{m}_{Q}$ for a heavy quark of mass ${m}_{Q}.$ We discuss the issue of large discretization errors, which scale as ${a}_{s}{m}_{Q}$ with ${a}_{s}$ the spatial lattice spacing. By performing one-loop calculations of the speed-of-light renormalization for several possible lattice actions in the limit of ${a}_{t}\ensuremath{\rightarrow}0,$ we show that one can eliminate the large systematic error on the anisotropic lattice.

An experimental study of strongly modified emission in inverse opal photonic crystals

We present the first experiments that demonstrate strong angle-independent modification of spontaneous emission spectra from laser dyes in photonic crystals, made of inverse opals in titania. We show that both the fluorescence quantum efficiency and weak disorder play a key role in interpreting the experimental data. We compare the angle-independent emission spectra of dye in photonic crystals with spectra from such crystals with much smaller lattice spacings, for which emission is in the long wavelength limit. The ratio of emission power spectra shows inhibition of emission up to a factor ∼ 5 over a large bandwidth of 13% of the first order Bragg resonance frequency. The inhibition shifts to increasing wavelength with the lattice parameter, confirming the photonic nature of the phenomenon. The center frequency and bandwidth of the inhibition agree with the calculated total density of states, but the measured inhibition of the vacuum fluctuations is much larger. This result is confirmed by experiments using different dyes. We likely probe the strongly modulated local photonic density of states, due to the spatially nonuniform distribution of dye molecules over the unit cell.

Exact lattice supersymmetry: The two-dimensionalN=2Wess-Zumino model

We study the two-dimensional Wess-Zumino model with extended N=2 supersymmetry on the lattice. The lattice prescription we choose has the merit of preserving {\it exactly} a single supersymmetric invariance at finite lattice spacing $a$. Furthermore, we construct three other transformations of the lattice fields under which the variation of the lattice action vanishes to $O(ga^2)$ where $g$ is a typical interaction coupling. These four transformations correspond to the two Majorana supercharges of the continuum theory. We also derive lattice Ward identities corresponding to these exact and approximate symmetries. We use dynamical fermion simulations to check the equality of the massgaps in the boson and fermion sectors and to check the lattice Ward identities. At least for weak coupling we see no problems associated with a lack of reflection positivity in the lattice action and find good agreement with theory. At strong coupling we provide evidence that problems associated with a lack of reflection positivity are evaded for small enough lattice spacing.

Broadband fivefold reduction of vacuum fluctuations probed by dyes in photonic crystals.

We observed for the first time a strong angle-independent modification of spontaneous emission spectra from laser dyes in photonic crystals, made of inverse opals in titania. Comparison with spectra from such crystals with much smaller lattice spacing, for which emission is in the long wavelength limit, reveals inhibition of emission up to a factor approximately 5 over a large bandwidth of 13% of the first order Bragg resonance frequency. The center frequency and bandwidth of the inhibition agree with calculated total density of states, while the measured inhibition of vacuum fluctuations is much larger. Because of the specific location of the dye molecules, we likely probe the strongly modulated local photonic density of states.

Global obstructions to gauge-invariance in chiral gauge theory on the lattice

It is shown that certain global obstructions to gauge-invariance in chiral gauge theory, described in the continuum by Alvarez-Gaume and Ginsparg, are exactly reproduced on the lattice in the Overlap formulation at small non-zero lattice spacing (i.e. close to the classical continuum limit). As a consequence, the continuum anomaly cancellation condition $d_R^{abc}=0$ is seen to be a necessary (although not necessarily sufficient) condition for anomaly cancellation on the lattice in the Overlap formulation.

