arXiv subjects

Takuya Matsumoto

Publications and source records attributed to Takuya Matsumoto.

At least 19 recordsLinked to original sources

arXiv2026

Rotation angles of a rotating disc as the holonomy of the Hopf fibration

We address the fundamental question of how rotation angles arise in classical rigid body motion from a geometric viewpoint. As a fundamental kinematical setting, we consider a rotating-disc model. We show that the rotation angle accumulated in a cyclic motion can be naturally decomposed into a dynamical phase and a geometric phase, and that the latter is obtained from the $U(1)$ holonomy of the Hopf fibration equipped with its canonical connection through a natural weight-two representation of the fiber group. By introducing a Gauss map based on a normal vector fixed at the center of the rotating disc, the physical periodic motion is mapped to a closed curve on the two-sphere $S^2$, whose horizontal lift in the Hopf bundle $S^3 \to S^2$ determines the geometric phase through the weight-two representation. This framework provides a conceptually clear interpretation of rotation angles as geometric phases and clarifies the geometric origin of their decomposition.

math-ph↗

arXiv2026

Rotation angles of a rotating disc -- A toy model exhibiting the geometric phase --

In this paper, we consider a simple kinematic model, which is a rotating disc on the edge of another fixed disc without slipping, and study the rotation angle of the rotating disc. The rotation angle consists of two parts, the dynamical phase $Δ_d$ and the geometric phase $Δ_g$. The former is a dynamical rotation of the disc itself, and the geometric motion of the disc characterizes the latter. In fact, $Δ_g$ is regarded as the geometric phase appearing in several important contexts in physics. The clue to finding the explicit form of $Δ_g$ is the Baumkuchen lemma, which we called. Due to the Gauss-Bonnet theorem, in the case that the rotating disc comes back to the initial position, $Δ_g$ is interpreted as the signed area of a two-sphere enclosed by the trajectory of the Gauss vector, which is a unit normal vector on the moving disc. We also comment on typical models sharing the common underlying structure, which include Foucault's pendulum, Dirac's monopole potentials, and Berry phase. Hence, our model is a very simple but distinguished one in the sense that it embodies the essential concepts in differential geometry and theoretical physics such as the Gauss-Bonnet theorem, the geometric phase, and the fiber bundles.

math-ph↗

arXiv2023

Radar-Based Noncontact Measurement of Heartbeat of Humans and Chimpanzees Using Millimeter-Wave Radar with Topology Method

This study proposes a method to determine the filter parameters required for the topology method, which is a radar-based noncontact method for measurement of heart inter-beat intervals. The effectiveness of the proposed method is evaluated by performing radar measurements involving both human participants and chimpanzee subjects. The proposed method is designed to enable setting of the filter cutoff frequency to eliminate respiratory components while maintaining the higher harmonics of the heartbeat components. Measurements using a millimeter-wave radar system and a reference contact-type electrocardiogram sensor demonstrate that the smallest errors that occur when measuring heart inter-beat intervals using the proposed method can be as small as 4.43 and 2.55 ms for humans and chimpanzees, respectively. These results indicate the possibility of using noncontact physiological measurements to monitor both humans and chimpanzees.

eess.SP↗

arXiv2022

Drinfeld realization of the centrally extended $\mathfrak{psl}(2|2)$ Yangian algebra with the manifest coproducts

The Lie superalgebra $\mathfrak{psl}(2|2)$ is recognized as a pretty special one in both mathematics and theoretical physics. In this paper, we present the Drinfeld realization of the Yangian algebra associated with the centrally extended Lie superalgebra $\mathfrak{psl}(2|2)$. Furthermore, we show that it possesses the Hopf algebra structures, particularly the coproducts. The idea to prove the existence of the manifest coproducts is the following. Firstly, we shall introduce them to Levendorskii's realization, a system of a finite truncation of the Drinfeld generators. Secondly, we show that Levendorskii's realization is isomorphic to the Drinfeld realization by induction.

