9 citations · 19 across the 8 of their papers we have counts for
9 papers
On the dispersive estimates for the discrete Schrödinger equation on a honeycomb lattice
Younghun Hong, Yukihide Tadano, Changhun Yang
The discrete Schrödinger equation on a two-dimensional honeycomb lattice is a fundamental tight-binding approximation model that describes the propagation of waves on graphene. For…
Non-smoothness of the fundamental solutions for Schrödinger equations with super-quadratic and spherically symmetric potential
Keiichi Kato, Wataru Nakahashi, Yukihide Tadano
We study non-smoothness of the fundamental solution for the Schrödinger equation with a spherically symmetric and super-quadratic potential in the sence that $V(x)\geq C|x|^{2+\var…
Continuum limit for Laplace and Elliptic operators on lattices
Keita Mikami, Shu Nakamura, Yukihide Tadano
Continuum limits of Laplace operators on general lattices are considered, and it is shown that these operators converge to elliptic operators on the Euclidean space in the sense of…
Continuum limit of the lattice quantum graph Hamiltonian
Pavel Exner, Shu Nakamura, Yukihide Tadano
We consider the quantum graph Hamiltonian on the square lattice in Euclidean space, and we show that the spectrum of the Hamiltonian converges to the corresponding Schrödinger oper…
Construction of Isozaki-Kitada modifiers for discrete Schrödinger operators on general lattices
Yukihide Tadano
We consider a scattering theory for convolution operators on perturbed with a long-range potential .…
On a continuum limit of discrete Schrödinger operators on square lattice
Shu Nakamura, Yukihide Tadano
The norm resolvent convergence of discrete Schrödinger operators to a continuum Schrödinger operator in the continuum limit is proved under relatively weak assumptions. This result…
Long-range scattering theory for discrete Schrödinger operators on graphene
Yukihide Tadano
We consider a long-range scattering theory for discrete Schrödinger operators on the hexagonal lattice, which describe tight-binding Hamiltonians on the graphene sheet. We construc…
Uniform bounds of discrete Birman-Schwinger operators
Yukihide Tadano, Kouichi Taira
In this note, uniform bounds of the Birman-Schwinger operators in the discrete setting are studied. For uniformly decaying potentials, we obtain the same bound as in the continuous…
Long-range scattering for discrete Schrödinger operators
Yukihide Tadano
In this paper, we define time-independent modifiers to construct a long-range scattering theory for discrete schrödinger operators on the square lattice . We prove th…