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Hajime Tanaka

Publications and source records attributed to Hajime Tanaka.

106 records · Page 6Linked to original sources
arXiv2008

Commutative association schemes

Association schemes were originally introduced by Bose and his co-workers in the design of statistical experiments. Since that point of inception, the concept has proved useful in the study of group actions, in algebraic graph theory, in algebraic coding theory, and in areas as far afield as knot theory and numerical integration. This branch of the theory, viewed in this collection of surveys as the "commutative case," has seen significant activity in the last few decades. The goal of the present survey is to discuss the most important new developments in several directions, including Gelfand pairs, cometric association schemes, Delsarte Theory, spin models and the semidefinite programming technique. The narrative follows a thread through this list of topics, this being the contrast between combinatorial symmetry and group-theoretic symmetry, culminating in Schrijver's SDP bound for binary codes (based on group actions) and its connection to the Terwilliger algebra (based on combinatorial symmetry). We propose this new role of the Terwilliger algebra in Delsarte Theory as a central topic for future work.

math.CO↗
arXiv2008

Multiple nonergodic disordered states in Laponite suspensions: a phase diagram

We study the time evolution of different Laponite suspensions from a low-viscosity ergodic state to a viscoelastic non-ergodic state over a wide range of volume fractions and salt contents. We find that the evolution of non-ergodicity parameter (Debye-Waller factor) splits into two branches for all the samples, which correspond to two distinct dynamically arrested states. At moderately high salt concentrations, on the other hand, a third and new nonergodic state appears that are different from the above two nonergodic states. Measurement of the conductivity of Laponite solutions in pure water shows that the contribution of counterions in the ionic strength is considerable and their role should be taken into account in interpretations of aging dynamics and the phase diagram. Based on these data and available data in the literature, we propose a new (non-equilibrium) phase diagram for Laponite suspensions.

cond-mat.soft↗
arXiv2008

Direct observation of hydrodynamic instabilities in driven non-uniform colloidal dispersions

A Rayleigh-Taylor-like instability of a dense colloidal layer under gravity in a capillary of microfluidic dimensions is considered. We access all relevant lengthscales with particle-level microscopy and computer simulations which incorporate long-range hydrodynamic interactions between the particles. By tuning the gravitational driving force, we reveal a mechanism whose growth is connected to the fluctuations of specific wavelengths, non-linear pattern formation and subsequent diffusion-dominated relaxation. Our linear stability theory captures the initial regime and thus predicts mixing conditions, with important implications for fields ranging from biology to nanotechnology.

cond-mat.soft↗
arXiv2008

Group-case commutative association schemes and their character tables

Leading towards the classification of primitive commutative association schemes as the ultimate goal, Bannai and some of his school have been trying to * identify the major sources of (primitive) commutative association schemes, * collect known group-case primitive commutative association schemes, and * compute their character tables over the last twenty years. The construction of their character tables are important first step for a systematic study of such association schemes and towards the classification of those schemes. In this talk, we briefly survey the progress made in this direction of research, and list some open problems.

math.CO↗
arXiv2006

Comments on "Best conventional solutions to the King's problem"

Conventional solutions to the (Mean) King's problem without using entanglement have been investigated by Aravind [P. K. Aravind, ``Best conventional solutions to the King's problem'', Z. Naturforsch. 58a, 682 (2003)]. We report that the upper bound for the success probability claimed there is not valid in general, and give a condition for the claim to be justified.

quant-ph↗
arXiv2006

Solution to the Mean King's problem with mutually unbiased bases for arbitrary levels

The Mean King's problem with mutually unbiased bases is reconsidered for arbitrary d-level systems. Hayashi, Horibe and Hashimoto [Phys. Rev. A 71, 052331 (2005)] related the problem to the existence of a maximal set of d-1 mutually orthogonal Latin squares, in their restricted setting that allows only measurements of projection-valued measures. However, we then cannot find a solution to the problem when e.g., d=6 or d=10. In contrast to their result, we show that the King's problem always has a solution for arbitrary levels if we also allow positive operator-valued measures. In constructing the solution, we use orthogonal arrays in combinatorial design theory.

quant-ph↗
arXiv2001

Physical Origin of the Boson Peak Deduced from a Two-Order-Parameter Model of Liquid

We propose that the boson peak originates from the (quasi-) localized vibrational modes associated with long-lived locally favored structures, which are intrinsic to a liquid state and are randomly distributed in a sea of normal-liquid structures. This tells us that the number density of locally favored structures is an important physical factor determining the intensity of the boson peak. In our two-order-parameter model of the liquid-glass transition, the locally favored structures act as impurities disturbing crystallization and thus lead to vitrification. This naturally explains the dependence of the intensity of the boson peak on temperature, pressure, and fragility, and also the close correlation between the boson peak and the first sharp diffraction peak (or prepeak).

