scholarly journals Inverse Scattering Theory for Discrete Schrödinger Operators on the Hexagonal Lattice

2012 ◽  
Vol 14 (2) ◽  
pp. 347-383 ◽  
Author(s):  
Kazunori Ando
Keyword(s):  
Inverse Scattering ◽  
Scattering Theory ◽  
Schrödinger Operators ◽  
Hexagonal Lattice ◽  
Schrodinger Operators ◽  
Discrete Schrödinger Operators ◽  
Inverse Scattering Theory

scholarly journals Inverse Scattering Theory for Schrodinger Operators with Steplike Potentials

2015 ◽  
Vol 11 (2) ◽  
pp. 123-158 ◽  
Author(s):  
I. Egorova ◽  
◽  
Z. Gladka ◽  
T.L. Lange ◽  
G. Teschl ◽  
...  
Keyword(s):  
Inverse Scattering ◽  
Scattering Theory ◽  
Schrödinger Operators ◽  
Schrodinger Operators ◽  
Inverse Scattering Theory

scholarly journals On the Spectra of Separable 2D Almost Mathieu Operators

2021 ◽  
Author(s):  
Alberto Takase
Keyword(s):  
Positive Measure ◽  
Schrödinger Operators ◽  
Cantor Sets ◽  
Schrodinger Operators ◽  
Discrete Schrödinger Operators ◽  
Mathieu Operator ◽  
Almost Mathieu Operator

AbstractWe consider separable 2D discrete Schrödinger operators generated by 1D almost Mathieu operators. For fixed Diophantine frequencies, we prove that for sufficiently small couplings the spectrum must be an interval. This complements a result by J. Bourgain establishing that for fixed couplings the spectrum has gaps for some (positive measure) Diophantine frequencies. Our result generalizes to separable multidimensional discrete Schrödinger operators generated by 1D quasiperiodic operators whose potential is analytic and whose frequency is Diophantine. The proof is based on the study of the thickness of the spectrum of the almost Mathieu operator and utilizes the Newhouse Gap Lemma on sums of Cantor sets.

Reconstruction of inclusions in electrical conductors

2020 ◽  
Author(s):  
Michele Di Cristo ◽  
Giacomo Milan
Keyword(s):  
Electrical Impedance Tomography ◽  
Inverse Scattering ◽  
Scattering Theory ◽  
Electrical Impedance ◽  
Functional Method ◽  
Impedance Tomography ◽  
Numerical Examples ◽  
Electrical Conductors ◽  
Inverse Scattering Theory

Abstract We investigate the reciprocity gap functional method, which has been developed in the inverse scattering theory, in the context of electrical impedance tomography. In particular, we aim to reconstruct an inclusion contained in a body, whose conductivity is different from the conductivity of the surrounding material. Numerical examples are given, showing the performance of our algorithm.

Inverse scattering theory for systems of the Zakharov–Shabat type

1983 ◽  
Vol 24 (6) ◽  
pp. 1502-1508 ◽  
Author(s):  
Helena M. A. de Castro ◽  
Walter F. Wreszinski
Keyword(s):  
Inverse Scattering ◽  
Scattering Theory ◽  
Inverse Scattering Theory
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