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20122026
most citedSpectral Properties of Schrödinger Operators on Perturbed Lattices

59 citations · 151 across the 21 of their papers we have counts for

collaborators

21 papers

math-ph2026

Resonant scattering for tunable quantum walks on graphs with tails

Kenta Higuchi, Ryuta Ishikawa, Hisashi Morioka +2

We study the resonant scattering for discrete time quantum walks on graphs with some tails. In our arguments, we reduce the study of resonances to the perturbation of eigenvalues o…

math.SP2024

A remark on the absence of eigenvalues in continuous spectra for discrete Schrödinger operators on periodic lattices

Kazunori Ando, Hiroshi Isozaki, Hisashi Morioka

We prove a Rellich-Vekua type theorem for Schrödinger operators with exponentially decreasing potentials on a class of lattices including square, triangular, hexagonal lattices and…

math.SP2023

Complex translation methods and its application to resonances for quantum walks

Kenta Higuchi, Hisashi Morioka

In this paper, some properties of resonances for multi-dimensional quantum walks are studied. Resonances for quantum walks are defined as eigenvalues of complex translated time evo…

math-ph2023

Resonance expansion for quantum walks and its applications to the long-time behavior

Kenta Higuchi, Hisashi Morioka, Etsuo Segawa

In this paper, resonances are introduced to a class of quantum walks on . Resonances are defined as poles of the meromorphically extended resolvent of the unitary time…

quant-ph2022

Comfortable place for quantum walkers on finite path

Yoshihiro Anahara, Norio Konno, Hisashi Morioka +1

We consider the stationary state of a quantum walk on the finite path, where the sink and source are set at the left and right boundaries. The quantum coin is uniformly placed at e…

math.SP2021

Resonances in finitely perturbed quantum walks, resonance expansion and generic simplicity

Kenta Higuchi, Hisashi Morioka, Etsuo Segawa

We define resonances for finitely perturbed quantum walks as poles of the scattering matrix in the lower half plane. We show a resonance expansion which describes the time evolutio…

math-ph2021

A discontinuity of the energy of quantum walk in impurities

Kenta Higuchi, Takashi Komatsu, Norio Konno +2

We consider the discrete-time quantum walk whose local dynamics is denoted by at the perturbed region and free at the other positions. We obtain the station…

math.AP2021

-stableness for solution to linearized KdV equation

Masaki Kawamoto, Hisashi Morioka

The linearized Korteweg-De Vries equation can be written as a Hamilton-like system. However, the Hamilton energy depends on the time, and is a nonsymmetric operator on $L^2({\bf R}…

math-ph2021★ 3 cited

Asymptotic properties of generalized eigenfunctions for multi-dimensional quantum walks

Takashi Komatsu, Norio Konno, Hisashi Morioka +1

We construct a distorted Fourier transformation associated with the multi-dimensional quantum walk. In order to avoid the complication of notations, almost all of our arguments are…

math-ph2021★ 1 cited

Inverse scattering on the quantum graph for graphene

Kazunori Ando, Hiroshi Isozaki, Evgeny Korotyaev +1

We consider the inverse scattering on the quantum graph associated with the hexagonal lattice. Assuming that the potentials on the edges are compactly supported and symmetric, we s…

math-ph2020★ 9 cited

Generalized eigenfunctions for quantum walks via path counting approach

Takashi Komatsu, Norio Konno, Hisashi Morioka +1

We consider the time-independent scattering theory for time evolution operators of one-dimensional two-state quantum walks. The scattering matrix associated with the position-depen…

quant-ph2019★ 3 cited

Explicit expression of scattering operator of some quantum walks on impurities

Takashi Komatsu, Norio Konno, Hisashi Morioka +1

In this paper, we consider the scattering theory for a one-dimensional quantum walk with impurities which make reflections and transmissions. We focus on an explicit expression of…

math-ph2019★ 1 cited

Inverse scattering on the quantum graph -- Edge model for graphen

Kazunori Ando, Hiroshi Isozaki, Evgeny Korotyaev +1

We consider the inverse scattering on the quantum graph associated with the hexagonal lattice. Assuming that the potentials on the edges are compactly supported, we show that the S…

math-ph2019

Non-scattering energies for acoustic-type equations on manifolds with a single flat end

Hisashi Morioka, Naotaka Shoji

In this paper, we consider the scattering theory for acoustic-type equations on non-compact manifolds with a single flat end. Our main purpose is to show an existence result of non…

math.SP2018★ 23 cited

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★ 15 cited

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★ 16 cited

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-…

math.SP2017★ 1 cited

Interior transmission eigenvalue problems on compact manifolds with boundary conductivity parameters

Hisashi Morioka, Naotaka Shoji

In this paper, we consider an interior transmission eigenvalue (ITE) problem on some compact -Riemannian manifolds with a common smooth boundary. In particular, these…

math.SP2014★ 59 cited

Spectral Properties of Schrödinger Operators on Perturbed Lattices

Kazunori Ando, Hiroshi Isozaki, Hisashi Morioka

We study the spectral properties of Schrödinger operators on perturbed lattices. We shall prove the non-existence or the discreteness of embedded eigenvalues, the limiting absorpti…

math.SP2012★ 19 cited

Inverse scattering at a fixed energy for discrere Schrödinger operators on the square lattice

Hiroshi Isozaki, Hisashi Morioka

We study an inverse scattering problem for the discrete Schrödinger operator on the multi-dimensional square lattice, with compactly supported potential. We show that the potential…

math.SP2012★ 1 cited

A Rellich Type Theorem for Discrete Schr{ö}dinger Operators

Hiroshi Isozaki, Hisashi Morioka

An analogue of Rellich's theorem is proved for discrete Laplacian on square lattice, and applied to show unique continuation property on certain domains as well as non-existence of…