Dynamics of lattice kinks

We consider a class of Hamiltonian nonlinear wave equations governing a field defined on a spatially discrete one-dimensional lattice, with discreteness parameter, d= h −1, where h>0 is the lattice spacing. The specific cases we consider in detail are the discrete sine-Gordon (SG) and discrete φ 4 models. For finite d and in the continuum limit ( d→∞) these equations have static kink-like (heteroclinic) states which are stable. In contrast to the continuum case, due to the breaking of Lorentz invariance, discrete kinks cannot be “Lorentz boosted” to obtain traveling discrete kinks. Peyrard and Kruskal pioneered the study of how a kink, initially propagating in the lattice, dynamically adjusts in the absence of an available family of traveling kinks. We study in detail the final stages of the discrete kink’s evolution during which it is pinned to a specified lattice site (equilibrium position in the Peierls–Nabarro barrier). We find the following: 1. For d sufficiently large (sufficiently small lattice spacing), the state of the system approaches an asymptotically stable ground state static kink (centered between lattice sites). 2. For d sufficiently small, d< d *, the static kink bifurcates to one or more time-periodic states. For the discrete φ 4 we have wobbling kinks which have the same spatial symmetry as the static kink as well as “ g-wobblers” and “ e-wobblers”, which have different spatial symmetry. In the discrete SG case, the “ e-wobbler” has the spatial symmetry of the kink, whereas the “ g-wobbler” has the opposite one. These time-periodic states may be regarded as a class of discrete breather/topological defect states; they are spatially localized and time-periodic oscillations mounted on a static kink background. The large time limit of solutions with initial data near a kink is marked by damped oscillation about one of these two types of asymptotic states. In case (1) we compute the characteristics of the damped oscillation (frequency and d-dependent rate of decay). In case (2) we prove the existence of, and give analytical and numerical evidence for the asymptotic stability of wobbling solutions. The mechanism for decay is the radiation of excess energy, stored in internal modes, away from the kink core to infinity. This process is studied in detail using general techniques of scattering theory and normal forms. In particular, we derive a dispersive normal form, from which one can anticipate the character of the dynamics. The methods we use are very general and are appropriate for the study of dynamical systems which may be viewed as a system of discrete oscillators (e.g. kink together with its internal modes) coupled to a field (e.g. dispersive radiation or phonons). The approach is based on and extends an approach of one of the authors (MIW) and Soffer in previous work. Changes in the character of the dynamics, as d varies, are manifested in topological changes in the phase portrait of the normal form. These changes are due to changes in the types of resonances which occur among the discrete internal modes and the continuum radiation modes as d varies. Though derived from a time-reversible dynamical system, this normal form has a dissipative character. The dissipation is of an internal nature, and corresponds to the transfer of energy from the discrete to continuum radiation modes. The coefficients which characterize the time-scale of damping (or lifetime of the internal mode oscillations) are a nonlinear analog of “Fermi’s golden rule”, which arises in the theory of spontaneous emission in quantum physics.

Monopole clusters,Z(2)vortices, and confinement in SU(2)

We extend our previous study of magnetic monopole currents in the maximally Abelian gauge [hep-lat/9712003] to larger lattices at small lattice spacings (20^4 at beta = 2.5 and 32^4 at beta = 2.5115). We confirm that at these weak couplings there continues to be one monopole cluster that is very much longer than the rest and that the string tension, K, is entirely due to it. The remaining clusters are compact objects whose population as a function of radius follows a power law that deviates from the scale invariant form, but much too weakly to suggest a link with the analytically calculable size distribution of small instantons. We also search for traces of Z(2) vortices in the Abelian projected fields; either as closed loops of `magnetic' flux or through appropriate correlations amongst the monopoles. We find, by direct calculation, that there is no confining condensate of such flux loops. We also find, through the calculation of doubly charged Wilson loops within the monopole fields, that there is no suppression of the q=2 effective string tension out to at distances of at least r ~ 1.6/sqrt{K}, suggesting that if there are any vortices they are not encoded in the monopole fields.

Simple observables from fat link fermion actions

A comparison is made of the (quenched) light hadron spectrum and of simple matrix elements for a hypercubic fermion action (based on a fixed point action) and the clover action, both using fat links, at a lattice spacing a= 0.18 fm. Renormalization constants for the naive and improved vector current and the naive axial current are computed using Ward identities. The renormalization factors are very close to unity, and the spectroscopy of light hadrons and the pseudoscalar and vector decay constants agree well with simulations at smaller lattice spacings (and with experiment).

Investigating and optimizing the chiral properties of lattice fermion actions

We study exceptional modes of both the Wilson and the clover action in order to understand why quenched clover spectroscopy suffers so severely from exceptional configurations. We show that, in contrast to the case of the Wilson action, a large clover coefficient can make the exceptional modes extremely localized and thus very sensitive to short distance fluctuations. We describe a way to optimize the chiral behavior of Wilson-type lattice fermion actions by studying their low energy real eigenmodes. We find a candidate action, the clover action with fat links with a tuned clover term. We present a calculation of spectroscopy and matrix elements at Wilson gauge coupling β = 5.7. When compared to simulations with the standard (non-perturbatively improved) clover action at small lattice spacing, the action shows good scaling behavior, with an apparent great reduction in the number of exceptional configurations.

High-temperature behavior of the Chern-Simons diffusion rate in the 1 + 1 dimensional abelian Higgs model

We give arguments that in the 1+1-dimensional abelian Higgs model the classical approximation can be good for the leading high-temperature behavior of real-time processes. The Chern-Simons diffusion rate (‘sphaleron rate’) is studied numerically in this approximation. New results at high-temperature show a T 2 3 behavior of the rate at sufficiently small lattice spacing.

