Almost-zero-energy Eigenvalues of Some Broken Supersymmetric Systems

For a quantum mechanical system with broken supersymmetry, we present a simple method of determining the ground state when the corresponding energy eigenvalue is sufficiently small. A concise formula is derived for the approximate ground state energy in an associated, well-separated, asymmetric double-well-type potential. Our discussion is also relevant for the analysis of the fermion bound state in the kink-antikink scalar background.Comment: revised version, to be pubilshed in PR

Use of geostatistical Bayesian updating to integrate airborne radiometrics and soil geochemistry to improve mapping for mineral exploration

Mineral exploration programmes around the world use data from remote sensing, geophysics, and direct sampling. On a regional scale, the combination of airborne geophysics and ground-based geochemical sampling can aid geological mapping and mineral exploration. Since airborne geophysical and traditional soil-sampling data are generated at different spatial resolutions, they are not immediately comparable due to their different sampling density. Several geostatistical techniques, including indicator cokriging and collocated cokriging, can be used to integrate different types of data into a geostatistical model. However, with increasing numbers of variables the inference of the crosscovariance model required for cokriging can be demanding in terms of effort and computational time. In this paper a Gaussian-based Bayesian updating approach is applied to integrate airborne radiometric data and ground-sampled geochemical soil data to maximize information generated from the soil survey, enabling more accurate geological interpretation for the exploration and development of natural resources. The Bayesian updating technique decomposes the collocated estimate into two models: prior and likelihood models. The prior model is built from primary information and the likelihood model is built from secondary information. The prior model is then updated with the likelihood model to build the final model. The approach allows multiple secondary variables to be simultaneously integrated into the mapping of the primary variable. The Bayesian updating approach is demonstrated using a case study from Northern Ireland. The geostatistical technique was used to improve the resolution of soil geochemistry, at a density of one sample per 2 km2, by integrating more closely measured airborne geophysical data from the GSNI Tellus Survey, measured over a footprint of 65 x 200 m. The directly measured geochemistry data were considered as primary data and the airborne radiometric data were used as secondary data. The approach produced more detailed updated maps and in particular enhanced information on the mapped distributions of zinc, copper, and lead. The enhanced delineation of an elongated northwest/southeast trending zone in the updated maps strengthened the potential for discovering stratabound base metal deposits

Deterministic and stochastic descriptions of gene expression dynamics

A key goal of systems biology is the predictive mathematical description of gene regulatory circuits. Different approaches are used such as deterministic and stochastic models, models that describe cell growth and division explicitly or implicitly etc. Here we consider simple systems of unregulated (constitutive) gene expression and compare different mathematical descriptions systematically to obtain insight into the errors that are introduced by various common approximations such as describing cell growth and division by an effective protein degradation term. In particular, we show that the population average of protein content of a cell exhibits a subtle dependence on the dynamics of growth and division, the specific model for volume growth and the age structure of the population. Nevertheless, the error made by models with implicit cell growth and division is quite small. Furthermore, we compare various models that are partially stochastic to investigate the impact of different sources of (intrinsic) noise. This comparison indicates that different sources of noise (protein synthesis, partitioning in cell division) contribute comparable amounts of noise if protein synthesis is not or only weakly bursty. If protein synthesis is very bursty, the burstiness is the dominant noise source, independent of other details of the model. Finally, we discuss two sources of extrinsic noise: cell-to-cell variations in protein content due to cells being at different stages in the division cycles, which we show to be small (for the protein concentration and, surprisingly, also for the protein copy number per cell) and fluctuations in the growth rate, which can have a significant impact.Comment: 23 pages, 5 figures; Journal of Statistical physics (2012

Quasi-Normal Modes of Schwarzschild Anti-De Sitter Black Holes: Electromagnetic and Gravitational Perturbations

We study the quasi-normal modes (QNM) of electromagnetic and gravitational perturbations of a Schwarzschild black hole in an asymptotically Anti-de Sitter (AdS) spacetime. Some of the electromagnetic modes do not oscillate, they only decay, since they have pure imaginary frequencies. The gravitational modes show peculiar features: the odd and even gravitational perturbations no longer have the same characteristic quasinormal frequencies. There is a special mode for odd perturbations whose behavior differs completely from the usual one in scalar and electromagnetic perturbation in an AdS spacetime, but has a similar behavior to the Schwarzschild black hole in an asymptotically flat spacetime: the imaginary part of the frequency goes as 1/r+, where r+ is the horizon radius. We also investigate the small black hole limit showing that the imaginary part of the frequency goes as r+^2. These results are important to the AdS/CFT conjecture since according to it the QNMs describe the approach to equilibrium in the conformal field theory.Comment: 2 figure

