Essential spectra and exponential estimates of eigenfunctions of lattice operators of quantum mechanics

This paper is devoted to estimates of the exponential decay of eigenfunctions of difference operators on the lattice Z^n which are discrete analogs of the Schr\"{o}dinger, Dirac and square-root Klein-Gordon operators. Our investigation of the essential spectra and the exponential decay of eigenfunctions of the discrete spectra is based on the calculus of so-called pseudodifference operators (i.e., pseudodifferential operators on the group Z^n) with analytic symbols and on the limit operators method. We obtain a description of the location of the essential spectra and estimates of the eigenfunctions of the discrete spectra of the main lattice operators of quantum mechanics, namely: matrix Schr\"{o}dinger operators on Z^n, Dirac operators on Z^3, and square root Klein-Gordon operators on Z^n

Localizations at infinity and essential spectrum of quantum Hamiltonians: I. General theory

We isolate a large class of self-adjoint operators H whose essential spectrum is determined by their behavior at large x and we give a canonical representation of their essential spectrum in terms of spectra of limits at infinity of translations of H. The configuration space is an arbitrary abelian locally compact not compact group.Comment: 63 pages. This is the published version with several correction

Demonstration of the difference Casimir force for samples with different charge carrier densities

A measurement of the Casimir force between a gold coated sphere and two Si plates of different carrier densities is performed using a high vacuum based atomic force microscope. The results are compared with the Lifshitz theory and good agreement is found. Our experiment demonstrates that by changing the carrier density of the semiconductor plate by several orders of magnitude it is possible to modify the Casimir interaction. This result may find applications in nanotechnology.Comment: 4 pages, 4 figures, to appear in Phys. Rev. Let

The 2004 Sumatra tsunami as recorded on the Atlantic coast of South America

The 2004 Sumatra tsunami propagated throughout the World Ocean and was clearly recorded by tide gauges on the Atlantic coast of South America. A total of 17 tsunami records were found and subsequently examined for this region. Tsunami wave heights and arrival times are generally consistent with numerical modeling results. Maximum wave heights of more than 1.2 m were observed on the coasts of Uruguay and southeastern Brazil. Marked differences in tsunami height from pairs of closely located tide gauge sites on the coast of Argentina illustrate the importance that local topographic resonance effects can have on the observed wave response. Findings reveal that, outside the Indian Ocean, the highest waves were recorded in the South Atlantic and not in the Pacific as has been previously suggested

Essential spectra of difference operators on \sZ^n-periodic graphs

Let (\cX, \rho) be a discrete metric space. We suppose that the group \sZ^n acts freely on $X$ and that the number of orbits of $X$ with respect to this action is finite. Then we call $X$ a \sZ^n-periodic discrete metric space. We examine the Fredholm property and essential spectra of band-dominated operators on $l^p(X)$ where $X$ is a \sZ^n-periodic discrete metric space. Our approach is based on the theory of band-dominated operators on \sZ^n and their limit operators. In case $X$ is the set of vertices of a combinatorial graph, the graph structure defines a Schr\"{o}dinger operator on $l^p(X)$ in a natural way. We illustrate our approach by determining the essential spectra of Schr\"{o}dinger operators with slowly oscillating potential both on zig-zag and on hexagonal graphs, the latter being related to nano-structures

An Analysis of the Representations of the Mapping Class Group of a Multi-Geon Three-Manifold

It is well known that the inequivalent unitary irreducible representations (UIR's) of the mapping class group $G$ of a 3-manifold give rise to ``theta sectors'' in theories of quantum gravity with fixed spatial topology. In this paper, we study several families of UIR's of $G$ and attempt to understand the physical implications of the resulting quantum sectors. The mapping class group of a three-manifold which is the connected sum of $\R^3$ with a finite number of identical irreducible primes is a semi-direct product group. Following Mackey's theory of induced representations, we provide an analysis of the structure of the general finite dimensional UIR of such a group. In the picture of quantized primes as particles (topological geons), this general group-theoretic analysis enables one to draw several interesting qualitative conclusions about the geons' behavior in different quantum sectors, without requiring an explicit knowledge of the UIR's corresponding to the individual primes.Comment: 52 pages, harvmac, 2 postscript figures, epsf required. Added an appendix proving the semi-direct product structure of the MCG, corrected an error in the characterization of the slide subgroup, reworded extensively. All our analysis and conclusions remain as befor

Comparison of the experimental data for the Casimir pressure with the Lifshitz theory at zero temperature

We perform detailed comparison of the experimental data of the experiment on the determination of the Casimir pressure between two parallel Au plates with the theoretical values computed using the Lifshitz formula at zero temperature. Computations are done using the optical data for the complex index of refraction of Au extrapolated to low frequencies by means of the Drude model with both most often used and other suggested Drude parameters. It is shown that the experimental data exclude the Lifshitz formula at zero temperature at a 70% confidence level if the Drude model with most often used values of the parameters is employed. If other values of the Drude parameters are used, the Lifshitz formula at zero frequency is experimentally excluded at a 95% confidence level. The Lifshitz formula at zero temperature combined with the generalized plasma-like model with most often used value of the plasma frequency is shown to be experimentally consistent. We propose a decisive experiment which will shed additional light on the role of relaxation properties of conduction electrons in the Casimir effect.Comment: 22 pages, 6 figures; Phys. Rev. B, to appea

Ghosts of the past and dreams of the future: the impact of temporal focus on responses to contextual ingroup devaluation.

addresses: University of Exeter, Exeter, UK. [email protected]: Journal Article; Research Support, Non-U.S. Gov'tCopyright © 2012 SAGE Publications. Author's draft version; post-print. Final version published by Sage available on Sage Journals Online http://online.sagepub.com/The authors investigated the impact of temporal focus on group members' responses to contextual ingroup devaluation. Four experimental studies demonstrated that following an induction of negative ingroup evaluation, participants primed with a past temporal focus reported behavioral intentions more consistent with this negative appraisal than participants primed with a future temporal focus. This effect was apparent only when a negative (but not a positive) evaluation was induced, and only among highly identified group members. Importantly, the interplay between temporal focus and group identification on relevant intentions was mediated by individual self-esteem, suggesting that focus on the future may be conducive to separating negative ingroup appraisals from individual self-evaluations. Taken together, the findings suggest that high identifiers' responses to ingroup evaluations may be predicated on their temporal focus: A focus on the past may lock such individuals within their group's history, whereas a vision of the future may open up opportunities for change

Improvement of Wear Performance of Nano-Multilayer PVD Coatings under Dry Hard End Milling Conditions Based on Their Architectural Development

The TiAlCrSiYN-based family of PVD (physical vapor deposition) hard coatings was specially designed for extreme conditions involving the dry ultra-performance machining of hardened tool steels. However, there is a strong potential for further advances in the wear performance of the coatings through improvements in their architecture. A few different coating architectures (monolayer, multilayer, bi-multilayer, bi-multilayer with increased number of alternating nano-layers) were studied in relation to cutting-tool life. Comprehensive characterization of the structure and properties of the coatings has been performed using XRD, SEM, TEM, micro-mechanical studies and tool-life evaluation. The wear performance was then related to the ability of the coating layer to exhibit minimal surface damage under operation, which is directly associated with the various micro-mechanical characteristics (such as hardness, elastic modulus and related characteristics; nano-impact; scratch test-based characteristics). The results presented exhibited that a substantial increase in tool life as well as improvement of the mechanical properties could be achieved through the architectural development of the coatings