On the diffeomorphism commutators of lattice quantum gravity

We show that the algebra of discretized spatial diffeomorphism constraints in Hamiltonian lattice quantum gravity closes without anomalies in the limit of small lattice spacing. The result holds for arbitrary factor-ordering and for a variety of different discretizations of the continuum constraints, and thus generalizes an earlier calculation by Renteln.

A flexible triangulation method to describe the solvent-accessible surface of biopolymers.

A relatively simple protein solvent-accessible surface triangulation method for continuum electrostatics applications employing the boundary element method is presented. First, the protein is placed onto a three-dimensional lattice with a specified lattice spacing. To each lattice point, a box is assigned. Boxes located in the solvent region and in the interior of the protein are removed from the set. Improper connections between boxes and the possible existence of cavities in the interior of the protein which would destroy the proper connectivity of the triangulated surface are taken care of. The remaining set of boxes define the outer contour of the protein. Each free face exposed to the solvent of the remaining set of boxes is triangulated after the surface defined by the free faces has been smoothed to follow the shape of the macromolecule more accurately. The final step consists of a mapping of triangle vertices onto a set of surface points which define the solvent-accessible surface. Normal vectors at triangle vertices are obtained also from the free faces which define the orientation of the surface. The algorithm was tested for six molecules including four proteins; a dipeptide, a helical peptide consisting of 25 residues, calbindin, lysozyme, calmodulin and cutinase. For each molecule, total areas have been calculated and compared with the result computed from a dotted solvent-accessible surface. Since the boundary element method requires a low number of vertices and triangles to reduce the number of unknowns for reasons of efficiency, the number of triangles should not be too high. Nevertheless, credible results are obtained for the total area with relative errors not exceeding 12% for a large lattice spacing (0.30 nm) while close to zero for a smaller lattice spacing (down to 0.16 nm). The output of the triangulation computer program (written in C++) is rather simple so that it can be easily converted to any format acceptable for any molecular graphics programs.

Steric effects on superconductivity in (Nd 1− yY y) 2− xCe xCuO 4−δ

We present here the results of SQUID magnetization and powder X-ray diffraction measurements for polycrystalline samples of (Nd 1 − y Y y ) 2 − x Ce x CuO 4 − δ for various x and y. The lattice constants and superconducting fractions were determined for each sample. The lattice contracts as more yttrium is substituted, and superconductivity is reduced. The trend is compared with the spacing of Gd 2 − x Ce x CuO 4 − δ to separate steric from magnetic causes for the lack of a superconducting phase in Gd 2 − x Ce x CuO 4 − δ. The lack of superconductivity in (Nd 0.7Y 0.3) 2 − x Ce x CuO 4 − δ, which is almost the same size as Gd 2 − x Ce x CuO 4 − δ, indicates that a small lattice spacing is the primary reason for the failure of Gd 2 − x Ce x CuO 4 − δ to be a superconductor. This contradicts a recent theoretical proposal which emphasized magnetic pair breaking.

The Phononic Lattice Solid By Interpolation For ModellingPWaves In Heterogeneous Media

SUMMARY The ‘pQononic lattice solid’ (PLS) approach based on simulating the movement, interaction and scattering of quasi-particles on a discrete lattice has been developed recently to model wave propagation through heterogeneous media. In the initial version, the quasi-particles carried pressure and the differential equation describing the transport of quasi-particle number densities on the discrete lattice was solved using a finite-difference scheme. The significant problems and the limitations of this method are that only compressional waves are considered, the convergence is slow in homogeneous regions, the results are inaccurate when impedance contrasts are large and small lattice spacings are required to specify sharp interfaces (cf the classical finite-difference solution to the wave equation). To address the last three points, we develop an improved PLS approach by interpolation (PLSI) to directly model the behaviour of the quasi-particle number densities on the discrete lattice rather than solving the corresponding macroscopic transport equation using finite differences. This involves simulating the three microscopic processes describing the behaviour of quasi-particles: movement along the links between lattice nodes, scattering by medium heterogeneities and interaction between quasi-particles arriving at lattice nodes. In the movement step, quasi-particle number densities are moved from the nodes along the links by an amount cAr where c is the quasi-particle speed and Ar is the time step as if there were no heterogeneity in the link. Number densities are then interpolated to the locations of interfaces between parts of links with different properties and scattering is taken into account using the known 1-D reflection and transmission coefficients. Theoretical analysis demonstrates that, in the macroscopic limit, the PLSI models the acoustic wave equation for N-D heterogeneous media (N = 1,2, 3). A 2-D numerical example illustrates the PLSI approach. The PLSI is comparable with the lattice Boltzmann lattice gas appproach in that no finite-difference errors are present but models wave phenomena in heterogeneous media rather than fluid flow and acoustic waves in a constant bulk modulus gas. Because the PLSI can handle sharp interfaces at any location (cf classical finite difference methods have difficulty handling sharp interfaces), it may enable numerical experiments to be conducted of wave propagation through complex fractured and porous rocks to study the causes of anisotropy and attenuation including the effect of non-linear solid-fluid interactions. This would require the extension of the approach to model shear waves in addition to compressional waves.

