Conductivity and the current-current correlation measure

We review various formulations of conductivity for one-particle Hamiltonians and relate them to the current-current correlation measure. We prove that the current-current correlation measure for random Schr\"odinger operators has a density at coincident energies provided the energy lies in a localization regime. The density vanishes at such energies and an upper bound on the rate of vanishing is computed. We also relate the current-current correlation measure to the localization length

Sufficient conditions for two-dimensional localization by arbitrarily weak defects in periodic potentials with band gaps

We prove, via an elementary variational method, 1d and 2d localization within the band gaps of a periodic Schrodinger operator for any mostly negative or mostly positive defect potential, V, whose depth is not too great compared to the size of the gap. In a similar way, we also prove sufficient conditions for 1d and 2d localization below the ground state of such an operator. Furthermore, we extend our results to 1d and 2d localization in d dimensions; for example, a linear or planar defect in a 3d crystal. For the case of D-fold degenerate band edges, we also give sufficient conditions for localization of up to D states.Comment: 9 pages, 3 figure

Wegner estimate for discrete alloy-type models

We study discrete alloy-type random Schr\"odinger operators on $\ell^2(\mathbb{Z}^d)$. Wegner estimates are bounds on the average number of eigenvalues in an energy interval of finite box restrictions of these types of operators. If the single site potential is compactly supported and the distribution of the coupling constant is of bounded variation a Wegner estimate holds. The bound is polynomial in the volume of the box and thus applicable as an ingredient for a localisation proof via multiscale analysis.Comment: Accepted for publication in AHP. For an earlier version see http://www.ma.utexas.edu/mp_arc-bin/mpa?yn=09-10

Coral development: from classical embryology to molecular control

The phylum Cnidaria is the closest outgroup to the triploblastic metazoans and as such offers unique insights into evolutionary questions at several levels. In the post-genomic era, a knowledge of the gene complement of representative cnidarians will be important for understanding the relationship between the expansion of gene families and the evolution of morphological complexity among more highly evolved metazoans. Studies of cnidarian development and its molecular control will provide information about the origins of the major bilaterian body axes, the origin of the third tissue layer, the mesoderm, and the evolution of nervous system patterning. We are studying the cnidarian Acropora millepora, a reef building scleractinian coral, and a member of the basal cnidarian class, the Anthozoa. We review ourwork on descriptive embryology and studies of selected transcription factor gene families, where our knowledge from Acropora is particularly advanced relative to other cnidarians. We also describe a recent preliminary whole genome initiative, a coral EST database.Eldon E. Ball, David C. Hayward, John S. Reece-Hoyes, Nikki R. Hislop, Gabrielle Samuel, Robert Saint, Peter L. Harrison and David J. Mille

Singular Modes of the Electromagnetic Field

We show that the mode corresponding to the point of essential spectrum of the electromagnetic scattering operator is a vector-valued distribution representing the square root of the three-dimensional Dirac's delta function. An explicit expression for this singular mode in terms of the Weyl sequence is provided and analyzed. An essential resonance thus leads to a perfect localization (confinement) of the electromagnetic field, which in practice, however, may result in complete absorption.Comment: 14 pages, no figure

Norm estimates of complex symmetric operators applied to quantum systems

This paper communicates recent results in theory of complex symmetric operators and shows, through two non-trivial examples, their potential usefulness in the study of Schr\"odinger operators. In particular, we propose a formula for computing the norm of a compact complex symmetric operator. This observation is applied to two concrete problems related to quantum mechanical systems. First, we give sharp estimates on the exponential decay of the resolvent and the single-particle density matrix for Schr\"odinger operators with spectral gaps. Second, we provide new ways of evaluating the resolvent norm for Schr\"odinger operators appearing in the complex scaling theory of resonances

SAT0583-HPR - Differences between service providers and users when defining feasible optimal NHS occupational therapy treatment for patients with thumb base OA : results from a Delphi study

Background: The OTTER (OsTeoarthritis Thumb ThERapy) trial is a two-year developmental study for a full randomised controlled trial (RCT) into the clinical and cost effectiveness of an occupational therapy and splint intervention for thumb base OA. To develop an optimal package of care for evaluation within a multi-centre RCT, the views of both clinicians and patients are crucial. Objectives: To conduct a Delphi study to obtain agreement between both patients with thumb base OA and AHPs concerning the most appropriate optimal NHS OT programme, splint and placebo splint intervention to use in the RCT. Methods: The Delphi panel consisted of 63 AHPs experienced in treating adults with thumb base OA, and 7 patients with thumb base OA. The panel were asked to rate how much they agreed or disagreed about what optimal NHS OT care for thumb base OA should include, and what method(s) of delivery (individual one-to-one, group, patient leaflets, or telephone advice) they deemed were more appropriate. The Delphi study comprised 3 rounds. A seven-point Likert-type scale was used. Pre-defined inclusion and exclusion criteria were applied in order to reach a final number of statements which, in turn, created the desired tool. Group differences were analysed using Mann-Whitney U tests. Results: Between-groups analyses showed significant differences in the ratings of overall importance of items to be included in an optimal NHS OT consultation (Table 1). Conclusions: AHPs and patients differed in their views about the importance of including ‘Education for Family/Significant Others/Carers’, ‘NHS Clinic Procedures’, ‘Prognosis Advice’, ‘Referral to other Health Care Professional’, ‘Sleep Assessment and Management’ and ‘Treatment Options’ in an optimal NHS OT consultation, and in the methods of delivery used in the consultation. AHPs placed significantly less importance than patients on ‘One-to-One Contact’, ‘Leaflets’ and ‘Telephone Advice’. These findings demonstrate the importance of consulting with patients at an early stage in developing an intervention

Low lying spectrum of weak-disorder quantum waveguides

We study the low-lying spectrum of the Dirichlet Laplace operator on a randomly wiggled strip. More precisely, our results are formulated in terms of the eigenvalues of finite segment approximations of the infinite waveguide. Under appropriate weak-disorder assumptions we obtain deterministic and probabilistic bounds on the position of the lowest eigenvalue. A Combes-Thomas argument allows us to obtain so-called 'initial length scale decay estimates' at they are used in the proof of spectral localization using the multiscale analysis.Comment: Accepted for publication in Journal of Statistical Physics http://www.springerlink.com/content/0022-471