28 research outputs found
Absence of mobility edge for the Anderson random potential on tree graphs at weak disorder
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
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
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
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
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 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 outcoming wires are attached to the leaves of
the tree. In terms of the transmission amplitudes , the total
Landauer transmission is , so that each channel
is characterized by the weight . We numerically measure the
typical multifractal singularity spectrum of these weights as a
function of the disorder strength and we obtain the following conclusions
for its left-termination point . In the delocalized phase ,
is strictly positive and is associated with a
moment index . At criticality, it vanishes and is
associated with the moment index . In the localized phase ,
is associated with some moment index . 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
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
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
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)
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