28 research outputs found

    Absence of mobility edge for the Anderson random potential on tree graphs at weak disorder

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    Our recently established criterion for the formation of extended states on tree graphs in the presence of disorder is shown to have the surprising implication that for bounded random potentials, as in the Anderson model, there is no transition to a spectral regime of Anderson localization, in the form usually envisioned, unless the disorder is strong enough

    Quasi-classical versus non-classical spectral asymptotics for magnetic Schroedinger operators with decreasing electric potentials

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    We consider the Schroedinger operator H on L^2(R^2) or L^2(R^3) with constant magnetic field and electric potential V which typically decays at infinity exponentially fast or has a compact support. We investigate the asymptotic behaviour of the discrete spectrum of H near the boundary points of its essential spectrum. If the decay of V is Gaussian or faster, this behaviour is non-classical in the sense that it is not described by the quasi-classical formulas known for the case where V admits a power-like decay.Comment: Corrected versio

    Existence and uniqueness of the integrated density of states for Schr\"odinger operators with magnetic fields and unbounded random potentials

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    The object of the present study is the integrated density of states of a quantum particle in multi-dimensional Euclidean space which is characterized by a Schr\"odinger operator with a constant magnetic field and a random potential which may be unbounded from above and from below. For an ergodic random potential satisfying a simple moment condition, we give a detailed proof that the infinite-volume limits of spatial eigenvalue concentrations of finite-volume operators with different boundary conditions exist almost surely. Since all these limits are shown to coincide with the expectation of the trace of the spatially localized spectral family of the infinite-volume operator, the integrated density of states is almost surely non-random and independent of the chosen boundary condition. Our proof of the independence of the boundary condition builds on and generalizes certain results by S. Doi, A. Iwatsuka and T. Mine [Math. Z. {\bf 237} (2001) 335-371] and S. Nakamura [J. Funct. Anal. {\bf 173} (2001) 136-152].Comment: This paper is a revised version of the first part of the first version of math-ph/0010013. For a revised version of the second part, see math-ph/0105046. To appear in Reviews in Mathematical Physic

    Ballistic transport in random magnetic fields with anisotropic long-ranged correlations

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    We present exact theoretical results about energetic and dynamic properties of a spinless charged quantum particle on the Euclidean plane subjected to a perpendicular random magnetic field of Gaussian type with non-zero mean. Our results refer to the simplifying but remarkably illuminating limiting case of an infinite correlation length along one direction and a finite but strictly positive correlation length along the perpendicular direction in the plane. They are therefore ``random analogs'' of results first obtained by A. Iwatsuka in 1985 and by J. E. M\"uller in 1992, which are greatly esteemed, in particular for providing a basic understanding of transport properties in certain quasi-two-dimensional semiconductor heterostructures subjected to non-random inhomogeneous magnetic fields

    Anderson localization on the Cayley tree : multifractal statistics of the transmission at criticality and off criticality

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    In contrast to finite dimensions where disordered systems display multifractal statistics only at criticality, the tree geometry induces multifractal statistics for disordered systems also off criticality. For the Anderson tight-binding localization model defined on a tree of branching ratio K=2 with NN generations, we consider the Miller-Derrida scattering geometry [J. Stat. Phys. 75, 357 (1994)], where an incoming wire is attached to the root of the tree, and where KNK^{N} outcoming wires are attached to the leaves of the tree. In terms of the KNK^{N} transmission amplitudes tjt_j, the total Landauer transmission is Tjtj2T \equiv \sum_j | t_j |^2, so that each channel jj is characterized by the weight wj=tj2/Tw_j=| t_j |^2/T. We numerically measure the typical multifractal singularity spectrum f(α)f(\alpha) of these weights as a function of the disorder strength WW and we obtain the following conclusions for its left-termination point α+(W)\alpha_+(W). In the delocalized phase W<WcW<W_c, α+(W)\alpha_+(W) is strictly positive α+(W)>0\alpha_+(W)>0 and is associated with a moment index q+(W)>1q_+(W)>1. At criticality, it vanishes α+(Wc)=0\alpha_+(W_c)=0 and is associated with the moment index q+(Wc)=1q_+(W_c)=1. In the localized phase W>WcW>W_c, α+(W)=0\alpha_+(W)=0 is associated with some moment index q+(W)<1q_+(W)<1. We discuss the similarities with the exact results concerning the multifractal properties of the Directed Polymer on the Cayley tree.Comment: v2=final version (16 pages

    The caCORE Software Development Kit: Streamlining construction of interoperable biomedical information services