math.QA↗

arXiv2021

Essential model parameters for nonreciprocal magnons in multisublattice systems

We theoretically investigate the microscopic conditions for emergent nonreciprocal magnons toward unified understanding on the basis of a microscopic model analysis. We show that the products of the Bogoliubov Hamiltonian obtained within the linear spin wave approximation is enough to obtain the momentum-space functional form and the key ingredients in the nonreciprocal magnon dispersions in an analytical way even without solving the eigenvalue problems. We find that the odd order of an effective antisymmetric Dzyaloshinskii-Moriya interaction and/or the even order of an effective symmetric anisotropic interaction in the spin rotated frame can be a source of the antisymmetric dispersions. We present possible kinetic paths of magnons contributing to the antisymmetric dispersions in the one- to four-sublattice systems with the general exchange interactions. We also test the formula for both ferromagnetic and antiferromagnetic orderings in the absence of spatial inversion symmetry.

cond-mat.str-el↗

arXiv2021

Nonreciprocal magnon excitations by the Dzyaloshinskii-Moriya interaction on the basis of bond magnetic toroidal multipoles

The microscopic conditions for the emergence of nonreciprocal magnon excitations in noncentrosymmetric magnets are theoretically investigated. We show that asymmetric magnon excitations appear when a bond magnetic toroidal dipole becomes active, which is defined as a parallel component between the Dzyaloshinskii-Moriya vector and the averaged spin moments at the ends of the bonds. Depending on magnetic structures accompanying the bond magnetic toroidal dipoles, the higher-rank magnetic toroidal multipoles can also be activated in a magnetic cluster, which describes various angle dependences of asymmetric magnon excitations. We demonstrate a variety of asymmetric magnon excitations for two magnetic systems in the noncentrosymmetric lattice structures; a one-dimensional breathing chain under a uniform crystalline electric field and a three-dimensional layered breathing kagome structure. We show that a bottom shift of magnon bands occurs by the magnetic toroidal dipole and a valley splitting occurs by the magnetic toroidal octupole under magnetic orderings.

cond-mat.str-el↗

arXiv2021

Classifying Topological Charge in SU(3) Yang-Mills Theory with Machine Learning

We apply a machine learning technique for identifying the topological charge of quantum gauge configurations in four-dimensional SU(3) Yang-Mills theory. The topological charge density measured on the original and smoothed gauge configurations with and without dimensional reduction is used as inputs for the neural networks (NN) with and without convolutional layers. The gradient flow is used for the smoothing of the gauge field. We find that the topological charge determined at a large flow time can be predicted with high accuracy from the data at small flow times by the trained NN; for example, the accuracy exceeds $99\%$ with the data at $t/a^2\le0.3$. High robustness against the change of simulation parameters is also confirmed with a fixed physical volume. We find that the best performance is obtained when the spatial coordinates of the topological charge density are fully integrated out in preprocessing, which implies that our convolutional NN does not find characteristic structures in multi-dimensional space relevant for the determination of the topological charge.

hep-lat↗

arXiv2020

On repetitiveness measures of Thue-Morse words

We show that the size $γ(t_n)$ of the smallest string attractor of the $n$th Thue-Morse word $t_n$ is 4 for any $n\geq 4$, disproving the conjecture by Mantaci et al. [ICTCS 2019] that it is $n$. We also show that $δ(t_n) = \frac{10}{3+2^{4-n}}$ for $n \geq 3$, where $δ(w)$ is the maximum over all $k = 1,\ldots,|w|$, the number of distinct substrings of length $k$ in $w$ divided by $k$, which is a measure of repetitiveness recently studied by Kociumaka et al. [LATIN 2020]. Furthermore, we show that the number $z(t_n)$ of factors in the self-referencing Lempel-Ziv factorization of $t_n$ is exactly $2n$.

cs.DS↗

arXiv2020

Nonreciprocal Magnon by Symmetric Anisotropic Exchange Interaction in Honeycomb Antiferromagnet

We investigate a microscopic origin of nonreciprocal magnon that is distinct from the Dzyaloshinskii-Moriya interaction in a honeycomb antiferromagnet. The key ingredient is a symmetric anisotropic exchange interaction depending on the bond direction, which results in a valley-type nonreciprocal magnon excitations under the staggered antiferromagnetic ordering. Furthermore, we find this type of nonreciprocal magnon exhibits a peculiar magnetic-field response; the nonreciprocal direction can be manipulated by the in-plane rotating magnetic field. The obtained results can be accounted for the emergence of the magnetic toroidal multipoles.

cond-mat.str-el↗

arXiv2020

Anisotropy of the transport properties of NdFeAs(O,F) thin films grown on vicinal substrates

