21,154 research outputs found
On the existence of impurity bound excitons in one-dimensional systems with zero range interactions
We consider a three-body one-dimensional Schr\"odinger operator with zero
range potentials, which models a positive impurity with charge
interacting with an exciton. We study the existence of discrete eigenvalues as
is varied. On one hand, we show that for sufficiently small
there exists a unique bound state whose binding energy behaves like ,
and we explicitly compute its leading coefficient. On the other hand, if
is larger than some critical value then the system has no bound
states
High-resolution 3D weld toe stress analysis and ACPD method for weld toe fatigue crack initiation
Weld toe fatigue crack initiation is highly dependent on the local weld toe stress-concentrating geometry including any inherent flaws. These flaws are responsible for premature fatigue crack initiation (FCI) and must be minimised to maximise the fatigue life of a welded joint. In this work, a data-rich methodology has been developed to capture the true weld toe geometry and resulting local weld toe stress-field and relate this to the FCI life of a steel arc-welded joint. To obtain FCI lives, interrupted fatigue test was performed on the welded joint monitored by a novel multi-probe array of alternating current potential drop (ACPD) probes across the weld toe. This setup enabled the FCI sites to be located and the FCI life to be determined and gave an indication of early fatigue crack propagation rates. To understand fully the local weld toe stress-field, high-resolution (5 mu m) 3D linear-elastic finite element (FE) models were generated from X-ray micro-computed tomography (mu-CT) of each weld toe after fatigue testing. From these models, approximately 202 stress concentration factors (SCFs) were computed for every 1 mm of weld toe. These two novel methodologies successfully link to provide an assessment of the weld quality and this is correlated with the fatigue performance
Temporal Ordering in Quantum Mechanics
We examine the measurability of the temporal ordering of two events, as well
as event coincidences. In classical mechanics, a measurement of the
order-of-arrival of two particles is shown to be equivalent to a measurement
involving only one particle (in higher dimensions). In quantum mechanics, we
find that diffraction effects introduce a minimum inaccuracy to which the
temporal order-of-arrival can be determined unambiguously. The minimum
inaccuracy of the measurement is given by dt=1/E where E is the total kinetic
energy of the two particles. Similar restrictions apply to the case of
coincidence measurements. We show that these limitations are much weaker than
limitations on measuring the time-of-arrival of a particle to a fixed location.Comment: New section added, arguing that order-of-arrival can be measured more
accurately than time-of-arrival. To appear in Journal of Physics
Applications of Magnetic PsiDO Techniques to Space-adiabatic Perturbation Theory
In this review, we show how advances in the theory of magnetic
pseudodifferential operators (magnetic DO) can be put to good use in
space-adiabatic perturbation theory (SAPT). As a particular example, we extend
results of [PST03] to a more general class of magnetic fields: we consider a
single particle moving in a periodic potential which is subjectd to a weak and
slowly-varying electromagnetic field. In addition to the semiclassical
parameter \eps \ll 1 which quantifies the separation of spatial scales, we
explore the influence of additional parameters that allow us to selectively
switch off the magnetic field.
We find that even in the case of magnetic fields with components in
, e. g. for constant magnetic fields, the results of
Panati, Spohn and Teufel hold, i.e. to each isolated family of Bloch bands,
there exists an associated almost invariant subspace of and an
effective hamiltonian which generates the dynamics within this almost invariant
subspace. In case of an isolated non-degenerate Bloch band, the full quantum
dynamics can be approximated by the hamiltonian flow associated to the
semiclassical equations of motion found in [PST03].Comment: 32 page
Long-Time Dynamics of Variable Coefficient mKdV Solitary Waves
We study the Korteweg-de Vries-type equation dt u=-dx(dx^2 u+f(u)-B(t,x)u),
where B is a small and bounded, slowly varying function and f is a
nonlinearity. Many variable coefficient KdV-type equations can be rescaled into
this equation. We study the long time behaviour of solutions with initial
conditions close to a stable, B=0 solitary wave. We prove that for long time
intervals, such solutions have the form of the solitary wave, whose centre and
scale evolve according to a certain dynamical law involving the function
B(t,x), plus an H^1-small fluctuation.Comment: 19 page
Dipoles in Graphene Have Infinitely Many Bound States
We show that in graphene charge distributions with non-vanishing dipole
moment have infinitely many bound states. The corresponding eigenvalues
accumulate at the edges of the gap faster than any power
Some remarks on quasi-Hermitian operators
A quasi-Hermitian operator is an operator that is similar to its adjoint in
some sense, via a metric operator, i.e., a strictly positive self-adjoint
operator. Whereas those metric operators are in general assumed to be bounded,
we analyze the structure generated by unbounded metric operators in a Hilbert
space. Following our previous work, we introduce several generalizations of the
notion of similarity between operators. Then we explore systematically the
various types of quasi-Hermitian operators, bounded or not. Finally we discuss
their application in the so-called pseudo-Hermitian quantum mechanics.Comment: 18page
Simplicity of extremal eigenvalues of the Klein-Gordon equation
We consider the spectral problem associated with the Klein-Gordon equation
for unbounded electric potentials. If the spectrum of this problem is contained
in two disjoint real intervals and the two inner boundary points are
eigenvalues, we show that these extremal eigenvalues are simple and possess
strictly positive eigenfunctions. Examples of electric potentials satisfying
these assumptions are given
Documentation of Apollo 15 samples
A catalog is presented of the documentation of Apollo 15 samples using photographs and verbal descriptions returned from the lunar surface. Almost all of the Apollo 15 samples were correlated with lunar surface photographs, descriptions, and traverse locations. Where possible, the lunar orientations of rock samples were reconstructed in the lunar receiving laboratory, using a collimated light source to reproduce illumination and shadow characteristics of the same samples shown in lunar photographs. In several cases, samples were not recognized in lunar surface photographs, and their approximate locations are known only by association with numbered sample bags used during their collection. Tables, photographs, and maps included in this report are designed to aid in the understanding of the lunar setting of the Apollo 15 samples
A high efficiency input/output coupler for small silicon photonic devices
Coupling light from an optical fibre to small optical waveguides is particularly problematic in semiconductors, since the refractive index of the silica fibre is very different from that of a semiconductor waveguide. There have been several published methods of achieving such coupling, but none are sufficiently efficient whilst being robust enough for commercial applications. In this paper experimental results of our approach called a Dual-Grating Assisted Directional Coupler, are presented. The principle of coupling by this novel method has been successfully demonstrated, and a coupling efficiency of 55% measured
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