arXiv subjects

Takuma Tomihisa

Publications and source records attributed to Takuma Tomihisa.

4 recordsLinked to original sources

arXiv2022

Development of homogeneous and high-performance REBCO bulks with flexibility in shapes by the single-direction melt growth (SDMG) method

We have developed a single-direction melt growth method in which REBCO melt-textured bulks grow only vertically from a seed plate utilizing the difference in peritectic temperatures of REBCO. Entirely c-grown YBCO, DyBCO and GdBCO bulks with various sizes and shapes were successfully fabricated with high reproducibility. Disk-shaped bulks showed high trapped fields with almost concentric field distributions, reflecting homogeneous and boundaryless bulky crystal. In particular, a YBCO bulk with a 32 mm diameter trapped a high field more than 1 T at 77 K. Furthermore, rectangular and joined hexagonal REBCO bulks were successfully fabricated, showing designed field-trapping distributions reflecting their shapes through well-connected superconducting joints among bulks.

cond-mat.supr-con↗

arXiv2021

Rarita-Schwinger fields on nearly Kähler manifolds

We study Rarita-Schwinger fields on 6-dimensional compact strict nearly Kähler manifolds. In order to investigate them, we clarify the relationship between some differential operators for the Hermitian connection and the Levi-Civita connection. As a result, we show that the space of the Rarita-Schwinger fields coincides with the space of the harmonic 3-forms. Applying the same technique to a deformation theory, we also find that the space of the infinitesimal deformations of Killing spinors coincides with the direct sum of a certain eigenspace of the Laplace operator and the space of the Killing spinors.

math.DG↗

arXiv2020

The spinor and tensor fields with higher spin on spaces of constant curvature

In this article, we give all the Weitzenböck-type formulas among the geometric first order differential operators on the spinor fields with spin $j+1/2$ over Riemannian spin manifolds of constant curvature. Then we find an explicit factorization formula of the Laplace operator raised to the power $j+1$ and understand how the spinor fields with spin $j+1/2$ are related to the spinors with lower spin. As an application, we calculate the spectra of the operators on the standard sphere and clarify the relation among the spinors from the viewpoint of representation theory. Next we study the case of trace-free symmetric tensor fields with an application to Killing tensor fields. Lastly we discuss the spinor fields coupled with differential forms and give a kind of Hodge-de Rham decomposition on spaces of constant curvature.

math.DG↗

arXiv2020

Spectra of the Rarita-Schwinger operator on some symmetric spaces

We give a method to calculate spectra of the square of the Rarita-Schwinger operator on compact symmetric spaces. According to Weitzenböck formulas, the operator can be written by the Laplace operator, which is the Casimir operator on compact symmetric spaces. Then we can obtain the spectra by using the Freudenthal's formula and branching rules. As examples, we calculate the spectra on the sphere, the complex projective space, and the quaternionic projective space.

math.DG↗