A remark on zeta functions of finite graphs via quantum walks

From the viewpoint of quantum walks, the Ihara zeta function of a finite graph can be said to be closely related to its evolution matrix. In this note we introduce another kind of zeta function of a graph, which is closely related to, as to say, the square of the evolution matrix of a quantum walk. Then we give to such a function two types of determinant expressions and derive from it some geometric properties of a finite graph. As an application, we illustrate the distribution of poles of this function comparing with those of the usual Ihara zeta function.Comment: 14 pages, 1 figur

Drum Beating and a Martial Art Bojutsu Performed by a Humanoid Robot

Over the past few decades a considerable number of studies have been made on impact dynamics. Zheng and Hemami discussed a mathematical model of a robot that collides with an environment (Zheng & Hemami, 1985). When a robot arm fixed on the ground collides with a hard environment, the transition from the free space to constrained space may bring instabilit

Skyrmion Burst and Multiple Quantum Walk in Thin Ferromagnetic Films

A giant Skyrmion collapses to a singular point by emitting spin waves in a thin ferromagnetic film, when external magnetic field is increased beyond the critical one. The remnant is a single-spin flipped (SSF) point. The SSF point has a quantum diffusion dynamics governed by the Heisenberg model. We determine its time evolution and show the diffusion process is a continuous-time quantum walk. We also analyze an interference of two SSF points after two Skyrmion bursts. Quantum walks for $S=1/2$ and 1 are exact solvable. The system presents a new type of quantum walk for $S>1/2$, where a SSF point breaks into 2S quantum walkers. It is interesting that we can create quantum walkers experimentally at any points in a magnetic thin film, first by creating Skyrmions sequentially and then by letting them collapse simultaneously.Comment: 4 pages, 3 figure

ホリー・リゲット法に対応する相関不等式の数値的評価

投稿論

Infinite Hopf family of elliptic algebras and bosonization

Elliptic current algebras E_{q,p}(\hat{g}) for arbitrary simply laced finite dimensional Lie algebra g are defined and their co-algebraic structures are studied. It is shown that under the Drinfeld like comultiplications, the algebra E_{q,p}(\hat{g}) is not co-closed for any g. However putting the algebras E_{q,p}(\hat{g}) with different deformation parameters together, we can establish a structure of infinite Hopf family of algebras. The level 1 bosonic realization for the algebra E_{q,p}(\hat{g}) is also established.Comment: LaTeX, 11 pages. This is the new and final versio

Structural Basis for Self-Renewal of Neural Progenitors in Cortical Neurogenesis

In mammalian brain development, neuroepithelial cells act as progenitors that produce self-renewing and differentiating cells. Recent technical advances in live imaging and gene manipulation now enable us to investigate how neural progenitors generate the 2 different types of cells with unprecedented accuracy and resolution, shedding new light on the roles of epithelial structure in cell fate decisions and also on the plasticity of neurogenesis