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One-dimensionalization by Geometrical Frustration in the Anisotropic Triangular Lattice of the 5d Quantum Antiferromagnet Ca3ReO5Cl2Apr 12 2019We report on the emergence of antiferromagnetic spin chains from two-dimensionally aligned spins on the anisotropic triangular lattice (ATL) in the insulating calcium rhenium oxychloride Ca3ReO5Cl2. The compound contains Re6+ ions each with one unpaired ... More

Anisotropic superconducting gaps in YNi$_2$B$_2$C: A first-principles investigationOct 24 2016We calculate superconducting gaps and quasiparticle density of states of YNi$_2$B$_2$C in the framework of the density functional theory for superconductors to investigate the origin of a highly anisotropic superconducting gaps in this material. Calculated ... More

Numerical Algorithm for Exact Finite Temperature Spectra and Its Application to Frustrated Quantum Spin SystemsFeb 08 2018A numerical algorithm to calculate exact finite-temperature spectra of many-body lattice Hamiltonians is formulated by combining the typicality approach and the shifted Krylov subspace method. The combined algorithm, which we name finite-temperature shifted ... More

"Visible" 5d orbital states in a pleochroic oxychlorideApr 12 2019Transition metal compounds sometimes exhibit beautiful colors. We report here on a new oxychloride Ca3ReO5Cl2 which shows unusually distinct pleochroism; that is, the material exhibits different colors depending on viewing directions. This ple-ochroism ... More

Scattering of Solitons and Dark Solitons by Potential Walls in the Nonlinear Schroedinger EquationOct 27 2004Scattering of solitons and dark solitons by potential walls is studied in the nonlinear Schroedinger equation under various conditions. We investigate the conditions under which solitons are split into two solitons at the potential wall. We find that ... More

First-principles study of the pressure and crystal-structure dependences of the superconducting transition temperature in compressed sulfur hydridesFeb 03 2015Jul 07 2015We calculate superconducting transition temperatures ($T_{\rm c}$) in sulfur hydrides H$_{2}$S and H$_{3}$S from first principles using the density functional theory for superconductors. At pressures of $\lesssim$150 GPa, the high values of $T_{\rm c}$ ... More

Dirac fermions in boropheneFeb 02 2017Honeycomb structures of group IV elements can host massless Dirac fermions with non-trivial Berry phases. Their potential for electronic applications has attracted great interest and spurred a broad search for new Dirac materials especially in monolayer ... More

Characterizing financial crisis by means of the three states random field Ising modelSep 19 2013We propose a formula of time-series prediction by means of three states random field Ising model (RFIM). At the economic crisis due to disasters or international disputes, the stock price suddenly drops. The macroscopic phenomena should be explained from ... More

Theory of vortex excitation imaging via an NMR relaxation measurementJun 07 1999The temperature dependence of the site-dependent nuclear spin relaxation time T_1 around vortices is studied in s-wave and d-wave superconductors.Reflecting low energy electronic excitations associated with the vortex core, temperature dependences deviate ... More

Quasiparticle heat transport in the mixed state of high $T_c$ superconductorsJun 19 2003Jul 06 2004The field dependence of low-temperature thermal conductivity $\kappa(H)$ observed on cuprates is explained by calculating $\kappa(H)$ microscopically. The heat current carried by low-lying quasiparticles around a vortex core decreases with $H$ due to ... More

Mordell-Weil Lattice via String JunctionsSep 17 1999We analyze the structure of singularities, Mordell-Weil lattices and torsions of a rational elliptic surface using string junctions in the background of 12 7-branes. The classification of the Mordell-Weil lattices due to Oguiso-Shioda is reproduced in ... More

Vortex Structure in Superconducting Stripe StatesDec 28 2000The vortex structure in superconducting stripe states is studied according to the Bogoliubov-de Gennes theory on the two-dimensional Hubbard model with nearest-neighbor sites pairing interaction. The vortex is trapped at the outside region of the stripe ... More

Quasiparticle structure in antiferromagnetism around the vortex and nuclear magnetic relaxation timeMar 26 2003Mar 11 2004On the basis of the Bogoliubov-de Gennes theory for the two-dimensional extended Hubbard model, the vortex structure in d-wave superconductors is investigated including the contribution of the induced incommensurate antiferromagnetism around the vortex ... More

