Landau-Zener Formula in a "Non-Adiabatic" regime for avoided crossings

We study a two-level transition probability for a finite number of avoided crossings with a small interaction. Landau-Zener formula, which gives the transition probability for one avoided crossing as $e^{-\pi\frac{\varepsilon^{2}}{h}}$, implies that the parameter $h$ and the interaction $\varepsilon$ play an opposite role when both tend to $0$. The exact WKB method produces a generalization of that formula under the optimal regime $\frac{h}{\varepsilon^2}$ tends to~0. In this paper, we investigate the case $\frac{\varepsilon^2}{h}$ tends to 0, called "non-adiabatic" regime. This is done by reducing the associated Hamiltonian to a microlocal branching model which gives us the asymptotic expansions of the local transfer matrices.Comment: 52 pages, 4 figures, accepted in Analysis and Mathematical Physics on 26 February 202

OBDD-Based Representation of Interval Graphs

A graph $G = (V,E)$ can be described by the characteristic function of the edge set $\chi_E$ which maps a pair of binary encoded nodes to 1 iff the nodes are adjacent. Using \emph{Ordered Binary Decision Diagrams} (OBDDs) to store $\chi_E$ can lead to a (hopefully) compact representation. Given the OBDD as an input, symbolic/implicit OBDD-based graph algorithms can solve optimization problems by mainly using functional operations, e.g. quantification or binary synthesis. While the OBDD representation size can not be small in general, it can be provable small for special graph classes and then also lead to fast algorithms. In this paper, we show that the OBDD size of unit interval graphs is $O(\ | V \ | /\log \ | V \ |)$ and the OBDD size of interval graphs is $O(\ | V \ | \log \ | V \ |)$which both improve a known result from Nunkesser and Woelfel (2009). Furthermore, we can show that using our variable order and node labeling for interval graphs the worst-case OBDD size is$\Omega(\ | V \ | \log \ | V \ |)$. We use the structure of the adjacency matrices to prove these bounds. This method may be of independent interest and can be applied to other graph classes. We also develop a maximum matching algorithm on unit interval graphs using$O(\log \ | V \ |)$operations and a coloring algorithm for unit and general intervals graphs using$O(\log^2 \ | V \ |)$ operations and evaluate the algorithms empirically.Comment: 29 pages, accepted for 39th International Workshop on Graph-Theoretic Concepts 201

Symmetry Breaking by Metaheuristic Search

Several methods exist for breaking symmetry in constraint problems, but most potentially suffer from high memory requirements, high computational overhead, or both. We describe a new partial symmetry breaking method that can be applied to arbitrary variable/value symmetries. It models dominance detection as a nonstationary optimisation problem, and solves it by resource-bounded metaheuristic search in the symmetry group. It has low memory requirement and computational overhead, yet in preliminary experiments on BIBD design it breaks most symmetries

On the strong coupling N(∗)N(∗)πN^{(*)}N^{(*)}\pi

We study the strong vertices $N^*N\pi$, $N^*N^*\pi$ and $NN\pi$ in QCD, where $N^*$ denotes the negative parity $N (1535)$ state. We use the most general form of the interpolating currents to calculate the corresponding strong coupling constants. It is obtained that the coupling associated to $N^*N\pi$ vertex is strongly suppressed compared to those related to two other vertices. The strong coupling corresponding to $N^*N^*\pi$ is obtained to be roughly half of that of $NN\pi$ vertex. We compare the obtained results on $N^*N\pi$ and $NN\pi$ vertices with the existing predictions of other theoretical studies as well as those extracted from the experimental data.Comment: 15 Pages, 4 Figures and 3 Table

El impacto espacial de las economías de aglomeración y su efecto sobre la estructura urbana.El caso de la industria en Barcelona, 1986-1996

Este trabajo trata sobre el papel de la accesibilidad espacial a las economías de aglomeración en el cambio de la estructura espacial del empleo industrial para el caso de la Región Metropolitana de Barcelona (RMB). Utilizando como indicador de cambios en la estructura espacial del empleo el crecimiento de la densidad bruta del empleo municipal entre 1986 y 1996 para siete subsectores industriales, se explora el impacto espacial de las economías de aglomeración que operan a escala local -el municipio y tres áreas de 5, 8 y 12 kilómetros que rodean al propio municipio-, aquellas que emergen del CBD y de los principales subcentros especializados de la región, y las economías de red asociadas al total de puestos de trabajo de la región cuyo acceso depende de la distancia respecto a las principales infraestructuras de transporte

Boron concentration profiling by high angle annular dark field-scanning transmission electron microscopy in homoepitaxial delta-doped diamond layers

To develop further diamond related devices, the concentration and spatial location of dopants should be controlled down to the nanometer scale. Scanning transmission electron microscopy using the high angle annular dark field mode is shown to be sensitive to boron doping in diamond epilayers. An analytical procedure is described, whereby local boron concentrations above 1020 cm-3 were quantitatively derived down to nanometer resolution from the signal dependence on thickness and boron content. Experimental boron local doping profiles measured on diamond p-/p++/p- multilayers are compared to macroscopic profiles obtained by secondary ion mass spectrometry, avoiding reported artefacts.4 page

Local boron doping quantification in homoepitaxial diamond structures

The capability of transmission electronmicroscopy (TEM) using the high angle annular dark fieldmode (HAADF,also labelled Z-contrast) to quantify boron concentration, in the high doping range between 1019cm−3 and 1021cm−3, is demonstrated. Thanks to the large relative variation of atomic number Z between carbon and boron, doping concentration maps and profiles are obtained with a nanometer-scale resolution. A novel numerical simulation procedure allows the boron concentration quantification and demonstrates the high sensitivity and spatial resolution of the technique.4 page