Spectral Duality for Planar Billiards

For a bounded open domain $\Omega$ with connected complement in ${\bf R}^2$ and piecewise smooth boundary, we consider the Dirichlet Laplacian $-\Delta_\Omega$ on $\Omega$ and the S-matrix on the complement $\Omega^c$. We show that the on-shell S-matrices ${\bf S}_k$ have eigenvalues converging to 1 as $k\uparrow k_0$ exactly when $-\Delta_\Omega$ has an eigenvalue at energy $k_0^2$. This includes multiplicities, and proves a weak form of ``transparency'' at $k=k_0$. We also show that stronger forms of transparency, such as ${\bf S}_{k_0}$ having an eigenvalue 1 are not expected to hold in general.Comment: 33 pages, Postscript, A

Universality of Frequency and Field Scaling of the Conductivity Measured by Ac-Susceptibility of a Ybco-Film

Utilizing a novel and exact inversion scheme, we determine the complex linear conductivity $\sigma (\omega )$ from the linear magnetic ac-susceptibility which has been measured from 3\,mHz to 50\,MHz in fields between 0.4\,T and 4\,T applied parallel to the c-axis of a 250\,nm thin disk. The frequency derivative of the phase $\sigma ''/\sigma '$ and the dynamical scaling of $\sigma (\omega)$ above and below $T_g(B)$ provide clear evidence for a continuous phase transition at $T_g$ to a generic superconducting state. Based on the vortex-glass scaling model, the resulting critical exponents $\nu$ and $z$ are close to those frequently obtained on films by other means and associated with an 'isotropic' vortex glass. The field effect on $\sigma(\omega)$ can be related to the increase of the glass coherence length, $\xi_g\sim B$.Comment: 8 pages (5 figures upon request), revtex 3.0, APK.94.01.0

On the third critical field in Ginzburg-Landau theory

Using recent results by the authors on the spectral asymptotics of the Neumann Laplacian with magnetic field, we give precise estimates on the critical field, $H_{C_3}$, describing the appearance of superconductivity in superconductors of type II. Furthermore, we prove that the local and global definitions of this field coincide. Near $H_{C_3}$ only a small part, near the boundary points where the curvature is maximal, of the sample carries superconductivity. We give precise estimates on the size of this zone and decay estimates in both the normal (to the boundary) and parallel variables

Physical Separation of Straw Stem Components to Reduce Silica

In this paper, we describe ongoing efforts to solve challenges to using straw for bioenergy and bioproducts. Among these, silica in straw forms a low-melting eutectic with potassium, causing slag deposits, and chlorides cause corrosion beneath the deposits. Straw consists principally of stems, leaves, sheaths, nodes, awns, and chaff. Leaves and sheaths are higher in silica, while chaff, leaves and nodes are the primary source of fines. Our approach to reducing silica is to selectively harvest the straw stems using an in-field physical separation, leaving the remaining components in the field to build soil organic matter and contribute soil nutrients

Towards a construction of inclusive collision cross-sections in the massless Nelson model

The conventional approach to the infrared problem in perturbative quantum electrodynamics relies on the concept of inclusive collision cross-sections. A non-perturbative variant of this notion was introduced in algebraic quantum field theory. Relying on these insights, we take first steps towards a non-perturbative construction of inclusive collision cross-sections in the massless Nelson model. We show that our proposal is consistent with the standard scattering theory in the absence of the infrared problem and discuss its status in the infrared-singular case.Comment: 23 pages, LaTeX. As appeared in Ann. Henri Poincar\'

Familial influences on sustained attention and inhibition in preschoolers

Background: In this study several aspects of attention were studied in 237 nearly 6-year-old twin pairs. Specifically, the ability to sustain attention and inhibition were investigated using a computerized test battery (Amsterdam Neuropsychological Tasks). Furthermore, the Teacher's Report Form (TRF) was filled out by the teacher of the child and the attention subscale of this questionnaire was analyzed. Methods: The variance in performance on the different tasks of the test battery and the score on the attention scale of the TRF were decomposed into a contribution of the additive effects of many genes (A), environmental effects that are shared by twins (C) and unique environmental influences not shared by twins (E) by using data from MZ and DZ twins. Results: The genetic model fitting results showed an effect of A and E for the attention scale of the TRF, and for some of the inhibition and sustained attention measures. For most of the attention variables, however, it was not possible to decide between a model with A and E or a model with C and E. Time-on-task effects on reaction time or number of errors and the delay after making an error did not show familial resemblances. A remarkable finding was that the heritability of the attention scale of the TRF was found to be higher than the heritability of indices that can be considered to be more direct measures of attention, such as mean tempo in the sustained attention task and response speed in the Go-NoGo task. Conclusion: In preschoolers, familial resemblances on sustained attention and inhibition were observed. © Association for Child Psychology and Psychiatry, 2004