Relation between Vortex Excitation and Thermal Conductivity in SuperconductorsApr 05 2002Apr 08 2002Thermal conductivity $\kappa_{xx}(T)$ under a field is investigated in $d_{x^2-y^2}$-wave superconductors and isotropic s-wave superconductors by the linear response theory, using a microscopic wave function of the vortex lattice states. To study the ... More

High Velocity Oblique Cloud Collision and Star and Star Cluster Formation through Gravitational Instability of the Shock-Compressed Slab with Rotation and Velocity ShearJul 26 1994We study the gravitational instability of an isothermal gaseous slab formed by cloud-cloud collision and compression at the cloud interface. The compressed gaseous slab rotates and has velocity shear except when the collision is not exactly head-on. The ... More

An invariant of states on Cuntz algebrasOct 06 2016For an arbitrary state $\omega$ on a Cuntz algebra, we define a number $1\leq \kappa(\omega)\leq \infty$ such that if GNS representations by $\omega$ and $\omega'$ are unitarily equivalent, then $\kappa(\omega)=\kappa(\omega')$. By using $\kappa$, we ... More

Classical and quantum chiral order in frustrated XY magnetsFeb 07 2002Recent studies on the chiral order of regularly frustrated XY magnets are reviewed both in classical and quantum cases. In the classical case, chiral transition is a thermal one, while in the quantum case, it is a quantum phase transition. Importance ... More

Universality of phase transitions of frustrated antiferromagnetsMay 12 1998Recent theoretical and experimental studies on the critical properties of frustrated antiferromagnets with the noncollinear spin order, including stacked-triangular antiferromagnets and helimagnets, are reviewed. Particular emphasis is put on the novel ... More

Structure of the group of automorphisms of C$^{*}$-algebrasSep 19 1998We obtain a kind of structure theorem for the automorphism group ${\rm Aut}{\cal A}$ of a unital C$^{*}$-algebra ${\cal A}$. According to it, ${\rm Aut}{\cal A}$ can be regarded as a subgroup of the semi-direct product of direct product group consisting ... More

Permutative representations of the Cuntz-Krieger algebrasAug 16 2005We generalize permutative representations of the Cuntz algebras for the \cka\ $\coa$ for any $A$. We characterize cyclic permutative representations by notions of cycle and chain, and show their existence and uniqueness. We show necessary and sufficient ... More

Local particle-ghost symmetryMay 20 2015We study the quantization of systems with local particle-ghost symmetries. The systems contain ordinary particles including gauge bosons and their counterparts obeying different statistics. The particle-ghost symmetry is a kind of fermionic symmetry, ... More

Temporary Grand Unified Theory in Unphysical WorldNov 28 2008Apr 21 2009We construct grand unified models on an orbifold based on unphysical grand unification. The reduction to the standard model or its supersymmetric one is carried out using a variant of Parisi-Sourlas mechanism and nontrivial $Z_2$ parity assignment.

Chimera Ising Walls in Forced Nonlocally Coupled OscillatorsMar 09 2007Nonlocally coupled oscillator systems can exhibit an exotic spatiotemporal structure called chimera, where the system splits into two groups of oscillators with sharp boundaries, one of which is phase-locked and the other is phase-randomized. Two examples ... More

Gauge Symmetry Reduction from the Extra Space $S^1/Z_2$Feb 22 1999Dec 28 2000We study a mechanism of symmetry transition upon compactification of a 5-dimensional field theory on $S^1/Z_2$. The transition occurs unless all components in a multiplet of a symmetry group have a common $Z_2$ parity on $S^1/Z_2$. This mechanism is applied ... More

On Low-Energy Theory from General SupergravityNov 16 1995Starting from non-minimal supergravity theory with unified gauge symmetry, we obtain the low-energy effective theory by taking the flat limit and integrating out the superheavy fields in a model-independent manner. The scalar potential has extra non-universal ... More

