6,471 research outputs found
On a selection principle for multivalued semiclassical flows
We study the semiclassical behaviour of solutions of a Schr ̈odinger equation with a scalar po- tential displaying a conical singularity. When a pure state interacts strongly with the singularity of the flow, there are several possible classical evolutions, and it is not known whether the semiclassical limit cor- responds to one of them. Based on recent results, we propose that one of the classical evolutions captures the semiclassical dynamics; moreover, we propose a selection principle for the straightforward calculation of the regularized semiclassical asymptotics. We proceed to investigate numerically the validity of the proposed scheme, by employing a solver based on a posteriori error control for the Schr ̈odinger equation. Thus, for the problems we study, we generate rigorous upper bounds for the error in our asymptotic approximation. For 1-dimensional problems without interference, we obtain compelling agreement between the regularized asymptotics and the full solution. In problems with interference, there is a quantum effect that seems to survive in the classical limit. We discuss the scope of applicability of the proposed regularization approach, and formulate a precise conjecture
Casimir stress in an inhomogeneous medium
The Casimir effect in an inhomogeneous dielectric is investigated using
Lifshitz's theory of electromagnetic vacuum energy. A permittivity function
that depends continuously on one Cartesian coordinate is chosen, bounded on
each side by homogeneous dielectrics. The result for the Casimir stress is
infinite everywhere inside the inhomogeneous region, a divergence that does not
occur for piece-wise homogeneous dielectrics with planar boundaries. A Casimir
force per unit volume can be extracted from the infinite stress but it diverges
on the boundaries between the inhomogeneous medium and the homogeneous
dielectrics. An alternative regularization of the vacuum stress is considered
that removes the contribution of the inhomogeneity over small distances, where
macroscopic electromagnetism is invalid. The alternative regularization yields
a finite Casimir stress inside the inhomogeneous region, but the stress and
force per unit volume diverge on the boundaries with the homogeneous
dielectrics. The case of inhomogeneous dielectrics with planar boundaries thus
falls outside the current understanding of the Casimir effect.Comment: 17 page
A method for delineation of bone surfaces in photoacoustic computed tomography of the finger
Photoacoustic imaging of interphalangeal peripheral joints is of interest in
the context of using the synovial membrane as a surrogate marker of rheumatoid
arthritis. Previous work has shown that ultrasound produced by absorption of
light at the epidermis reflects on the bone surfaces within the finger. When
the reflected signals are backprojected in the region of interest, artifacts
are produced, confounding interpretation of the images. In this work, we
present an approach where the photoacoustic signals known to originate from the
epidermis, are treated as virtual ultrasound transmitters, and a separate
reconstruction is performed as in ultrasound reflection imaging. This allows us
to identify the bone surfaces. Further, the identification of the joint space
is important as this provides a landmark to localize a region-of-interest in
seeking the inflamed synovial membrane. The ability to delineate bone surfaces
allows us not only to identify the artifacts, but also to identify the
interphalangeal joint space without recourse to new US hardware or a new
measurement. We test the approach on phantoms and on a healthy human finger
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