Theory of the optical spectrum of Na<Subscript>2</Subscript> on <Superscript>4</Superscript>He droplets: effects of the zero-point energy of the nearest atoms

We investigate, using first-principles calculations, the electronic structure of substitutional and vacancy defects in a boron nitride monolayer. We found that the incorporation of a substitutional carbon atom induces appreciable modification on the electronic properties, when compared to a non-defective boron nitride sheet. The incorporation of substitutional carbon impurity also induces a significant reduction of the work function. In addition, we found that defects introduce electronic states in the energy-gap region, with strong impact on the optical properties of the material. The calculation results indicate that spin polarization is obtained when substitutional impurities or vacancy defects are introduced in the structure     

The ring of an outer von Neumann frame in modular lattices

We prove the following theorem. Let (a ₁, . . . , a _m , c ₁₂, . . . , c _1m ) be a spanning von Neumann m-frame of a modular lattice L, and let (u ₁, . . . , u _n , v ₁₂, . . . , v _1n ) be a spanning von Neumann n-frame of the interval [0, a ₁]. Assume that either m ≥ 4, or L is Arguesian and m ≥ 3. Let R* denote the coordinate ring of (a ₁, . . . , a _m , c ₁₂, . . . , c _1m ). If n ≥ 2, then there is a ring S* such that R* is isomorphic to the ring of all n × n matrices over S*. If n ≥ 4 or L is Arguesian and n ≥ 3, then we can choose S* as the coordinate ring of (u ₁, . . . , u _n , v ₁₂, . . . , v _1n ).     

Discrepancy of Arithmetic Progressions in Higher Dimensions

K. F. Roth (1964, Acta. Arith.9, 257-260) proved that the discrepancy of arithmetic progressions contained in [1, N]={1, 2, …, N} is at least cN^1/4, and later it was proved that this result is sharp. We consider the d-dimensional version of this problem. We give a lower estimate for the discrepancy of arithmetic progressions on [1, N]^d and prove that this result is nearly sharp. We use our results to give an upper estimate for the discrepancy of lines on an N×N lattice, and we also give an estimate for the discrepancy of a related random hypergraph.     

Surface energy for brittle fracture of alkali halides from lattice dynamics

A lattice dynamics approach to the surface energy γ for brittle fracture of several ionic crystals is presented, based on recent work on surface dynamics and a reformulation of a model previously worked out for metals. The model requires the knowledge of the crystal structure, the eigenfrequencies and eigenvectors of the normal modes of vibration, as well as an analytical definition of the critical interplanar displacement appropriate to the cleavage mode. Some temperature dependent values of γ are also computed for the (100) and (110) planes. Qualitatively the results indicate the correct cleavage systems for all cases and quantitively are reasonably consistent with the available experimental values.     

Electron-phonon interaction in carbon clathrate hex- $\mathsf{C_{40}}$

We investigate an extended spin ladder with diagonal frustrated exchanges in a wide parameter regime. By representing the model as a sum of semidefinite positive projection operators, we prove that this model has exactly a dimer ground state. Smoothly changing parameters may lead the model cover several exactly known models. Starting from this ladder model, we proposed two two-dimensional net models with exact ground states. The quantum phase transition of the ground state, due to the change of exchange strengths along perpendicular rungs, is also discussed. Received 13 October 2002 Published online 27 January 2003 RID="a" ID="a"e-mail: schen@thphy.uni.duesseldorf.de     

Study of the equilibrium surface composition of Co1−yFe2+yO4—II: The role of vacant and chemisorbed oxygen and charge transfer effect

In Part I of this work we have calculated the equilibrium cation composition at the surface of Co_1?yFe_2+yO₄ considering a stoichiometric oxygen content. In this paper we extend our model to include the effect on the cation surface composition of the equilibrium with the gas-phase. We take into account both the formation of surface oxygen vacancies and chemisorption. This model allows for an interpretation of AES experimental data obtained after different thermal treatments under gas fluxes or in UHV. While all previous calculations were based on the assumption that Co³⁺ and Fe²⁺ ions are never present simultaneously, here we discuss finally the effects of the charge transfer from Co²⁺ to Fe³⁺.     

Pre-resonant enhancement of the Raman scattering from KI:Tl+

E_g and T_2g spectra at room and nitrogen temperature at several laser wavelengths are reported for KI:Tl⁺. As resonance with Tl⁺ -absorption bands is approached the optic phonon parts of the spectra are enhanced relative to the acoustic phonon parts, and distortions occur within the acoustic and optic parts of the spectra. A model for the scattering is employed which involves electron-phonon coupling to nearest and nn neighbors. Exchange and crystal field contributions to the electron-phonon coupling are distinguished.     

Some remarks on the Green's function calculation of electronic states at solid surfaces

Summary The LCAO tight-binding method for computing electronic states in insulators and semiconductors has been recently recovered, in the Green's function formalism, for treating localized perturbations in ideal lattices. After a brief review of this method applied to surfaces, we face out the problem of a symmetry transformation turning an infinitely thick slab into a semi-infinite crystal. In this way conceptual and computational simplifications are achieved. We derive a formal expression for the charge density excess produced by a localized perturbation on the surface layer. This quantity is useful for the problem of inelastic scattering of atoms by surface phonons.

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Riassunto Il metodo LCAO di legame forte, in uso per calcolare gli stati elettronici d'isolanti e semiconduttori, è stato recentemente rivisitato, nel formalismo della funzione di Green, per studiare perturbazioni localizzate in cristalli ideali. Dopo una breve rassegna di questo metodo applicato alle superfici, si affronta il problema di una transformazione di simmetria, che porta da una lastra infinitamente spesso ad un cristallo semiinfinito. Cosí si ottengono delle semplificazioni sia concettuali che di calcolo. Infine si sviluppa un'espressione formale per il cambiamento nella densità di carica prodotta da una perturbazione localizzata che si trovi sullo strato superficiale. Questa quantità è di rilevanza nel problema dello scattering anelastico di atomi da parte di superfici libere.

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Резюме Недавно был развит метод ЛСАО сильной связи для вычисления электронных состояний в изоляторах и полупроводниках в формализме триновских функций, для рассмотрения локализованных возбуждений в идеальных решетках. Проводится краткий облему симметричното преобразования бесконечно толстой пластины в полубесконечный кристалл. Зтот подход позволяет получитв схематические и вычислителвные упрощения. Мы выводим формалвное выражение для приращения плотновти заряда, образованното локлизованным возмущнием на поверхности. Зто выражение полезно для решения проблемы неупругого рассеяния атомов на поверхностных фононах.

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Gruppo Nazionale di Struttura della Materia del CNR.