Low-Energy Effective Lagrangian from Non-Minimal Supergravity with Unified Gauge SymmetryAug 14 1995From general supergravity theory with unified gauge symmetry, we obtain the low-energy effective Lagrangian by taking the flat limit and integrating out the superheavy fields in model-independent manner. The scalar potential possesses some excellent features. ... More

Finiteness, duality, and fermionic symmetryMar 13 2015Mar 17 2015We propose a framework for a new type of finite field theories based on a hidden duality between an ultra-violet and an infra-red region. Physical quantities do not receive radiative corrections at a fundamental scale or the fixed point of the duality ... More

Cubic Matrix, Generalized Spin Algebra and Uncertainty RelationApr 17 2003Apr 06 2004We propose a generalization of spin algebra using three-index objects. There is a possibility that a triple commutation relation among three-index objects implies a kind of uncertainty relation among their expectation values.

Serre-Swan theorem for non-commutative C$^{*}$-algebrasFeb 19 2000Aug 21 2006We generalize the Serre-Swan theorem to non-commutative C$^{*}$-algebras. For a Hilbert C$^{*}$-module $X$ over a C$^{*}$-algebra ${\cal A}$, we introduce a hermitian vector bundle $\exx$ associated to $X$. We show that there is a linear subspace $\Gamma_{X}$ ... More

At which points exactly has Lebesgue's singular function the derivative zero ?Dec 26 2010Let L_a(x) be Lebesgue's singular function with a real parameter a (0<a<1, a not equal to 1/2). As is well known, L_a(x) is strictly increasing and has a derivative equal to zero almost everywhere. However, what sets of x in [0,1] actually have L_a'(x)=0 ... More

Pure states on Cuntz algebras arising from geometric progressionsSep 25 2015Jan 28 2016Let ${\cal O}_n$ denote the Cuntz algebra for $n\geq 2$. We introduce an embedding $f$ of ${\cal O}_m$ into ${\cal O}_n$ arising from a geometric progression of Cuntz generaters of ${\cal O}_n$. By identifying ${\cal O}_m$ with $f({\cal O}_m)$, we extend ... More

Biideals and a lattice of C$^{*}$-bialgebras associated with prime numbersApr 28 2009Let ${\cal O}_{*}$ be the C$^{*}$-algebra defined as the direct sum of all Cuntz algebras. Then ${\cal O}_{*}$ has a non-cocommutative comultiplication $\Delta_{\phi}$ and a counit $\epsilon$. Let ${\rm BI}({\cal O}_{*})$ denote the set of all closed ... More

Non-existence of universal $R$-matrix for some C$^{*}$-bialgebrasDec 18 2009For a C$^{*}$-bialgebra $A$ with a comultiplication $\Delta$, a universal $R$-matrix of $(A,\Delta)$ is defined as a unitary element in the multiplier algebra $M(A\otimes A)$ of $A\otimes A$ which is an intertwiner between $\Delta$ and its opposite comultiplication ... More

Recursive boson system in the Cuntz algebra ${\cal O}_{\infty}$Apr 27 2007Bosons and fermions are often written by elements of other algebras. M. Abe gave a recursive realization of the boson by formal infinite sums of the canonical generators of the Cuntz algebra ${\cal O}_{\infty}$. We show that such formal infinite sum always ... More

An invariant of states on Cuntz algebrasOct 06 2016Feb 16 2017For an arbitrary state $\omega$ on a Cuntz algebra, we define a number $1\leq \kappa(\omega)\leq \infty$ such that if the GNS representations of $\omega$ and $\omega'$ are unitarily equivalent, then $\kappa(\omega)=\kappa(\omega')$. By using $\kappa$, ... More

Classification and realizations of type III factor representations of Cuntz-Krieger algebras associated with quasi-free statesJun 19 2008Feb 25 2009We completely classify type III factor representations of Cuntz-Krieger algebras associated with quasi-free states up to unitary equivalence. Furthermore, we realize these representations on concrete Hilbert spaces without using GNS construction. Free ... More

Tensor products of type III factor representations of Cuntz-Krieger algebrasMay 06 2008We introduced a non-symmetric tensor product of any two states or any two representations of Cuntz-Krieger algebras associated with a certain non-cocommutative comultiplication in previous our work. In this paper, we show that a certain set of KMS states ... More

