Generalized eigenfunctions and scattering matrices for position-dependent quantum walks

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 generalized eigenfunctions of the time evolution operator. Roughly speaking, the generalized eigenfunctions are not square summable but belong to $\ell^{\infty}$-space on ${\bf Z}$. Moreover, we derive a characterization of the set of generalized eigenfunctions in view of the time-harmonic scattering theory. Thus we show that the S-matrix associated with the quantum walk appears in the singularity expansion of generalized eigenfunctions

The Trolley Problem and the Dropping of Atomic Bombs

In this paper, the ethical and spiritual aspects of the trolley problem are discussed in connection with the dropping of atomic bombs on Hiroshima and Nagasaki. First, I show that the dropping of atomic bombs was a typical example of the events that contained the logic of the trolley problems in their decision-making processes and justifications. Second, I discuss five aspects of “the problem of the trolley problem;” that is to say, “Rarity,” “Inevitability,” “Safety Zone,” “Possibility of Becoming a Victim,” and “Lack of Perspective of the Dead Victims Who Were Deprived of Freedom of Choice,” in detail. Third, I argue that those who talk about the trolley problem are automatically placed in the sphere of the expectation of response on the spiritual level. I hope that my contribution will shed light on the trolley problem from a very different angle, which has not been made by our fellow philosophers

Detection of edge defects by embedded eigenvalues of quantum walks

We consider a position-dependent quantum walk on ${\bf Z}$. In particular, we derive a detection method for edge defects by embedded eigenvalues of its time evolution operator. In the present paper, the set of edge defects is that of points in ${\bf Z}$ on which the coin operator is an anti-diagonal matrix. In fact, under some suitable assumptions, the existence of a finite number of edge defects is equivalent to the existence of embedded eigenvalues of the time evolution operator

Spectral Properties of Schr\"odinger Operators on Perturbed Lattices

We study the spectral properties of Schr\"{o}dinger operators on perturbed lattices. We shall prove the non-existence or the discreteness of embedded eigenvalues, the limiting absorption principle for the resolvent, construct a spectral representation, and define the S-matrix. Our theory covers the square, triangular, diamond, Kagome lattices, as well as the ladder, the graphite and the subdivision of square lattice

A DC to 40GHz Low Cost Surface Mountable RF-VIA TM Package

The ultimate goal for low cost packages for millimeterwave MMIC is to realize a miniature, light weight surface mount type package. This paper describes the design technologies of newly developed package, where we optimized via design by multilayer ceramic structure. As a result, insertion loss is about –0.5dB at 40 GHz (measurement include mounting board + one feedthrough) has been realized

Maturity, age and growth of Oreochromis karongae (Teleostei: cichlidae) in Lake Malawi and Lake Malombe

Size-at-50% maturity, age and growth, of Oreochromis (Nyasalapia) karongae (‘chambo’) in Lakes Malawi and Malombe were studied. Similar size-at-50% maturity and growth patterns were found for populations in Lake Malawi, but differences were observed for Lake Malombe populations, suggesting that current chambo fisheries management regulations, based on findings from the southern part of Lake Malawi, may be applicable to the central and southern parts of that lake, but not to Lake Malombe