cond-mat.mtrl-sci↗
arXiv1998

Universal Seesaw Mechanism with Universal Strength for Yukawa Couplings

Hypotheses of the universal seesaw mechanism and the {\it universal strength for Yukawa couplings} are applied to explain one possible origin of quasi-democratic mass matrices of a special type in a left-right symmetric model with the gauge group $SU(3)_c\times SU(2)_L\times SU(2)_R\times U(1)$. Two kinds of Higgs doublets are postulated to mediate scalar interactions between the $i$-th generation of light fermion doublets and the $j$-th generation of heavy fermion singlets with relative Yukawa coupling constants of the exponential form $e^{iϕ_{ij}}$, where $ϕ_{ij}$ are real phase constants. The lowest seesaw approximation results effectively in self-adjoint mass matrices which are quasi-democratic and have the same diagonal elements. A set of values for the parameters $ϕ_{ij}$ is found which reproduces the present experimental data for the absolute values of the CKM matrix elements, the Jarlskog parameter and the Wolfenstein parameters.

hep-ph↗
arXiv1998

A simple physical model of liquid-glass transition: intrinsic fluctuating interactions and random fields hidden in glass-forming liquids

We propose that glass-forming liquids are intrinsically under the influences of both fluctuating interactions and random fields well-known in the field of spin systems. This is due to the frustration between the isotropic and anisotropic parts of effective intermolecular interactions. Our model indicates the existence of two key temperatures relevant to glass transition, the density ordering point T^*_m and the Vogel-Fulcher temperature T_0. Between T^*_m and T_0, a system has features similar to the `Griffiths phase', while below $T_0$ it has those peculiar to the `spin-glass phase'. This picture naturally and universally explains vitrification behavior from its strong to fragile limit.

cond-mat.dis-nn↗
arXiv1997

New mechanisms of droplet coarsening in phase-separating fluid mixtures

We propose here a new mechanism of droplet coarsening in phase-separating fluid mixtures. In contrast to the conventional understanding that there are no interactions between droplets in the late stage of spinodal decomposition, we demonstrate the existence of interactions between droplets that is caused by the coupling between diffuse concentration change around droplets. We show the possibility that this mechanism plays an important role in droplet phase separation together with Brownian-coagulation mechanism. We also discuss the coupling between hydrodynamic and diffusion modes, namely, "collision-induced collision" phenomena.

cond-mat.soft↗
arXiv1997

A Viscoelastic model of phase separation

We show here a general model of phase separation in isotropic condensed matter, namely, a viscoelastic model. We propose that the bulk mechanical relaxation modulus that has so far been ignored in previous theories plays an important role in viscoelastic phase separation in addition to the shear relaxation modulus. In polymer solutions, for example, attractive interactions between polymers under a poor-solvent condition likely cause the transient gellike behavior, which makes both bulk and shear modes active. Although such attractive interactions between molecules of the same component exist universally in the two-phase region of a mixture, the stress arising from attractive interactions is asymmetrically divided between the components only in dynamically asymmetric mixtures such as polymer solutions and colloidal suspensions. Thus, the interaction network between the slower components, which can store the elastic energy against its deformation through bulk and shear moduli, is formed. It is the bulk relaxation modulus associated with this interaction network that is primarily responsible for the appearance of the sponge structure peculiar to viscoelastic phase separation and the phase inversion. We demonstrate that a viscoelastic model of phase separation including this new effect is a general model that can describe all types of isotropic phase separation including solid and fluid models as its special cases without any exception, if there is no coupling with additional order parameter. The physical origin of volume shrinking behavior during viscoelastic phase separation and the universality of the resulting spongelike structure are also discussed.

cond-mat.soft↗
arXiv1997

Two-Order-Parameter Description of Liquids: Critical Phenomena and Phase Separation of Supercooled Liquids

Because of the isotropic and disordered nature of liquids, the anisotropy hidden in intermolecular interactions are often neglected. Accordingly, the order parameter describing a simple liquid has so far been believed to be only density. In contrast to this common sense, we propose that two order parameters, namely, density and bond order parameters, are required to describe the phase behavior of liquids since they intrinsically tend to form local bonds. This model gives us clear physical explanations for two poorly-understood phenomena in supercooled liquids: (i) large-scale density fluctuations and (ii) phase separation of a one-component liquid into two liquid phases.

cond-mat.soft↗
arXiv1996

Renormalization Group Effects on the Mass Relation Predicted by the Standard Model with Generalized Covariant Derivatives

Renormalization group analysis is made on the relation $m_{\rm H} \simeq \sqrt{2}m_t$ for masses of the top quark and the Higgs boson, which is predicted by the standard model based on generalized covariant derivatives with gauge and Higgs fields. This relation is a low energy manifestation of a tree level constraint which holds among the quartic Higgs self-coupling constant and the Yukawa coupling constants at a certain high energy scale $μ_0$. With the renormalization group equation at one-loop level, the evolution of the constraint is calculated from $μ_0$ down to the low energy region around the observed top quark mass. The result of analysis shows that the Higgs boson mass is in $m_t \lesssim m_{\rm H} \lesssim \sqrt{2}m_t$ for a wide range of the energy scale $μ_0 \gtrsim m_t$ and it approaches to 177 GeV ($\approx m_t$) for large values of $μ_0$.

hep-ph↗