Quantization of systems with $OSp(2|2)$ symmetryFeb 03 2015Feb 21 2015We study the quantization of systems that contain both ordinary fields with a positive norm and their counterparts obeying different statistics. The systems have novel fermionic symmetries different from the space-time supersymmetry and the BRST symmetry. ... More

Release of physical modes from unphysical fieldsSep 01 2014Sep 30 2015We present a basic idea and a toy model that physical modes originate from unobservable fields. The model is defined on a higher-dimensional space-time and has fermionic symmetries that make fields unphysical, and observable modes can appear through a ... More

Dynamical Theory of Generalized MatricesApr 04 2005We propose a generalization of spin algebra using multi-index objects, and a dynamical system analogous to matrix theory. The system has a solution described by generalized spin representation matrices and possesses a symmetry similar to the volume preserving ... More

Generalized Matrix MechanicsMar 01 2002Jun 21 2002We propose a generalization of Heisenbergs' matrix mechanics based on many-index objects. It is shown that there exists a solution describing a harmonic oscillator and many-index objects lead to a generalization of spin algebra.

Misleading Coupling Unification and Lifshitz Type Gauge TheoryJun 20 2009Aug 14 2009We propose a new grand unification scenario for ensuring proton stability. Our scenario is based on the idea that the proton decay problem is an artificial one, which is caused from the identification of the gauge coupling unification scale with the grand ... More

Model-independent analysis of soft masses in heterotic string models with anomalous U(1) symmetryNov 12 1998Nov 19 1998We study the magnitudes of soft masses in heterotic string models with anomalous U(1) symmetry model-independently. In most cases, D-term contribution to soft scalar masses is expected to be comparable to or dominant over other contributions provided ... More

Infinitesimal Takesaki duality of Hamiltonian vector fields on a symplectic manifoldJun 20 1997Oct 21 1997For an infinitesimal symplectic action of a Lie algebra ${\goth g}$ on a symplectic manifold, we construct an infinitesimal crossed product of Hamiltonian vector fields and Lie algebra ${\goth g}$. We obtain its second crossed product in case ${\goth ... More

Anomalous Hall effect as a probe of the chiral order in spin glassesOct 01 2002Dec 13 2002Anomalous Hall effect arising from the noncoplanar spin configuration (chirality) is discussed as a probe of the chiral order in spin glasses. It is shown that the Hall coefficient yields direct information about the linear and nonlinear chiral susceptibilities ... More

The ordering of XY spin glassesFeb 17 2011Ordering properties of XY-like spin-glass magnets with an easy-plane magnetic anisotropy are studied based on a symmetry consideration and the results of recent numerical simulations on the pure Heisenberg and XY spin-glass models. The effects of an easy-plane-type ... More

Spatiotemporal Correlations of EarthquakesMar 13 2006Statistical properties of earthquakes are studied both by the analysis of real earthquake catalog of Japan and by numerical computer simulations of the spring-block model in both one and two dimensions. Particular attention is paid to the spatiotemporal ... More

Quantum Mechanics and Operator algebras on the Hilbert ballOct 21 1997Jul 24 2007Cirelli, Mani\`{a} and Pizzocchero generalized quantum mechanics by K\"{a}hler geometry. Furthermore they proved that any unital C$^{*}$-algebra is represented as a function algebra on the set of pure states with a noncommutative $*$-product as an application. ... More

Classification of sub-Cuntz statesAug 06 2014Let ${\cal O}_n$ denote the Cuntz algebra for $2\leq n<\infty$. With respect to a homogeneous embedding of ${\cal O}_{n^m}$ into ${\cal O}_n$, an extension of a Cuntz state on ${\cal O}_{n^m}$ to ${\cal O}_n$ is called a sub-Cuntz state, which was introduced ... More

Triangular C$^{*}$-bialgebra defined as the direct sum of matrix algebrasJan 12 2010Let $M_{*}({\bf C})$ denote the C$^{*}$-algebra defined as the direct sum of all matrix algebras $\{M_{n}({\bf C}):n\geq 1\}$. It is known that $M_{*}({\bf C})$ has a non-cocommutative comultiplication $\Delta_{\varphi}$. We show that the C$^{*}$-bialgebra ... More

