23,264 research outputs found
L^p boundedness of the wave operator for the one dimensional Schroedinger operator
Given a one dimensional perturbed Schroedinger operator H=-(d/dx)^2+V(x) we
consider the associated wave operators W_+, W_- defined as the strong L^2
limits as s-> \pm\infty of the operators e^{isH} e^{-isH_0} We prove that the
wave operators are bounded operators on L^p for all 1<p<\infty, provided
(1+|x|)^2 V(x) is integrable, or else (1+|x|)V(x) is integrable and 0 is not a
resonance. For p=\infty we obtain an estimate in terms of the Hilbert
transform. Some applications to dispersive estimates for equations with
variable rough coefficients are given.Comment: 26 page
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Upgrade to the SHARP EUV mask microscope
The Sharp High-NA Actinic Reticle review Project (SHARP) is a synchrotron-based, extreme ultraviolet (EUV) microscope dedicated to photomask research. A potential upgrade to the SHARP microscope is presented. The upgrade includes changing the light path in the instrument from its current off-Axis configuration to an on-Axis configuration. This change allows for an increased working distance of 2.5 mm or more. A central obscuration, added to the zoneplate aperture, blocks stray light from reaching the central part of the image, thus improving the image contrast. The imaging performance of the two configurations is evaluated by means of ray tracing
Lattice-corrected strain-induced vector potentials in graphene
The electronic implications of strain in graphene can be captured at low
energies by means of pseudovector potentials which can give rise to
pseudomagnetic fields. These strain-induced vector potentials arise from the
local perturbation to the electronic hopping amplitudes in a tight-binding
framework. Here we complete the standard description of the strain-induced
vector potential, which accounts only for the hopping perturbation, with the
explicit inclusion of the lattice deformations or, equivalently, the
deformation of the Brillouin zone. These corrections are linear in strain and
are different at each of the strained, inequivalent Dirac points, and hence are
equally necessary to identify the precise magnitude of the vector potential.
This effect can be relevant in scenarios of inhomogeneous strain profiles,
where electronic motion depends on the amount of overlap among the local Fermi
surfaces. In particular, it affects the pseudomagnetic field distribution
induced by inhomogeneous strain configurations, and can lead to new
opportunities in tailoring the optimal strain fields for certain desired
functionalities.Comment: Errata for version
Properties of Nucleon Resonances by means of a Genetic Algorithm
We present an optimization scheme that employs a Genetic Algorithm (GA) to
determine the properties of low-lying nucleon excitations within a realistic
photo-pion production model based upon an effective Lagrangian. We show that
with this modern optimization technique it is possible to reliably assess the
parameters of the resonances and the associated error bars as well as to
identify weaknesses in the models. To illustrate the problems the optimization
process may encounter, we provide results obtained for the nucleon resonances
(1230) and (1700). The former can be easily isolated and thus
has been studied in depth, while the latter is not as well known
experimentally.Comment: 12 pages, 10 figures, 3 tables. Minor correction
Techniques for the realization of ultrareliable spaceborne computers Interim scientific report
Error-free ultrareliable spaceborne computer
Statistics of Oscillator Strengths in Chaotic Systems
The statistical description of oscillator strengths for systems like hydrogen
in a magnetic field is developed by using the supermatrix nonlinear
-model. The correlator of oscillator strengths is found to have a
universal parametric and frequency dependence, and its analytical expression is
given. This universal expression applies to quantum chaotic systems with the
same generality as Wigner-Dyson statistics.Comment: 11 pages, REVTeX3+epsf, two EPS figures. Replaced by the published
version. Minor changes
Surface criticality in random field magnets
The boundary-induced scaling of three-dimensional random field Ising magnets
is investigated close to the bulk critical point by exact combinatorial
optimization methods. We measure several exponents describing surface
criticality: for the surface layer magnetization and the surface
excess exponents for the magnetization and the specific heat, and
. The latter ones are related to the bulk phase transition by the
same scaling laws as in pure systems, but only with the same violation of
hyperscaling exponent as in the bulk. The boundary disorders faster
than the bulk, and the experimental and theoretical implications are discussed.Comment: 6 pages, 9 figures, to appear in Phys. Rev.
Exciton mediated one phonon resonant Raman scattering from one-dimensional systems
We use the Kramers-Heisenberg approach to derive a general expression for the
resonant Raman scattering cross section from a one-dimensional (1D) system
explicitly accounting for excitonic effects. The result should prove useful for
analyzing the Raman resonance excitation profile lineshapes for a variety of 1D
systems including carbon nanotubes and semiconductor quantum wires. We apply
this formalism to a simple 1D model system to illustrate the similarities and
differences between the free electron and correlated electron-hole theories.Comment: 10 pages, 6 figure
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