923 research outputs found
High-Velocity Estimates and Inverse Scattering for Quantum N-Body Systems with Stark Effect
In an N-body quantum system with a constant electric field, by inverse
scattering, we uniquely reconstruct pair potentials, belonging to the optimal
class of short-range potentials and long-range potentials, from the
high-velocity limit of the Dollard scattering operator. We give a
reconstruction formula with an error term.Comment: In this published version we have added remarks and we have edited
the pape
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
A rigorous analysis of high order electromagnetic invisibility cloaks
There is currently a great deal of interest in the invisibility cloaks
recently proposed by Pendry et al. that are based in the transformation
approach. They obtained their results using first order transformations. In
recent papers Hendi et al. and Cai et al. considered invisibility cloaks with
high order transformations. In this paper we study high order electromagnetic
invisibility cloaks in transformation media obtained by high order
transformations from general anisotropic media. We consider the case where
there is a finite number of spherical cloaks located in different points in
space. We prove that for any incident plane wave, at any frequency, the
scattered wave is identically zero. We also consider the scattering of finite
energy wave packets. We prove that the scattering matrix is the identity, i.e.,
that for any incoming wave packet the outgoing wave packet is the same as the
incoming one. This proves that the invisibility cloaks can not be detected in
any scattering experiment with electromagnetic waves in high order
transformation media, and in particular in the first order transformation media
of Pendry et al. We also prove that the high order invisibility cloaks, as well
as the first order ones, cloak passive and active devices. The cloaked objects
completely decouple from the exterior. Actually, the cloaking outside is
independent of what is inside the cloaked objects. The electromagnetic waves
inside the cloaked objects can not leave the concealed regions and viceversa,
the electromagnetic waves outside the cloaked objects can not go inside the
concealed regions. As we prove our results for media that are obtained by
transformation from general anisotropic materials, we prove that it is possible
to cloak objects inside general crystals.Comment: The final version is now published in Journal of Physics A:
Mathematical and Theoretical, vol 41 (2008) 065207 (21 pp). Included in
IOP-Selec
On Inverse Scattering at a Fixed Energy for Potentials with a Regular Behaviour at Infinity
We study the inverse scattering problem for electric potentials and magnetic
fields in \ere^d, d\geq 3, that are asymptotic sums of homogeneous terms at
infinity. The main result is that all these terms can be uniquely reconstructed
from the singularities in the forward direction of the scattering amplitude at
some positive energy.Comment: This is a slightly edited version of the previous pape
Inverse Scattering at a Fixed Quasi-Energy for Potentials Periodic in Time
We prove that the scattering matrix at a fixed quasi--energy determines
uniquely a time--periodic potential that decays exponentially at infinity. We
consider potentials that for each fixed time belong to in space. The
exponent 3/2 is critical for the singularities of the potential in space. For
this singular class of potentials the result is new even in the
time--independent case, where it was only known for bounded exponentially
decreasing potentials.Comment: In this revised version I give a more detailed motivation of the
class of potentials that I consider and I have corrected some typo
Malignant pleural mesothelioma: ESMO clinical recommendations for diagnosis, treatment and follow-up
Entanglement Creation in Low-Energy Scattering
We study the entanglement creation in the low-energy scattering of two
particles in three dimensions, for a general class of interaction potentials
that are not required to be spherically symmetric. The incoming asymptotic
state, before the collision, is a product of two normalized Gaussian states.
After the scattering the particles are entangled. We take as a measure of the
entanglement the purity of one of them. We provide a rigorous explicit
computation, with error bound, of the leading order of the purity at
low-energy. The entanglement depends strongly in the difference of the masses.
It takes its minimum when the masses are equal, and it increases rapidly with
the difference of the masses. It is quite remarkable that the anisotropy of the
potential gives no contribution to the leading order of the purity, on spite of
the fact that entanglement is a second order effect.Comment: The paper has been edited and some comments have been adde
Malignant pleural mesothelioma: ESMO Clinical Practice Guidelines for diagnosis, treatment and follow-up
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