Classification of sectors of the Cuntz algebras by graph invariantsJul 19 2005A unitary equivalence class of endomorphisms of a unital C$^{*}$-algebra ${\cal A}$ is called a {\it sector} of ${\cal A}$. We introduced permutative endomorphisms of the Cuntz algebra ${\cal O}_N$ in the previous work. Branching laws of permutative representations ... More

Generalized permutative representations of Cuntz algebrasMay 06 2005Mar 23 2006We introduce representations of the Cuntz algebra $\con$ which are parameterized by sequences in the set of unit vectors in ${\bf C}^{N}$. These representations are natural generalizations of permutative representations by Bratteli-Jorgensen and Davidson-Pitts. ... More

Automata computation of branching laws for endomorphisms of Cuntz algebrasJan 30 2006In our previous articles, we have presented a class of endomorphisms of the Cuntz algebras which are defined by polynomials of canonical generators and their conjugates. We showed the classification of some case under unitary equivalence by help of branching ... More

Spin-chirality decoupling in Heisenberg spin glasses and related systemsSep 26 2006Recent studies on the spin and the chirality orderings of the three-dimensional Heisenberg spin glass and related systems are reviewed with particular emphasis on the possible spin-chirality decoupling phenomena. Chirality scenario of real spin-glass ... More

Nature of the vortex-glass order in strongly type-II superconductorsFeb 14 2003Mar 14 2003The stability and the critical properties of the three-dimensional vortex-glass order in random type-II superconductors with point disorder is investigated in the unscreened limit based on a lattice {\it XY} model with a uniform field. By performing equilibrium ... More

Dynamical simulation of spin-glass and chiral-glass orderings in three-dimensional Heisenberg spin glassesMay 11 1998Spin-glass and chiral-glass orderings in three-dimensional Heisenberg spin glasses are studied with and without randaom magnetic anisotropy by dynamical Monte Carlo simulations. In isotropic case, clear evidence of a finite-temperature chiral-glass transition ... More

Fluctuation-dissipation ratio of the Heisenberg spin glassDec 25 2002Jun 10 2003Fluctuation-dissipation (FD) relation of the three-dimensional Heisenberg spin glass with weak random anisotropy is studied by off-equilibrium Monte Carlo simulation. Numerically determined FD ratio exhibits a ``one-step-ike''behavior, the effective temperature ... More

Dynamical Properties of Chiral-Glass Order in Ceramic High-Tc SuperconductorsDec 02 1999There recently accumulated growing numerical and experimental evidence that a novel glassy zero-field phase characterized by the spontaneously broken time-reversal symmetry, a chiral-glass phase, is realized in certain ceramic high-$T_c$ superconductors. ... More

From the Kuramoto-Sakaguchi model to the Kuramoto-Sivashinsky equationJan 14 2014We derive the Kuramoto-Sivashinsky-type phase equation from the Kuramoto-Sakaguchi-type phase model via the Ott-Antonsen-type complex amplitude equation and demonstrate heterogeneity-induced collective-phase turbulence in nonlocally coupled individual-phase ... More

SUSY Breaking from Exotic U(1)May 18 2012We propose a mechanism that the soft supersymmetry breaking masses can be induced from the dynamical rearrangement of local U(1) symmetry in a five-dimensional model. The U(1) symmetry possesses several extraordinary features. The eigenstates of U(1) ... More

Topological Grand UnificationOct 08 2008Feb 10 2009We propose a new grand unification scenario for ensuring proton stability and triplet-doublet Higgs mass splitting with the help of topological symmetry and dynamics.

