Semimetal bismuth (Bi) plays an irreplaceable role in condensed matter physics due to extreme properties stemming from its tiny carrier pockets and three-dimensional Dirac dispersion. Moreover, the largest spin–orbit coupling has made Bi a central element in recent topological studies. Here, we review recent experimental studies on various topological phases and an insulating phase in Bi films by utilizing quantized electronic structures emerging at the nanoscale. The studies demonstrate fertile grounds for novel properties of matter and unique capabilities of direct observation in surface physics.
In this article, we describe our recent works on multiple Schramm–Loewner evolution (SLE). After recalling that the family of SLEs are characterized by the domain Markov property and the conformal invariance, we formulate our problem of choosing driving processes for a multiple SLE. We present our solution to this problem relying on the theory of coupling between SLE and Gaussian free field (GFF). Specifically, we discover that a multiple SLE is correctly coupled with a certain GFF if and only if the driving processes are given by the Dyson model.
Statistical mechanics of a deep neural network, feedforward network of perceptrons, is studied using the replica method. We considered two scenarios 1) random scenario 2) teacher-student scenario in a Bayes optimal setting. The analysis performed in the thermodynamics limit revealed characteristic wetting transitions in the solution space.
Symmetry and symmetry breaking underpin wide range of biological phenomena. We studied positioning mechanism of a nucleus-like cluster driven by actomyosin confined in a water-in-oil droplet capsule as a simplified cell model. We found that periodic actomyosin waves move cluster to the center, while actomyosin bridges contract cluster to the droplet interface. Combining active gel theory and percolation theory, we showed that the positioning symmetry is controlled by the tug-of-war between the two distinct actomyosin structures.