Chern-Simons number diffusion in (1+1)-dimensional Higgs theory

We study the Chern-Simons number diffusion rate in the (1+1)-dimensional latticeAbelian Higgs model at temperatures much higher than, as well as comparable to, the sphaleron energy. It is found that in the high-temperature limit the rate is likely to grow as power 2/3 of the temperature. In the intermediate-temperature regime, our numerical simulations show that very weak temperature dependence of the rate, found in previous work, persists at smaller lattice spacings. We discuss possibilities of relating the observed behavior of the rate to static finite-temperature properties of the model.

Observation of Interference Fringes with a Lattice Spacing of 1.92 Å in Convergent-Beam Electron Diffraction

The interference fringes with a lattice spacing of 1.92 A for the 220 reflection of Si have been observed in convergent-beam electron diffraction patterns using a JEM 2010F electron microscope equipped with a field-emission gun. The fringes observed in the present study have the smallest lattice spacing among the fringes reported to date

High-resolution imaging on a field emission TEM

A field emission gun (FEG) on a TEM brings a strong improvement in the spatial and temporal coherence, thereby enhancing the contrast from small lattice spacings in the image in comparison with LaB 6 instruments. Other parameters of importance for high-resolution imaging are the size of the isoplanatic patch (the coma-free area in the image), which is small with a cold FEG but sufficiently large with a Schottky FEG, and the method of aligning the objective lens, which should be coma-free alignment. The much improved contrast transfer has proven to hinder astigmatism correction, and as a consequence focusing and coma-free alignment, due to the continuous presence of high spatial frequencies. A practical solution is to converge the beam, thereby deteriorating the spatial coherence, and to defocus it again once all conditions are set correctly. The occurrence of Fourier images over a large range of focus conditions makes it necessary to use the thin specimen edge to set the focus. Delocalisation effects, where image details are displaced from their true locations, also occur in the images. These effects cannot be avoided altogether but are minimised within 50 to 100 nm of Scherzer focus. In order to make effective use of all the information contained in high-resolution images from a FEG TEM, image retrieval through holography or through-focus methods is expected to be most effective.

Relationship between Self-Texture and Interfacial Restriction on the Epitaxy of ZNO Thinfilms I

ABSTRACTWe investigated relationships between self-texture and interfacial restriction on the epitaxy of directed, bonded, thin films. Defect structures in ZnO films grown epitaxially on (0001)sapphire mere evaluated by 3—dimensional maping of k—spacing using an X—ray double crystal spectrometer. The orientation distribution and variation in lattice spacing of the films wre individually measured to elucidate the mechanism of growth. The growth mode was found to change at a film thickness of approximately 100 Å. The layer within 100Å of the interface had a small orientation distribution (1.8'), a large lattice spacing distribution, and a large cumpressive stress.The layer that was more than 100Å from the interface had a larger orientation distribution, a smaller lattice spacing distribution, and a smaller compressive stress.

Lattice spacing measurements around dislocations in an undoped GaAs crystal grown by the liquid-encapsulated Czochralski method

Abstract The lattice spacing in a cellular structure of an undoped liquid-encapsulated Czochralski GaAs crystal has been measured by synchrotron X-ray topography with a (+n, −n, +n) triple-crystal system. Distinguishable lattice spacing variations were observed in dislocation-related regions. One region, neighbouring to the cell walls, shows a small lattice spacing compared with the average value. Another region, where dislocations intersect with the crystal surface inside the cell, shows a large lattice spacing. The lattice spacing variation depends on the dislocation features.

Annular dark field electron microscope images with better than 2 Å resolution at 100 kV

High-resolution scanning transmission electron microscope (STEM) images in the annular dark field (ADF) imaging mode approaching the theoretical point-to-point resolution limit are presented. The ADF images were obtained from a high Tc superconducting YBa2Cu3O7−x thin-film specimen at 100 kV. The 1.9 Å resolution lattice image, which is the smallest lattice spacing in the specimen, corresponds to the minimum resolvable spatial frequency with 5% contrast in the contrast transfer function for annular dark field, and is smaller than the resolution limit given by the Rayleigh criterion. This demonstrates that STEM ADF imaging can have a resolution approximately 40% better than that of the bright field conventional transmission electron microscope (CTEM) imaging at Scherzer condition.