The expressions for the 2nd-order mixed partial derivatives of Slater-Koster matrix elements at spherical coordinate singularities

In a recent publication it has been shown how to generate derivatives with respect to atom coordinates of Slater-Koster matrix elements for the tight binding (TB) modelling of a system. For the special case of a mixed second partial derivative at coordinate singularities only the results were stated in that publication. In this work, the derivation of these results is given in detail. Though it may seem rather `technical' and only applicable to a very special case, atomic configurations where the connecting vector between the two atoms involved in a two-centre matrix element is aligned along the z-axis (in the usual approach) require results for precisely this case. The expressions derived in this work have been implemented in the DINAMO code.Comment: 9 pages, no figure

Robust non-adiabatic molecular dynamics for metals and insulators

We present a new formulation of the correlated electron-ion dynamics (CEID) scheme, which systematically improves Ehrenfest dynamics by including quantum fluctuations around the mean-field atomic trajectories. We show that the method can simulate models of non-adiabatic electronic transitions, and test it against exact integration of the time-dependent Schroedinger equation. Unlike previous formulations of CEID, the accuracy of this scheme depends on a single tunable parameter which sets the level of atomic fluctuations included. The convergence to the exact dynamics by increasing the tunable parameter is demonstrated for a model two level system. This algorithm provides a smooth description of the non-adiabatic electronic transitions which satisfies the kinematic constraints (energy and momentum conservation) and preserves quantum coherence. The applicability of this algorithm to more complex atomic systems is discussed.Comment: 36 pages, 5 figures. Accepted for publication in Journal of Chemical Physic

Automatic Generation of Matrix Element Derivatives for Tight Binding Models

Tight binding (TB) models are one approach to the quantum mechanical many particle problem. An important role in TB models is played by hopping and overlap matrix elements between the orbitals on two atoms, which of course depend on the relative positions of the atoms involved. This dependence can be expressed with the help of Slater-Koster parameters, which are usually taken from tables. Recently, a way to generate these tables automatically was published. If TB approaches are applied to simulations of the dynamics of a system, also derivatives of matrix elements can appear. In this work we give general expressions for first and second derivatives of such matrix elements. Implemented in a computer program they obviate the need to type all the required derivatives of all occuring matrix elements by hand.Comment: 11 pages, 2 figure

Radiometric Quality of the MODIS Bands at 667 and 678nm

The MODIS instruments on Terra and Aqua were designed to allow the measurement of chlorophyll fluorescence effects over ocean. The retrieval algorithm is based on the difference between the water-leaving radiances at 667nm and 678nm. The water-leaving radiances at these wavelengths are usually very low relative to the top- of-atmosphere radiances. The high radiometric accuracy needed to retrieve the small fluorescence signal lead to a dual gain design for the 667 and 678nm bands. This paper discusses the benefits obtained from this design choice and provides justification for the use of only one set of gains for global processing of ocean color products. Noise characteristics of the two bands and their related products are compared to other products of bands from 412nm to 2130nm. The impact of polarization on the two bands is discussed. In addition, the impact of stray light on the two bands is compared to other MODIS bands

Dynamic predictive coding by the retina

Retinal ganglion cells convey the visual image from the eye to the brain. They generally encode local differences in space and changes in time rather than the raw image intensity. This can be seen as a strategy of predictive coding, adapted through evolution to the average image statistics of the natural environment. Yet animals encounter many environments with visual statistics different from the average scene. Here we show that when this happens, the retina adjusts its processing dynamically. The spatio-temporal receptive fields of retinal ganglion cells change after a few seconds in a new environment. The changes are adaptive, in that the new receptive field improves predictive coding under the new image statistics. We show that a network model with plastic synapses can account for the large variety of observed adaptations

Deconvolution for an atomic distribution: rates of convergence

Let $X_1,..., X_n$ be i.i.d.\ copies of a random variable $X=Y+Z,$ where $X_i=Y_i+Z_i,$ and $Y_i$ and $Z_i$ are independent and have the same distribution as $Y$ and $Z,$ respectively. Assume that the random variables $Y_i$'s are unobservable and that $Y=AV,$ where $A$ and $V$ are independent, $A$ has a Bernoulli distribution with probability of success equal to $1-p$ and $V$ has a distribution function $F$ with density $f.$ Let the random variable $Z$ have a known distribution with density $k.$ Based on a sample $X_1,...,X_n,$ we consider the problem of nonparametric estimation of the density $f$ and the probability $p.$ Our estimators of $f$ and $p$ are constructed via Fourier inversion and kernel smoothing. We derive their convergence rates over suitable functional classes. By establishing in a number of cases the lower bounds for estimation of $f$ and $p$ we show that our estimators are rate-optimal in these cases.Comment: 27 page

Radiative corrections to all charge assignments of heavy quark baryon semileptonic decays

In semileptonic decays of spin-1/2 baryons containing heavy quarks up to six charge assignments for the baryons and lepton are possible. We show that the radiative corrections to four of these possibilities can be directly obtained from the final results of the two possibilities previously studied. There is no need to recalculate integrals over virtual or real photon momentum or any traces.Comment: 15 pages, 2 figures, RevTex. Extended discussion. Final version to appear in Physical Review

Ultra-thin Topological Insulator Bi2Se3 Nanoribbons Exfoliated by Atomic Force Microscopy

Ultra-thin topological insulator nanostructures, in which coupling between top and bottom surface states takes place, are of great intellectual and practical importance. Due to the weak Van der Waals interaction between adjacent quintuple layers (QLs), the layered bismuth selenide (Bi2Se3), a single Dirac-cone topological insulator with a large bulk gap, can be exfoliated down to a few QLs. In this paper, we report the first controlled mechanical exfoliation of Bi2Se3 nanoribbons (> 50 QLs) by an atomic force microscope (AFM) tip down to a single QL. Microwave impedance microscopy is employed to map out the local conductivity of such ultra-thin nanoribbons, showing drastic difference in sheet resistance between 1~2 QLs and 4~5 QLs. Transport measurement carried out on an exfoliated (\leq 5 QLs) Bi2Se3 device shows non-metallic temperature dependence of resistance, in sharp contrast to the metallic behavior seen in thick (> 50 QLs) ribbons. These AFM-exfoliated thin nanoribbons afford interesting candidates for studying the transition from quantum spin Hall surface to edge states

Adjustments to the MODIS Terra Radiometric Calibration and Polarization Sensitivity in the 2010 Reprocessing

The Moderate-Resolution Imaging Spectroradiometer (MODIS) on NASA s Earth Observing System (EOS) satellite Terra provides global coverage of top-of-atmosphere (TOA) radiances that have been successfully used for terrestrial and atmospheric research. The MODIS Terra ocean color products, however, have been compromised by an inadequate radiometric calibration at the short wavelengths. The Ocean Biology Processing Group (OBPG) at NASA has derived radiometric corrections using ocean color products from the SeaWiFS sensor as truth fields. In the R2010.0 reprocessing, these corrections have been applied to the whole mission life span of 10 years. This paper presents the corrections to the radiometric gains and to the instrument polarization sensitivity, demonstrates the improvement to the Terra ocean color products, and discusses issues that need further investigation. Although the global averages of MODIS Terra ocean color products are now in excellent agreement with those of SeaWiFS and MODIS Aqua, and image quality has been significantly improved, the large corrections applied to the radiometric calibration and polarization sensitivity require additional caution when using the data