(1+1)-Dirac particle with position-dependent mass in complexified Lorentz scalar interactions: effectively PT-symmetric

The effect of the built-in supersymmetric quantum mechanical language on the spectrum of the (1+1)-Dirac equation, with position-dependent mass (PDM) and complexified Lorentz scalar interactions, is re-emphasized. The signature of the "quasi-parity" on the Dirac particles' spectra is also studied. A Dirac particle with PDM and complexified scalar interactions of the form S(z)=S(x-ib) (an inversely linear plus linear, leading to a PT-symmetric oscillator model), and S(x)=S_{r}(x)+iS_{i}(x) (a PT-symmetric Scarf II model) are considered. Moreover, a first-order intertwining differential operator and an $\eta$-weak-pseudo-Hermiticity generator are presented and a complexified PT-symmetric periodic-type model is used as an illustrative example.Comment: 11 pages, no figures, revise

Identifying topological edge states in 2D optical lattices using light scattering

We recently proposed in a Letter [Physical Review Letters 108 255303] a novel scheme to detect topological edge states in an optical lattice, based on a generalization of Bragg spectroscopy. The scope of the present article is to provide a more detailed and pedagogical description of the system - the Hofstadter optical lattice - and probing method. We first show the existence of topological edge states, in an ultra-cold gas trapped in a 2D optical lattice and subjected to a synthetic magnetic field. The remarkable robustness of the edge states is verified for a variety of external confining potentials. Then, we describe a specific laser probe, made from two lasers in Laguerre-Gaussian modes, which captures unambiguous signatures of these edge states. In particular, the resulting Bragg spectra provide the dispersion relation of the edge states, establishing their chiral nature. In order to make the Bragg signal experimentally detectable, we introduce a "shelving method", which simultaneously transfers angular momentum and changes the internal atomic state. This scheme allows to directly visualize the selected edge states on a dark background, offering an instructive view on topological insulating phases, not accessible in solid-state experiments.Comment: 17 pages, 10 figures. Revised and extended version, to appear in EJP Special Topic for the special issue on "Novel Quantum Phases and Mesoscopic Physics in Quantum Gases". Extended version of arXiv:1203.124

Supersymmetrization of Quaternion Dirac Equation for Generalized Fields of Dyons

The quaternion Dirac equation in presence of generalized electromagnetic field has been discussed in terms of two gauge potentials of dyons. Accordingly, the supersymmetry has been established consistently and thereafter the one, two and component Dirac Spinors of generalized quaternion Dirac equation of dyons for various energy and spin values are obtained for different cases in order to understand the duality invariance between the electric and magnetic constituents of dyons.Comment: Key words: Supersymmetry, quaternion, Dirac equation, dyons PACS No.: 11.30.Pb, 14.80.Ly, 03.65.G

A Group-Theoretical Method for Natanzon Potentials in Position-Dependent Mass Background

A new manner for deriving the exact potentials is presented. By making use of conformal mappings, the general expression of the effective potentials deduced under su(1,1) algebra can be brought back to the general Natanzon hypergeometric potentials

Aspectos microscópicos da interação feijoeiro-Colletotrichum lindemuthianum mediados pelo silício

A antracnose, causada pelo fungo Colletotrichum lindemuthianum, é uma das doenças mais destrutivas que afetam a cultura do feijoeiro. Com o objetivo de encontrar alternativas para o controle dessa doença, o presente trabalho investigou, em nível microscópico, o efeito do silício (Si) na resistência do feijoeiro à infecção por C. lindemuthianum. Plantas de feijoeiro (cv. Pérola) foram cultivadas em solução nutritiva contendo 0 (-Si) ou 2 mM (+Si) de Si e inoculadas no estádio de crescimento V4 com uma suspensão de conídios de C. lindemuthianum. A severidade da antracnose decresceu cerca de 52% nas folhas das plantas supridas com Si (4,4%) em relação às folhas das plantas não supridas (8,5%). Observações de folhas de feijoeiro das plantas não supridas com Si no microscópio eletrônico de varredura revelaram alterações morfológicas nas nervuras em contraste com as folhas de plantas supridas com Si. Utilizando-se a microanálise de raios-X, verificou-se maior concentração dos minerais enxofre, potássio e Si nas folhas das plantas supridas com Si. Em conclusão, o suprimento de Si em plantas de feijoeiro foi importante para reduzir os sintomas da antracnose