39,302 research outputs found
Inverse scattering results for manifolds hyperbolic near infinity
We study the inverse resonance problem for conformally compact manifolds
which are hyperbolic outside a compact set. Our results include compactness of
isoresonant metrics in dimension two and of isophasal negatively curved metrics
in dimension three. In dimensions four or higher we prove topological
finiteness theorems under the negative curvature assumption.Comment: 25 pages. v3: Minor corrections, references adde
On the quantum inverse scattering problem
A general method for solving the so-called quantum inverse scattering problem
(namely the reconstruction of local quantum (field) operators in term of the
quantum monodromy matrix satisfying a Yang-Baxter quadratic algebra governed by
an R-matrix) for a large class of lattice quantum integrable models is given.
The principal requirement being the initial condition (R(0) = P, the
permutation operator) for the quantum R-matrix solving the Yang-Baxter
equation, it applies not only to most known integrable fundamental lattice
models (such as Heisenberg spin chains) but also to lattice models with
arbitrary number of impurities and to the so-called fused lattice models
(including integrable higher spin generalizations of Heisenberg chains). Our
method is then applied to several important examples like the sl(n) XXZ model,
the XYZ spin-1/2 chain and also to the spin-s Heisenberg chains.Comment: Latex, 20 page
Non-scattering wavenumbers and far field invisibility for a finite set of incident/scattering directions
We investigate a time harmonic acoustic scattering problem by a penetrable
inclusion with compact support embedded in the free space. We consider cases
where an observer can produce incident plane waves and measure the far field
pattern of the resulting scattered field only in a finite set of directions. In
this context, we say that a wavenumber is a non-scattering wavenumber if the
associated relative scattering matrix has a non trivial kernel. Under certain
assumptions on the physical coefficients of the inclusion, we show that the
non-scattering wavenumbers form a (possibly empty) discrete set. Then, in a
second step, for a given real wavenumber and a given domain D, we present a
constructive technique to prove that there exist inclusions supported in D for
which the corresponding relative scattering matrix is null. These inclusions
have the important property to be impossible to detect from far field
measurements. The approach leads to a numerical algorithm which is described at
the end of the paper and which allows to provide examples of (approximated)
invisible inclusions.Comment: 20 pages, 7 figure
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