NdFeAs(O,F) thin films having different fluorine contents were grown on 5 deg. or 10 deg. vicinal cut MgO and CaF2 single crystalline substrates by molecular beam epitaxy. Structural characterisations by reflection high-energy electron diffraction and x-ray diffraction confirmed the epitaxial growth of NdFeAs(O,F). The resistivities of the ab-plane and along the c-axis were derived from the resistivity measurements in the longitudinal and transversal directions. The c-axis resistivity was always higher than the ab-plane resistivity, resulting from the anisotropic electronic structure. The resistivity anisotropy at 300 K was almost constant in the range of 50-90 irrespective of the F content. On the other hand, the resistivity anisotropy at 56 K showed a strong fluorine dependence: the resistivity anisotropy was over 200 for the films with optimum F contents (superconducting transition temperature Tc around 50 K), whereas the resistivity anisotropy was around 70 for the films in the under-doped regime (Tc between 35 and 45 K). The mass anisotropy are the effective masses along the c-axis and on the ab-plane) close to Tc derived from the anisotropic Ginzburg-Landau approach using the angular-dependency of the ab-plane resistivity was in the range from 2 to 5. On the assumption that the square of the mass anisotropy is equal to the resistivity anisotropy, those values are small compared to the normal state anisotropy.

cond-mat.supr-con↗

arXiv2019

Classifying topological sector via machine learning

We employ a machine learning technique for an estimate of the topological charge $Q$ of gauge configurations in SU(3) Yang-Mills theory in vacuum. As a first trial, we feed the four-dimensional topological charge density with and without smoothing into the convolutional neural network and train it to estimate the value of $Q$. We find that the trained neural network can estimate the value of $Q$ from the topological charge density at small flow time with high accuracy. Next, we perform the dimensional reduction of the input data as a preprocessing and analyze lower dimensional data by the neural network. We find that the accuracy of the neural network does not have statistically-significant dependence on the dimension of the input data. From this result we argue that the neural network does not find characteristic features responsible for the determination of $Q$ in the higher dimensional space.

hep-lat↗

arXiv2019

Grain boundary characteristics of oxypnictide NdFeAs(O,F) superconductors

We have systematically investigated the grain boundary (GB) angle dependence of transport properties for NdFeAs(O,F) fabricated on [001]-tilt symmetric MgO bicrystal substrates. In our previous study, NdFeAs(O,F) bicrystal films showed a weak-link behaviour even at a GB angle of 6°. However, this was caused by an extrinsic effect originating from the damage to both NdFeAs(O,F) and MgO substrate by excess F-diffusion along the grain boundary. To investigate the intrinsic nature of grain boundaries, we minimized the damage to NdFeAs(O,F) and MgO by reducing the deposition temperature of NdOF over-layer needed for F-doping. The resultant NdFeAs(O,F) bicrystal films have a critical angle of 8.5°, above which Jc starts to decrease exponentially. This critical angle is almost the same as those of other Fe-based superconductors.

cond-mat.supr-con↗

arXiv2018

Kinetic theory for a simple modeling of phase transition: Dynamics out of local equilibrium

This is a continuation of the previous work (Takata & Noguchi, J. Stat. Phys., 2018) that introduces the presumably simplest model of kinetic theory for phase transition. Here, main concern is to clarify the stability of uniform equilibrium states in the kinetic regime, rather than that in the continuum limit. It is found by the linear stability analysis that the linear neutral curve is invariant with respect to the Knudsen number, though the transition process is dependent on the Knudsen number. In addition, numerical computations of the (nonlinear) kinetic model are performed to investigate the transition processes in detail. Numerical results show that (unexpected) incomplete transitions may happen as well as clear phase transitions.

cond-mat.stat-mech↗

arXiv2018

Fabrication of grain boundary junctions using NdFeAs(O,F) superconducting thin films

We report on the growth of NdFeAs(O,F) thin films on [001]-tilt MgO bicrystal substrates with misorientation angle theta_GB=6°, 12°, 24° and 45°, and their inter- and intra-grain transport properties. X-ray diffraction study confirmed that all our NdFeAs(O,F) films are epitaxially grown on the MgO bicrystals. The theta_GB dependence of the inter-grain critical current density Jc shows that, unlike Co-doped BaFe2As2 and Fe(Se,Te), its decay with theta_GB is rather significant. As a possible reason of this result, fluorine may have diffused preferentially to the grain boundary region and eroded the crystal structure.

