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math.SP2018
Generalized eigenfunctions and scattering matrices for position-dependent quantum walks
Hisashi Morioka
We study the spectral analysis and the scattering theory for time evolution operators of position-dependent quantum walks. Our main purpose of this paper is construction of general…
math.SP2018
Detection of edge defects by embedded eigenvalues of quantum walks
Hisashi Morioka, Etsuo Segawa
We consider a position-dependent quantum walk on . In particular, we derive a detection method for edge defects by embedded eigenvalues of its time evolution operator. In…
math.SP2018
Inverse scattering for Schrödinger operators on perturbed lattices
Kazunori Ando, Hiroshi Isozaki, Hisashi Morioka
We study the inverse scattering for Schr{ö}dinger operators on locally perturbed periodic lattices. We show that the associated scattering matrix is equivalent to the Dirichlet-to-…