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math-ph2020
Threshold between short and long-range potentials for non-local Schrödinger operators
Atsuhide Ishida, Kazuyuki Wada
We develop scattering theory for non-local Schrödinger operators defined by functions of the Laplacian that include its fractional power with . In particula…
math-ph2019
A weak limit theorem for a class of long range type quantum walks in 1d
Kazuyuki Wada
We derive the weak limit theorem for a class of long range type quantum walks. To do it, we analyze spectral properties of a time evolution operator and prove that modified wave op…
math-ph2018
Absence of wave operators for one-dimensional quantum walks
Kazuyuki Wada
We show that there exist pairs of two time evolution operators which do not have wave operators in a context of one-dimensional discrete time quantum walks. As a consequence, the b…