Triplet-doublet Splitting, Proton Stability and Extra DimensionDec 12 2000Jun 19 2001We propose a new possibility to reconcile the coupling unification scenario with the triplet-doublet mass splitting based on a 5-dimensional supersymmetric model with SU(5) gauge symmetry. It is shown that the minimal supersymmetric standard model is ... More

Fermionic scalar fieldJun 24 2014Oct 11 2014We reexamine the connection between spin and statistics through the quantization of a complex scalar field, using the formulation with the property that the hermitian conjugate of canonical momentum for a variable is just the canonical momentum for the ... More

Unitary isomorphism of Fock spaces of bosons and fermions arising from a representation of the Cuntz algebra $\co{2}$Jul 17 2008Bosons and fermions are described by using canonical generators of Cuntz algebras on any permutative representation. According to branching laws associated with these descriptions, a certain representation of the Cuntz algebra $\co{2}$ induces Fock representations ... More

A tensor product of representations of Cuntz algebrasNov 04 2006We introduce a nonsymmetric, associative tensor product among representations of Cuntz algebras by using embeddings. We show the decomposition formulae of tensor products for permutative representations explicitly We apply decomposition formulae to determine ... More

Generalized Semimagic Squares for Digital HalftoningSep 07 2010Completing Aronov et al.'s study on zero-discrepancy matrices for digital halftoning, we determine all (m, n, k, l) for which it is possible to put mn consecutive integers on an m-by-n board (with wrap-around) so that each k-by-l region holds the same ... More

Some inverse limits of Cuntz algebrasDec 13 2011We construct a nontrivial inverse system of Cuntz algebras $\{{\cal O}_{n}:2\leq n<\infty\}$, whose inverse limit is *-isomorphic onto ${\cal O}_{\infty}$. By using this result, it is shown that the $K_{0}$-functor is discontinuous with respect to the ... More

Phase synchronization between collective rhythms of fully locked oscillator groupsApr 30 2014We study the phase synchronization between collective rhythms of fully locked oscillator groups. For weakly interacting groups of two oscillators with global sinusoidal coupling, we analytically derive the collective phase coupling function, which determines ... More

Gauge hierarchy problem, supersymmetry and fermionic symmetryNov 11 2013Sep 30 2015We reconsider the gauge hierarchy problem from the viewpoint of effective field theories and a high-energy physics, motivated by the alternative scenario that the standard model holds up to a high-energy scale such as the Planck scale. The problem is ... More

Tera Scale Remnants of Unification and Supersymmetry at Planck ScaleApr 30 2013May 06 2013We predict new particles at the Tera scale based on the assumptions that the standard model gauge interactions are unified around the gravitational scale with a big desert and new particles originate from hypermultiplets as remnants of supersymmetry, ... More

Search for a Realistic Orbifold Grand UnificationFeb 22 2008Feb 29 2008We review the prototype model of a grand unified theory on the orbifold $S^1/Z_2$ and discuss topics related to the choice of boundary conditions; the dynamical rearrangement of gauge symmetry and the equivalence classes of BCs. We explore a family unification ... More

Cubic Matrix, Nambu Mechanics and BeyondJul 06 2002Apr 18 2003We propose a generalization of cubic matrix mechanics by introducing a canonical triplet and study its relation to Nambu mechanics. The generalized cubic matrix mechanics we consider can be interpreted as a 'quantum' generalization of Nambu mechanics. ... More

Split Multiplets, Coupling Unification and Extra DimensionDec 28 2000We study a gauge coupling unification scenario based on a non-supersymmetric 5-dimensional model. Through an orbifold compactification, we obtain the Standard Model with split multiplets on a 4-dimensional wall, which is compatible with a grand unification. ... More

Limitation on Magnitude of $D$-componentsAug 31 2010Dec 24 2010We study the magnitude of $D$-components in a generic supersymmetric field theory. There exists $F$-component whose vacuum expectation value is comparable to or bigger than that of $D$-component, in the absence of Fayet-Iliopoulos term, the large hierarchy ... More

Electroweak Sudakov corrections at 2 loop levelFeb 14 2001In processes at the energy much higher than electroweak scale, weak boson mass act as the infrared cutoff in weak boson loops and resulting Sudakov log corrections can be as large as 10%. Since electroweak theory is off-diagonally broken gauge theory, ... More

Simulation Studies on the Stability of the Vortex-Glass OrderJul 23 1999Dec 03 1999The stability of the three-dimensional vortex-glass order in random type-II superconductors with point disorder is investigated by equilibrium Monte Carlo simulations based on a lattice XY model with a uniform field threading the system. It is found that ... More

