Theoretical analysis of the electronic structure of the stable and metastable c(2x2) phases of Na on Al(001): Comparison with angle-resolved ultra-violet photoemission spectra

Using Kohn-Sham wave functions and their energy levels obtained by density-functional-theory total-energy calculations, the electronic structure of the two c(2x2) phases of Na on Al(001) are analysed; namely, the metastable hollow-site structure formed when adsorption takes place at low temperature, and the stable substitutional structure appearing when the substrate is heated thereafter above ca. 180K or when adsorption takes place at room temperature from the beginning. The experimentally obtained two-dimensional band structures of the surface states or resonances are well reproduced by the calculations. With the help of charge density maps it is found that in both phases, two pronounced bands appear as the result of a characteristic coupling between the valence-state band of a free c(2x2)-Na monolayer and the surface-state/resonance band of the Al surfaces; that is, the clean (001) surface for the metastable phase and the unstable, reconstructed "vacancy" structure for the stable phase. The higher-lying band, being Na-derived, remains metallic for the unstable phase, whereas it lies completely above the Fermi level for the stable phase, leading to the formation of a surface-state/resonance band-structure resembling the bulk band-structure of an ionic crystal.Comment: 11 pages, 11 postscript figures, published in Phys. Rev. B 57, 15251 (1998). Other related publications can be found at http://www.rz-berlin.mpg.de/th/paper.htm

Model study of adsorbed metallic quantum dots: Na on Cu(111)

We model electronic properties of the second monolayer Na adatom islands (quantum dots) on the Cu(111) surface covered homogeneously by the first Na monolayer. An axially-symmetric three-dimensional jellium model, taking into account the effects due to the first Na monolayer and the Cu substrate, has been developed. The electronic structure is solved within the local-density approximation of the density-functional theory using a real-space multigrid method. The model enables the study of systems consisting of thousands of Na-atoms. The results for the local density of states are compared with differential conductance ($dI/dV$) spectra and constant current topographs from Scanning Tunneling Microscopy.Comment: 10 pages, 8 figures. For better quality figures, download http://www.fyslab.hut.fi/~tto/cylart1.pd

Regularizing Portfolio Optimization

The optimization of large portfolios displays an inherent instability to estimation error. This poses a fundamental problem, because solutions that are not stable under sample fluctuations may look optimal for a given sample, but are, in effect, very far from optimal with respect to the average risk. In this paper, we approach the problem from the point of view of statistical learning theory. The occurrence of the instability is intimately related to over-fitting which can be avoided using known regularization methods. We show how regularized portfolio optimization with the expected shortfall as a risk measure is related to support vector regression. The budget constraint dictates a modification. We present the resulting optimization problem and discuss the solution. The L2 norm of the weight vector is used as a regularizer, which corresponds to a diversification "pressure". This means that diversification, besides counteracting downward fluctuations in some assets by upward fluctuations in others, is also crucial because it improves the stability of the solution. The approach we provide here allows for the simultaneous treatment of optimization and diversification in one framework that enables the investor to trade-off between the two, depending on the size of the available data set

Effects of boundary conditions on magnetization switching in kinetic Ising models of nanoscale ferromagnets

Magnetization switching in highly anisotropic single-domain ferromagnets has been previously shown to be qualitatively described by the droplet theory of metastable decay and simulations of two-dimensional kinetic Ising systems with periodic boundary conditions. In this article we consider the effects of boundary conditions on the switching phenomena. A rich range of behaviors is predicted by droplet theory: the specific mechanism by which switching occurs depends on the structure of the boundary, the particle size, the temperature, and the strength of the applied field. The theory predicts the existence of a peak in the switching field as a function of system size in both systems with periodic boundary conditions and in systems with boundaries. The size of the peak is strongly dependent on the boundary effects. It is generally reduced by open boundary conditions, and in some cases it disappears if the boundaries are too favorable towards nucleation. However, we also demonstrate conditions under which the peak remains discernible. This peak arises as a purely dynamic effect and is not related to the possible existence of multiple domains. We illustrate the predictions of droplet theory by Monte Carlo simulations of two-dimensional Ising systems with various system shapes and boundary conditions.Comment: RevTex, 48 pages, 13 figure