Osamu Ogurisu

Ground state of a spin-1/2 charged particle in a two-dimensional magnetic field

It is investigated that the structure of the kernel of the Dirac–Weyl operator D of a charged particle in the magnetic-field B=B0+B1, given by the sum of a strongly singular magnetic field B0(⋅)=Σνγνδ(⋅−aν) with some singular points aν and a magnetic-field B1 with a bounded support. Here the magnetic field B1 may have some singular points with the order of the singularity less than 2. At a glance, it seems that, following “Aharonov–Casher Theorem” [Phys. Rev. A 19, 2461 (1979)], the dimension of the kernel of D, dim ker D, is a function of one variable of the total magnetic flux (=Σνγν+∫R2B1dxdy) of B. However, since the influence of the strongly singular points works, dim ker D indeed is a function of several variables of the total magnetic flux and each of γν’s.

Quantum walks on simplicial complexes

We construct a new type of quantum walks on simplicial complexes as a natural extension of the well-known Szegedy walk on graphs. One can numerically observe that our proposing quantum walks possess linear spreading and localization as in the case of the Grover walk on lattices. Moreover, our numerical simulation suggests that localization of our quantum walks reflects not only topological but also geometric structures. On the other hand, our proposing quantum walk contains an intrinsic problem concerning exhibition of non-trivial behavior, which is not seen in typical quantum walks such as Grover walks on graphs.

On the spectrum of a discrete Laplacian on ℤ with finitely supported potential

We study spectral properties of the discrete Laplacian L = −Δ + V on ℤ with finitely supported potential V. We give sufficient and necessary conditions for L to satisfy that the number of negative (resp. positive) eigenvalues is equal to one of the points x on which V(x) is negative (resp. positive). In addition, we prove that L has at least one discrete eigenvalue. If ∑ x∈ℤ V(x) = 0, then L has both negative and positive discrete eigenvalues.

Practical band estimation for periodic superlattices by using semi-infinite periodic model

In this paper, we propose a practical band estimation method for periodic superlattices by using semi-infinite periodic model, which is located in the middle of finite periodic model and infinite periodic model. According to the model proposed, we can estimate not only band structures but also ripples in passbands for periodic superlattices with simple calculation by applying image parameters in circuit theory. This model may be useful for energy filter designing, since the ripples in passbands are the essential information related with energy filter abilities.

Anomalous Pauli Electron States for Magnetic Fields with Tails

AbstractWe consider a two-dimensional electron with an anomalous magnetic moment, g>2, interacting with a nonzero magnetic field B perpendicular to the plane which gives rise to a flux F. Recent results about the discrete spectrum of the Pauli operator are extended to fields with the

Real-Passband Estimation for Modulated Superlattices Based on Circuit Theory

\mathcal{O}\left( {r^{ - 2 - \delta } } \right)

A Note on the Spectral Mapping Theorem of Quantum Walk Models

decay at infinity: we show that if