cond-mat.supr-con↗

arXiv2016

Explicit examples of DIM constraints for network matrix models

Dotsenko-Fateev and Chern-Simons matrix models, which describe Nekrasov functions for SYM theories in different dimensions, are all incorporated into network matrix models with the hidden Ding-Iohara-Miki (DIM) symmetry. This lifting is especially simple for what we call balanced networks. Then, the Ward identities (known under the names of Virasoro/W-constraints or loop equations or regularity condition for qq-characters) are also promoted to the DIM level, where they all become corollaries of a single identity.

hep-th↗

arXiv2016

Chiral Unitary Quantum Phase Transition in 2H-Fe$_x$TaSe$_2$

We have observed a metal-insulator transition of a quasi-two dimensional electronic system in transition metal dichalcogenide $2H$-TaSe$_2$ caused by doping iron. The sheet resistance of $2H$-Fe$_x$TaSe$_2$ ($0 \leq x \leq 0.120$) single crystals rises about $10^6$ times with the increasing of $x$ at the lowest temperature. We investigated the temperature dependence of the resistance and found a metal-insulator transition with a critical sheet resistance $11.7 \pm 5.4$ k$\rmΩ$. The critical exponent of the localization length $ν$ is estimated $0.31 \pm 0.18$. The values of the critical sheet resistance and $ν$ are accordant to those of the \textit{chiral unitary class} (less than $h/1.49e^2=17.3$ k$\rmΩ$ and $0.35 \pm 0.03$, respectively). We suggest that $2H$-Fe$_x$TaSe$_2$ is classified as the chiral unitary class, not as standard unitary class.

cond-mat.mes-hall↗

arXiv2015

Towards the gravity/CYBE correspondence beyond integrability -- Yang-Baxter deformations of $T^{1,1}$

Yang-Baxter sigma models, proposed by Klimcik and Delduc-Magro-Vicedo, have been recognized as a powerful framework for studying integrable deformations of two-dimensional non-linear sigma models. In this short article, as an important generalization, we review a non-integrable sigma model in the Yang-Baxter sigma model approach based on [arXiv:1406.2249]. In particular, we discuss a family of deformations of the 5D Sasaki-Einstein manifold $T^{1,1}$, instead of the standard deformations of the $5$-sphere S$^5$. For this purpose, we first describe a novel construction of $T^{1,1}$ as a supercoset, and provide a physical interpretation of this construction from viewpoint of the dual Klebanov-Witten field theory. Secondly, we consider a $3$-parameter deformation of $T^{1,1}$ by using classical $r$-matrices satisfying the classical Yang--Baxter equation (CYBE). The resulting metric and NS-NS two-form completely agree with the ones previously obtained via TsT (T-dual -- shift -- T-dual) transformations, and contain the Lunin-Maldacena background as a special case. Our result indicates that what we refer to as the gravity/CYBE(Classical Yang-Baxter Equation) correspondence can be extended beyond integrable cosets.

hep-th↗

arXiv2015

Strong Coupling Superconductivity in the Vicinity of the Structural Quantum Critical Point in (Ca$_x$Sr$_{1-x}$)$_3$Rh$_4$Sn$_{13}$

The family of the superconducting quasi-skutterudites (Ca$_x$Sr$_{1-x}$)$_3$Rh$_4$Sn$_{13}$ features a structural quantum critical point at $x_c=0.9$, around which a dome-shaped variation of the superconducting transition temperature $T_c$ is found. Using specific heat, we probe the normal and the superconducting states of the entire series straddling the quantum critical point. Our analysis indicates a significant lowering of the effective Debye temperature on approaching $x_c$, which we interpret as a result of phonon softening accompanying the structural instability. Furthermore, a remarkably large enhancement of $2Δ/k_BT_c$ and $ΔC/γT_c$ beyond the Bardeen-Cooper-Schrieffer (BCS) values is found in the vicinity of the structural quantum critical point. The phase diagram of (Ca$_{x}$Sr$_{1-x}$)$_3$Rh$_4$Sn$_{13}$ thus provides a model system to study the interplay between structural quantum criticality and strong electron-phonon coupling superconductivity.

cond-mat.supr-con↗