Chirality scenario of the spin-glass orderingJul 24 2009Jun 19 2010Detailed account is given of the chirality scenario of experimental spin-glass transitions. In this scenario, the spin glass order of weakly anisotropic Heisenberg-like spin-glass magnets including canonical spin glasses are essentially chirality driven. ... More

An invariant of states on Cuntz algebrasOct 06 2016Oct 14 2016For an arbitrary state $\omega$ on a Cuntz algebra, we define a number $1\leq \kappa(\omega)\leq \infty$ such that if GNS representations by $\omega$ and $\omega'$ are unitarily equivalent, then $\kappa(\omega)=\kappa(\omega')$. By using $\kappa$, we ... More

C$^{*}$-bialgebra defined by the direct sum of Cuntz algebrasFeb 13 2007Mar 14 2007We show that a tensor product among representation of certain C$^{*}$-algebras induces a bialgebra. Let $\tilde{{\cal O}}_{*}$ be the smallest unitization of the direct sum of Cuntz algebras \[{\cal O}_{*}\equiv {\bf C}\oplus {\cal O}_{2}\oplus {\cal ... More

Pentagon equation arising from state equations of a C$^{*}$-bialgebraJun 14 2009The direct sum ${\cal O}_{*}$ of all Cuntz algebras has a non-cocommutative comultiplication $\Delta_{\varphi}$ such that there exists no antipode of any dense subbialgebra of the C$^{*}$-bialgebra $({\cal O}_{*},\Delta_{\varphi})$. From states equations ... More

Lipschitz Continuous Ordinary Differential Equations are Polynomial-Space CompleteApr 26 2010In answer to Ko's question raised in 1983, we show that an initial value problem given by a polynomial-time computable, Lipschitz continuous function can have a polynomial-space complete solution. The key insight is simple: the Lipschitz condition means ... More

Differential Recursion and Differentially Algebraic FunctionsApr 03 2007Moore introduced a class of real-valued "recursive" functions by analogy with Kleene's formulation of the standard recursive functions. While his concise definition inspired a new line of research on analog computation, it contains some technical inaccuracies. ... More

Z2-vortex order of frustrated Heisenberg antiferromagnets in two dimensionsFeb 17 2011We discuss the recent experimental data on various frustrated quasi-two-dimensional Heisenberg antiferromagnets from the viewpoint of the Z2-vortex order, which include S=3/2 triangular-lattice antiferromagnet NaCrO2, S=1 triangular-lattice antiferromagnet ... More

Successive transitions and intermediate chiral phase in a superfuilid ^3He filmDec 22 1998Superfluidity ordering of thin ^3He films is studied by Monte Carlo simulations based on a two-dimensional lattice spin model with Z_2\times U(1)\times SO(3) symmetry. Successive phase transitions with an intermediate `chiral' phase, in which the l-vector ... More

QCD Analysis of Twist-4 Contributions to the $g_1$ Structure FunctionsJun 03 1996We analyze the twist-4 contributions to Bjorken and Ellis-Jaffe sum rules for spin-dependent structure function $g_1(x, Q^2 )$. We investigate the anomalous dimensions of the twist-4 operators which determine the logarithmic correction to the $1/Q^2$ ... More

Two models of spin glasses -- Ising versus HeisenbergMar 18 2010Brief review is given on recent numerical research of the ordering of two typical models of spin glasses (SGs), the three-dimensional (3D) Ising SG and the 3D Heisenberg SG models. Particular attention is paid to the questions of whether there is a thermodynamic ... More

Spin and Chirality Orderings of Frustrated Magnets -- Stacked-Triangular Antiferromagnets and Spin GlassesNov 05 2001``Chirality'' is a multispin quantity representing the sense or the handedness of the noncollinear spin structures induced by spin frustration. Recent studies have revealed that the chirality often plays an important role in the ordering of certain frustrated ... More

