In the large N limit, the SU (N) lattice gauge theory becomes identical to the twisted Eguchi–Kawai model having only one space-time point. The purpose of this review is to explain the mechanism which leads to this identification and to show why one point matrix model can have space-time degrees of freedom. Using numerical simulations, string tension and meson masses in the large N limit are determined non-perturbatively.

Stochastic chaos in random dynamical systems is overviewed in relation to noise-induced phenomena, stochastic bifurcation, and time series analysis. Moreover our recent study on a random strange attractor in the von Karman swirling flow is reviewed.

Inelastic electron tunneling spectroscopy (IETS) combined with scanning tunneling microscopy (STM) is a powerful tool for investigating the vibrational energies of a single molecule at the atomic scale resolution. However, it is known that the intensity of IETS varies strongly for various tips, and the vibrational energies acquired by IETS are significantly influenced by the distance between the tip and molecule. To overcome the aforementioned problems, we have incorporated atomic force microscopy into STM-IETS in collaboration with Franz J. Giessibl of Regensburg University. Consequently, we have found that a metallic tip whose apex consists of a single atom provides a stronger IETS signal to the CO molecule on a Cu (111) surface, whereas a metallic tip whose apex consists of multiple atoms provides a weaker IETS signal. Further, we have found that the vibrational energies of the CO molecule are highly influenced by a tip that exerts a stronger force. Subsequently, these findings have been rationalized by a classical mechanical model assuming that the motion of the CO molecule is similar to that of a double pendulum, where the perturbation force between the tip and molecule and the weakening of the chemical bond because of the tip are taken into account.

We review the notion of quantum information capsule as a new information carrier in entangled quantum systems. Its applications to chaotic systems and communication protocols are presented.

We review a recent progress on higher-order topological systems. We start with a brief history of higher-order topological insulators (HOTIs). Then, we discuss two types of HOTIs. One is the Wannier-type HOTIs, which are extensions of the Su–Schrieffer–Heeger model, and the others are mass-type HOTIs, which are constructed based on topological insulators by adding extra terms. We also explain how these systems are realized in electric circuits. Finally, we extend the notion to non-Hermitian topological systems, where non-Hermitian terms are introduced by dissipation or nonreciprocity.