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Recovery of a time-dependent Hermitian connection and potential appearing in the dynamic Schr\"odinger equation
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In this paper, the Dirichlet-to-Neumann map is used to uniquely determine both the connection form and the potential appearing in the Schrodinger equation, under the assumption that the manifold is either a two-dimensional and simple, or b) of higher dimension with strictly convex boundary and admits a smooth, pure convex function.Abstract:
We consider, on a trivial vector bundle over a Riemannian manifold with boundary, the inverse problem of uniquely recovering time- and space-dependent coefficients of the dynamic, vector-valued Schrodinger equation from the knowledge of the Dirichlet-to-Neumann map. We show that the D-to-N map uniquely determines both the connection form and the potential appearing in the Schrodinger equation, under the assumption that the manifold is either a) two-dimensional and simple, or b) of higher dimension with strictly convex boundary and admits a smooth, strictly convex function.read more
Citations
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Inverse problems for non-linear Schr\"odinger equations with time-dependent coefficients
TL;DR: In this paper , the authors studied the inverse problem of reconstructing the coefficient β(t, x) of the nonlinear term and the potential V (t,x) of a nonlinear Schrödinger equation in time-domain, (i ∂ ∂t + ∆ + V )u + βu = f in (0, T ) × M , where M ⊂ R is a convex and compact set with smooth boundary.
Retrieving Yang--Mills--Higgs fields in Minkowski space from active local measurements
TL;DR: In this article , a source-to-solution type data associated with the classical Yang-Mills-Higgs equations in Minkowski space R 1+3 was used to recover the Higgs potential and Higgs equation up to gauge.
References
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Book
Inverse Boundary Spectral Problems
TL;DR: Chapman and Hall as discussed by the authors developed a rigorous theory for solving several types of inverse boundary problems exactly, and applied methods of Riemannian geometry, modern control theory, and the theory of localized wave packets, also known as Gaussian beams.
Journal ArticleDOI
The Calderón problem in transversally anisotropic geometries
TL;DR: In this article, it was shown that the boundary measurements uniquely determine a mixed Fourier transform or attenuated geodesic ray transform (or integral against a more general semiclassical limit measure) of an unknown coefficient.
Journal ArticleDOI
Global Uniqueness in the Inverse Scattering Problem¶for the Schrödinger Operator¶with External Yang–Mills Potentials
TL;DR: In this article, the authors considered the Schrodinger equation in Rn, n ≥ 3, with external Yang-Mills potentials having compact supports and proved the uniqueness modulo a gauge transformation of the solution of the inverse boundary value problem in a bounded convex domain.
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The Calderon problem in transversally anisotropic geometries
TL;DR: In this article, the authors considered the anisotropic Calderon problem of recovering a conductivity matrix or a Riemannian metric from electrical boundary measurements in three and higher dimensions, and showed that the boundary measurements uniquely determine a mixed Fourier transform / attenuated geodesic ray transform (or integral against a more general semiclassical limit measure) of an unknown coefficient.