Collective phase dynamics of globally coupled oscillators: Noise-induced anti-phase synchronizationDec 26 2013We formulate a theory for the collective phase description of globally coupled noisy limit-cycle oscillators exhibiting macroscopic rhythms. Collective phase equations describing such macroscopic rhythms are derived by means of a two-step phase reduction. ... More

Naturalness, Conformal Symmetry and DualityAug 23 2013Oct 21 2013We reconsider the naturalness from the viewpoint of effective field theories, motivated by the alternative scenario that the standard model holds until a high-energy scale such as the Planck scale. We propose a calculation scheme of radiative corrections ... More

Hole Structures in Nonlocally Coupled Noisy Phase OscillatorsAug 10 2007We demonstrate that a system of nonlocally coupled noisy phase oscillators can collectively exhibit a hole structure, which manifests itself in the spatial phase distribution of the oscillators. The phase model is described by a nonlinear Fokker-Planck ... More

Equivalence Classes in Gauge Theory on the Orbifold $S^1/Z_2$Sep 08 2004After a brief review of orbifold grand unified theory, we discuss two topics related to the choice of boundary conditions on the orbifold $S^1/Z_2$: dynamical rearrangement of gauge symmetry and equivalence classes of boundary conditions.

Generalized Heisenberg's DynamicsApr 06 2004We formulate a dynamical system based on many-index objects. These objects yield a generalization of the Heisenberg's equation. Systems describing harmonic oscillators are given.

Structure of Cubic Matrix MechanicsJun 20 2002Apr 18 2003We study the structure of cubic matrix mechanics based on three-index objects. It is shown that there exists a counterpart of canonical structure in classical mechanics.

On soft SUSY breaking parameters in string models with anomalous U(1) symmetrySep 10 1999We study the magnitudes of soft SUSY breaking parameters in heterotic string models with anomalous U(1) symmetry. In most cases, D-term contribution to soft scalar masses is expected to be comparable to or dominant over other contributions provided that ... More

Chasing after flavor symmetries of quarks from bottom upApr 02 2019We explore a flavor structure of quarks in the standard model under the assumption that flavor symmetries exist in a theory beyond the standard model, and chase after their properties, using a bottom-up approach. We reacknowledge that a flavor-symmetric ... More

$R$-matrices and the Yang-Baxter equation on GNS representations of C$^{*}$-bialgebrasJul 14 2009Jan 05 2012A new construction method of $R$-matrix is given. Let $A$ be a C$^{*}$-bialgebra with a comultiplication $\Delta$. For two states $\omega$ and $\psi$ of $A$ which satisfy certain conditions, we construct a unitary $R$-matrix $R(\omega,\psi)$ of the C$^{*}$-bialgebra ... More

C$^{*}$-bialgebra defined as the direct sum of UHF algebrasSep 14 2011Let ${\cal A}_{0}(*)$ denote the direct sum of a certain set of UHF algebras and let ${\cal A}(*)\equiv {\bf C}\oplus {\cal A}_{0}(*)$. We introduce a non-cocommutative comultiplication $\Delta_{\phi}$ on ${\cal A}(*)$, and give an example of comodule-C$^{*}$-algebra ... More

Non-cocommutative C$^{*}$-bialgebra defined as the direct sum of free group C$^{*}$-algebrasNov 28 2010Jul 24 2013Let ${\Bbb F}_{n}$ be the free group of rank $n$ and let $\bigoplus C^{*}({\Bbb F}_{n})$ denote the direct sum of full group C$^{*}$-algebras $C^{*}({\Bbb F}_{n})$ of ${\Bbb F}_{n}$ $(1\leq n<\infty$). We introduce a new comultiplication $\Delta_{\varphi}$ ... More

Inductive limit violates quasi-cocommutativityMar 19 2010We show that the inductive limit of a certain inductive system of quasi-cocommutative C$^{*}$-bialgebras is not quasi-cocommutative. This implies that the category of quasi-cocommutative C$^{*}$-bialgebras is not closed with respect to the inductive limit. ... More

A tensor product of representations of UHF algebras arising from Kronecker productsOct 08 2009We introduce a non-symmetric tensor product of representations of UHF algebras by using Kronecker products of matrices. We prove tensor product formulae of GNS representations by product states and show examples.