Density functional theory for molecular multiphoton ionization in the perturbative regime

A general implementation of the lowest nonvanishing order perturbation theory for the calculation of molecular multiphoton ionization cross sections is proposed in the framework of density functional theory. Bound and scattering wave functions are expanded in a multicentric basis set and advantage is taken of the full molecular point group symmetry, thus enabling the application of the formalism to medium-size molecules. Multiphoton ionization cross sections and angular asymmetry parameters have been calculated for the two- and four-photon ionization of the H2+ molecule, for linear and circular light polarizations. Both fixed and random orientations of the target molecule have been considered. To demonstrate the efficiency of the proposed methodology, the two-photon cross section and angular asymmetry parameters for the HOMO and HOMO-1 orbital ionization of benzene are also presented

Why 'scaffolding' is the wrong metaphor : the cognitive usefulness of mathematical representations.

The metaphor of scaffolding has become current in discussions of the cognitive help we get from artefacts, environmental affordances and each other. Consideration of mathematical tools and representations indicates that in these cases at least (and plausibly for others), scaffolding is the wrong picture, because scaffolding in good order is immobile, temporary and crude. Mathematical representations can be manipulated, are not temporary structures to aid development, and are refined. Reflection on examples from elementary algebra indicates that Menary is on the right track with his ‘enculturation’ view of mathematical cognition. Moreover, these examples allow us to elaborate his remarks on the uniqueness of mathematical representations and their role in the emergence of new thoughts.Peer reviewe

Three-Qubit Gate Realization Using Single Quantum Particle

Using virtual spin formalism it is shown that a quantum particle with eight energy levels can store three qubits. The formalism allows to realize a universal set of quantum gates. Feasible formalism implementation is suggested which uses nuclear spin-7/2 as a storage medium and radio frequency pulses as the gates. One pulse realization of all universal gates has been found, including three-qubit Toffoli gate.Comment: LaTeX, 6 pages, no figures; Submitted to "Pis'ma v Zh. Eksp. Teor. Fiz.

Quantum lattice gases and their invariants

The one particle sector of the simplest one dimensional quantum lattice gas automaton has been observed to simulate both the (relativistic) Dirac and (nonrelativistic) Schroedinger equations, in different continuum limits. By analyzing the discrete analogues of plane waves in this sector we find conserved quantities corresponding to energy and momentum. We show that the Klein paradox obtains so that in some regimes the model must be considered to be relativistic and the negative energy modes interpreted as positive energy modes of antiparticles. With a formally similar approach--the Bethe ansatz--we find the evolution eigenfunctions in the two particle sector of the quantum lattice gas automaton and conclude by discussing consequences of these calculations and their extension to more particles, additional velocities, and higher dimensions.Comment: 19 pages, plain TeX, 11 PostScript figures included with epsf.tex (ignore the under/overfull \vbox error messages

First-principles investigation of Nox and Sox adsorption on anatase-supported BaO and Pt overlayers

Cataloged from PDF version of article.We present a density functional theory investigation of the adsorption properties of NO and NO2 as well as SO2 and SO3 on BaO and Pt overlayers on anatase TiO2(001) surface. Mono layers, bilayers, and trilayers of BaO grow without strain-induced large scale reconstructions. While the bilayer and trilayer preserve, to a large extent, the NO2 adsorption characteristics of the clean BaO(100) surface, the effect of the support is evident in SO2 and SO3 adsorption energies, which are somewhat reduced with respect to the clean BaO(100) surface. When a Pt(100) layer is added on the TiO2 surface, four stable adsorption geometries are identified in the case of NO while NO2 is found to adsorb in only two configurations

Collaborative Computation in Self-Organizing Particle Systems

Many forms of programmable matter have been proposed for various tasks. We use an abstract model of self-organizing particle systems for programmable matter which could be used for a variety of applications, including smart paint and coating materials for engineering or programmable cells for medical uses. Previous research using this model has focused on shape formation and other spatial configuration problems (e.g., coating and compression). In this work we study foundational computational tasks that exceed the capabilities of the individual constant size memory of a particle, such as implementing a counter and matrix-vector multiplication. These tasks represent new ways to use these self-organizing systems, which, in conjunction with previous shape and configuration work, make the systems useful for a wider variety of tasks. They can also leverage the distributed and dynamic nature of the self-organizing system to be more efficient and adaptable than on traditional linear computing hardware. Finally, we demonstrate applications of similar types of computations with self-organizing systems to image processing, with implementations of image color transformation and edge detection algorithms

Simple Realization Of The Fredkin Gate Using A Series Of Two-body Operators

The Fredkin three-bit gate is universal for computational logic, and is reversible. Classically, it is impossible to do universal computation using reversible two-bit gates only. Here we construct the Fredkin gate using a combination of six two-body reversible (quantum) operators.Comment: Revtex 3.0, 7 pages, 3 figures appended at the end, please refer to the comment lines at the beginning of the manuscript for reasons of replacemen

Density Functional Theory for the Photoionization Dynamics of Uracil

Photoionization dynamics of the RNA base Uracil is studied in the framework of Density Functional Theory (DFT). The photoionization calculations take advantage of a newly developed parallel version of a multicentric approach to the calculation of the electronic continuum spectrum which uses a set of B-spline radial basis functions and a Kohn-Sham density functional hamiltonian. Both valence and core ionizations are considered. Scattering resonances in selected single-particle ionization channels are classified by the symmetry of the resonant state and the peak energy position in the photoelectron kinetic energy scale; the present results highlight once more the site specificity of core ionization processes. We further suggest that the resonant structures previously characterized in low-energy electron collision experiments are partly shifted below threshold by the photoionization processes. A critical evaluation of the theoretical results providing a guide for future experimental work on similar biosystems