Stationary scattering theory for one-body Stark operators, I
T. Adachi, K. Itakura, K. Ito, E. Skibsted
TL;DR
This paper develops a stationary scattering theory framework for one-body Stark operators, establishing key properties like existence, completeness, and asymptotics of eigenfunctions, and constructing the scattering matrix.
Contribution
It introduces a comprehensive stationary scattering theory for perturbed 1-body Stark operators, including wave operators, Fourier transforms, and eigenfunction asymptotics.
Findings
Existence and completeness of stationary wave operators.
Construction of generalized Fourier transforms.
Characterization of eigenfunction asymptotics via the scattering matrix.
Abstract
We study the stationary scattering theory for a perturbed 1-body Stark operator. We prove existence and completeness of the stationary wave operators, construct the associated generalized Fourier transforms, and characterize asymptotics of the generalized eigenfunctions of minimal growths in terms of the stationary scattering matrix.
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Taxonomy
TopicsSpectral Theory in Mathematical Physics · Random Matrices and Applications · Lanthanide and Transition Metal Complexes