arXiv subjects

Takumi Ichikawa

Publications and source records attributed to Takumi Ichikawa.

2 recordsLinked to original sources

arXiv2024

Influence of trapped magnetic field of Sn-Pb solders on electrical resistivity measurement: an example of superconducting transition of Sn

We examined the affection of the flux-trapped states of Sn60-Pb40 solders on superconducting properties of a Sn wire. The temperature dependence of electrical resistivity at H = 0 Oe after zero-field cooling (ZFC) showed a sharp superconducting transition at T = 3.7 K. In contrast, that after field cooling (FC) resulted in broadening of the transition. The difference between ZFC and FC data evidences critical affection of trapped fluxes at solders on superconducting states. We propose that, in electrical measurements where magnetic fields of several hundred Oe are critical, field experience should be seriously considered when using solders.

cond-mat.mtrl-sci↗

arXiv2020

The super Frobenius-Schur indicator and finite group gauge theories on pin$^-$ surfaces

It is well-known that the value of the Frobenius-Schur indicator $|G|^{-1} \sum_{g\in G} χ(g^2)=\pm1$ of a real irreducible representation of a finite group $G$ determines which of the two types of real representations it belongs to, i.e. whether it is strictly real or quaternionic. We study the extension to the case when a homomorphism $φ:G\to \mathbb{Z}/2\mathbb{Z}$ gives the group algebra $\mathbb{C}[G]$ the structure of a superalgebra. Namely, we construct of a super version of the Frobenius-Schur indicator whose value for a real irreducible super representation is an eighth root of unity, distinguishing which of the eight types of irreducible real super representations described in [Wall1964] it belongs to. We also discuss its significance in the context of two-dimensional finite-group gauge theories on pin$^-$ surfaces.

math.RT↗