Kinetic Monte Carlo simulation of faceted islands in heteroepitaxy using multi-state lattice model

A solid-on-solid model is generalized to study the formation of Ge pyramid islands bounded by (105) facets on Si(100) substrates in two dimensions. Each atomic column is not only characterized by the local surface height but also by two deformation state variables dictating the local surface tilt and vertical extension. These deformations phenomenologically model surface reconstructions in (105) facets and enable the formation of islands which better resemble faceted pyramids. We demonstrate the model by application to a kinetic limited growth regime. We observe significantly reduced growth rates after faceting and a continuous nucleation of new islands until overcrowding occurs.Comment: 7 pages, 5 figure

On Multistage Learning a Hidden Hypergraph

Learning a hidden hypergraph is a natural generalization of the classical group testing problem that consists in detecting unknown hypergraph $H_{un}=H(V,E)$ by carrying out edge-detecting tests. In the given paper we focus our attention only on a specific family $F(t,s,\ell)$ of localized hypergraphs for which the total number of vertices $|V| = t$, the number of edges $|E|\le s$, $s\ll t$, and the cardinality of any edge $|e|\le\ell$, $\ell\ll t$. Our goal is to identify all edges of $H_{un}\in F(t,s,\ell)$ by using the minimal number of tests. We develop an adaptive algorithm that matches the information theory bound, i.e., the total number of tests of the algorithm in the worst case is at most $s\ell\log_2 t(1+o(1))$. We also discuss a probabilistic generalization of the problem.Comment: 5 pages, IEEE conferenc

Nonclassical Moments and their Measurement

Practically applicable criteria for the nonclassicality of quantum states are formulated in terms of different types of moments. For this purpose the moments of the creation and annihilation operators, of two quadratures, and of a quadrature and the photon number operator turn out to be useful. It is shown that all the required moments can be determined by homodyne correlation measurements. An example of a nonclassical effect that is easily characterized by our methods is amplitude-squared squeezing.Comment: 12 pages, 6 figure