Relative Oscillation Theory, Weighted Zeros of the Wronskian, and the Spectral Shift Function

We develop an analog of classical oscillation theory for Sturm-Liouville operators which, rather than measuring the spectrum of one single operator, measures the difference between the spectra of two different operators. This is done by replacing zeros of solutions of one operator by weighted zeros of Wronskians of solutions of two different operators. In particular, we show that a Sturm-type comparison theorem still holds in this situation and demonstrate how this can be used to investigate the finiteness of eigenvalues in essential spectral gaps. Furthermore, the connection with Krein's spectral shift function is established.Comment: 26 page

The ^4He trimer as an Efimov system

We review the results obtained in the last four decades which demonstrate the Efimov nature of the $^4$He three-atomic system.Comment: Review article for a special issue of the Few-Body Systems journal devoted to Efimov physic

Coherent electron-phonon coupling and polaron-like transport in molecular wires

We present a technique to calculate the transport properties through one-dimensional models of molecular wires. The calculations include inelastic electron scattering due to electron-lattice interaction. The coupling between the electron and the lattice is crucial to determine the transport properties in one-dimensional systems subject to Peierls transition since it drives the transition itself. The electron-phonon coupling is treated as a quantum coherent process, in the sense that no random dephasing due to electron-phonon interactions is introduced in the scattering wave functions. We show that charge carrier injection, even in the tunneling regime, induces lattice distortions localized around the tunneling electron. The transport in the molecular wire is due to polaron-like propagation. We show typical examples of the lattice distortions induced by charge injection into the wire. In the tunneling regime, the electron transmission is strongly enhanced in comparison with the case of elastic scattering through the undistorted molecular wire. We also show that although lattice fluctuations modify the electron transmission through the wire, the modifications are qualitatively different from those obtained by the quantum electron-phonon inelastic scattering technique. Our results should hold in principle for other one-dimensional atomic-scale wires subject to Peierls transitions.Comment: 21 pages, 8 figures, accepted for publication in Phys. Rev. B (to appear march 2001

Order and Chaos in some Trigonometric Series: Curious Adventures of a Statistical Mechanic

This paper tells the story how a MAPLE-assisted quest for an interesting undergraduate problem in trigonometric series led some "amateurs" to the discovery that the one-parameter family of deterministic trigonometric series \pzcS_p: t\mapsto \sum_{n\in\Nset}\sin(n^{-{p}}t), $p>1$, exhibits both order and apparent chaos, and how this has prompted some professionals to offer their expert insights. It is proved that \pzcS_p(t) = \alpha_p\rm{sign}(t)|t|^{1/{p}}+O(|t|^{1/{(p+1)}})\;\forall\;t\in\Rset, with explicitly computed constant $\alpha_p$. Experts' commentaries are reproduced stating the fluctuations of \pzcS_p(t) - \alpha_p{\rm{sign}}(t)|t|^{1/{p}} are presumably not Gaussian. Inspired by a central limit type theorem of Marc Kac, a well-motivated conjecture is formulated to the effect that the fluctuations of the $\lceil t^{1/(p+1)}\rceil$-th partial sum of \pzcS_p(t), when properly scaled, do converge in distribution to a standard Gaussian when $t\to\infty$, though --- provided that $p$ is chosen so that the frequencies \{n^{-p}\}_{n\in\Nset} are rationally linear independent; no conjecture has been forthcoming for rationally dependent \{n^{-p}\}_{n\in\Nset}. Moreover, following other experts' tip-offs, the interesting relationship of the asymptotics of \pzcS_p(t) to properties of the Riemann $\zeta$ function is exhibited using the Mellin transform.Comment: Based on the invited lecture with the same title delivered by the author on Dec.19, 2011 at the 106th Statistical Mechanics Meeting at Rutgers University in honor of Michael Fisher, Jerry Percus, and Ben Widom. (19 figures, colors online). Comments of three referees included. Conjecture 1 revised. Accepted for publication in J. Stat. Phy