579 research outputs found
Spectral Duality for Planar Billiards
For a bounded open domain with connected complement in
and piecewise smooth boundary, we consider the Dirichlet Laplacian
on and the S-matrix on the complement . We
show that the on-shell S-matrices have eigenvalues converging to 1
as exactly when has an eigenvalue at energy
. This includes multiplicities, and proves a weak form of
``transparency'' at . We also show that stronger forms of transparency,
such as 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 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 and the dynamical scaling of
above and below provide clear evidence for a
continuous phase transition at to a generic superconducting state. Based
on the vortex-glass scaling model, the resulting critical exponents and
are close to those frequently obtained on films by other means and
associated with an 'isotropic' vortex glass. The field effect on
can be related to the increase of the glass coherence length,
.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, , describing the appearance of superconductivity in
superconductors of type II. Furthermore, we prove that the local and global
definitions of this field coincide. Near 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
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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 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), , 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 . 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 -th partial sum of \pzcS_p(t),
when properly scaled, do converge in distribution to a standard Gaussian when
, though --- provided that 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 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
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