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    BACKGROUND: Robust, programmatically accessible biomedical information services that syntactically and semantically interoperate with other resources are challenging to construct. Such systems require the adoption of common information models, data representations and terminology standards as well as documented application programming interfaces (APIs). The National Cancer Institute (NCI) developed the cancer common ontologic representation environment (caCORE) to provide the infrastructure necessary to achieve interoperability across the systems it develops or sponsors. The caCORE Software Development Kit (SDK) was designed to provide developers both within and outside the NCI with the tools needed to construct such interoperable software systems. RESULTS: The caCORE SDK requires a Unified Modeling Language (UML) tool to begin the development workflow with the construction of a domain information model in the form of a UML Class Diagram. Models are annotated with concepts and definitions from a description logic terminology source using the Semantic Connector component. The annotated model is registered in the Cancer Data Standards Repository (caDSR) using the UML Loader component. System software is automatically generated using the Codegen component, which produces middleware that runs on an application server. The caCORE SDK was initially tested and validated using a seven-class UML model, and has been used to generate the caCORE production system, which includes models with dozens of classes. The deployed system supports access through object-oriented APIs with consistent syntax for retrieval of any type of data object across all classes in the original UML model. The caCORE SDK is currently being used by several development teams, including by participants in the cancer biomedical informatics grid (caBIG) program, to create compatible data services. caBIG compatibility standards are based upon caCORE resources, and thus the caCORE SDK has emerged as a key enabling technology for caBIG. CONCLUSION: The caCORE SDK substantially lowers the barrier to implementing systems that are syntactically and semantically interoperable by providing workflow and automation tools that standardize and expedite modeling, development, and deployment. It has gained acceptance among developers in the caBIG program, and is expected to provide a common mechanism for creating data service nodes on the data grid that is under development

    Bounds on the heat kernel of the Schroedinger operator in a random electromagnetic field

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    We obtain lower and upper bounds on the heat kernel and Green functions of the Schroedinger operator in a random Gaussian magnetic field and a fixed scalar potential. We apply stochastic Feynman-Kac representation, diamagnetic upper bounds and the Jensen inequality for the lower bound. We show that if the covariance of the electromagnetic (vector) potential is increasing at large distances then the lower bound is decreasing exponentially fast for large distances and a large time.Comment: some technical improvements, new references, to appear in Journ.Phys.

    The CAP cancer protocols – a case study of caCORE based data standards implementation to integrate with the Cancer Biomedical Informatics Grid

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    BACKGROUND: The Cancer Biomedical Informatics Grid (caBIG™) is a network of individuals and institutions, creating a world wide web of cancer research. An important aspect of this informatics effort is the development of consistent practices for data standards development, using a multi-tier approach that facilitates semantic interoperability of systems. The semantic tiers include (1) information models, (2) common data elements, and (3) controlled terminologies and ontologies. The College of American Pathologists (CAP) cancer protocols and checklists are an important reporting standard in pathology, for which no complete electronic data standard is currently available. METHODS: In this manuscript, we provide a case study of Cancer Common Ontologic Representation Environment (caCORE) data standard implementation of the CAP cancer protocols and checklists model – an existing and complex paper based standard. We illustrate the basic principles, goals and methodology for developing caBIG™ models. RESULTS: Using this example, we describe the process required to develop the model, the technologies and data standards on which the process and models are based, and the results of the modeling effort. We address difficulties we encountered and modifications to caCORE that will address these problems. In addition, we describe four ongoing development projects that will use the emerging CAP data standards to achieve integration of tissue banking and laboratory information systems. CONCLUSION: The CAP cancer checklists can be used as the basis for an electronic data standard in pathology using the caBIG™ semantic modeling methodology

    A small new species of Crenicichla Heckel, 1840 from middle rio Xingu, Brazil (Teleostei: Cichlidae)

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    A new species of Crenicichla is described from the middle rio Xingu and tributaries, upstream from Volta Grande do Xingu. The largest specimen measured 47.8 mm SL. The new species can be distinguished from all other Crenicichla species by the combination of the following character states: presence of serrae on supracleithrum (diagnostic of Crenicichla wallacii species group), large caudal blotch centrally located on caudal lateral line (shared with C. urosema and C. virgatula), vertical dark stripes on the caudal fin and up to three series of teeth on premaxilla and maxilla (vs. more than four series of teeth). The new species described herein is the eleventh species of Crenicichla listed from the rio Xingu basin. Similarities of color pattern among small species of Crenicichla is discussed. © 2015, Sociedade Brasileira de Ictiologia
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