Tetsuji Tokihiro

We investigate the link between a periodic box-ball system (PBBS) and a solvable lattice model. Introducing a PBBS with an integer parameter corresponding to the dimensionality of the auxiliary space for the lattice model, we prove an important relationship between the conserved quantities of states of the PBBS and eigenvectors constructed through the string hypothesis. (c) 2006 American Institute of Physics.

In recent works, we have proposed a stochastic cellular automaton model of traffic flow connecting two exactly solvable stochastic processes, i.e., the asymmetric simple exclusion process and the zero range process, with an additional parameter. It is also regarded as an extended version of the optimal velocity model, and moreover it shows particularly notable properties. In this paper, we report that when taking optimal velocity function to be a step function, all of the flux-density graph (i.e. the fundamental diagram) can be estimated. We first find that the fundamental diagram consists of two line segments resembling an inversed-lambda form, and next identify their end-points from a microscopic behaviour of vehicles. It is notable that by using a microscopic parameter which indicates a driver's sensitivity to the traffic situation, we give an explicit formula for the critical point at which a traffic jam phase arises. We also compare these analytical results with those of the optimal velocity model, and point out the crucial differences between them.

In the present paper, we investigate the asymmetric simple exclusion process with parallel dynamics on a ring of finite sites. We focus on the correspondence between the asymmetric exclusion process and the zero-range process, and exploit the recursion formula for the partition function of the zero-range process. Then, we find that the explicit formulas for the partition function and the average velocity (or the flux) in the steady state are expressed by the Gauss hypergeometric functions.

In recent studies on traffic flow, cellular automata (CA) have been efficiently applied for simulating the motion of vehicles. Since each vehicle has an exclusion volume and moves by itself not being ruled by the Newton's laws of motion, CA is quite suitable for modelling traffic flow. In the present paper, we propose a stochastic CA model for traffic flow and show the availability of CA modelling for the complex phenomena that occur in real traffic flow.

We review the novel properties of the fundamental cycle of periodic Box-Ball systems (PBBSs). According to integrable nature of the PBBS, the explicit formula for the fundamental cycle exists and its asymptotic behaviour can be estimated when the system size N goes to infinity. The upper and lower bounds for the maximum fundamental cycle is given and almost all fundamental cycle is shown to be of order of N-log N.

In this paper, we propose a stochastic cellular automaton model of traffic flow extending two exactly solvable stochastic models, i.e., the asymmetric simple exclusion process and the zero range process. Moreover, it is regarded as a stochastic extension of the optimal velocity model. In the fundamental diagram (flux-density diagram), our model exhibits several regions of density where more than one stable state coexists at the same density in spite of the stochastic nature of its dynamical rule. Moreover, we observe that two long-lived metastable states appear for a transitional period, and that the dynamical phase transition from a metastable state to another metastable/stable state occurs sharply and spontaneously.

A number theoretical aspect of the fundamental cycle of a periodic box-ball system is investigated. Using the formulae for the fundamental cycle of a class of initial states, we point out that the asymptotic behaviour of the fundamental cycle is closely related to the celebrated Riemann hypothesis.

We investigate conserved quantities of periodic box-ball systems (PBBS) with arbitrary kinds of balls and box capacity greater than or equal to 1. We introduce the notion of nonintersecting paths on the two dimensional array of boxes, and give a combinatorial formula for the conserved quantities of the generalized PBBS using these paths. (C) 2005 American Institute of Physics.

We propose a method of constructing differential equations directly from cellular automata. Any elementary cellular automata (ECAs) introduced by Wolfram can be transformed into a partial differential equation (PDE) which preserves the time evolution patterns of the ECAs. In particular, some PDEs constructed by the method reproduce complex fractal and self-organizing patterns found in their corresponding ECAs. It is expected that the method can be extended for general cellular automata with more complex rules and/or in higher dimensions.

We investigate periodic box-ball systems (PBBSs) with several kinds of balls and box capacity greater than or equal to one. Conserved quantities of the PBBSs are constructed from those of the nonautonomous discrete KP (ndKP) equation using the Lax representation of the ndKP equation.

Ultradiscretization is a limiting procedure which allows one to obtain a cellular automaton (CA) from continuous equations. Using this method, we can construct integrable CAs from integrable partial difference equations. In this course, we focus on a typical integrable CA, called a Box and Ball system (BBS), and review its peculiar features. Since a BBS is an ultradiscrete limit of the discrete KP equation and discrete Toda equation, we can obtain explicit solutions and conserved quantities for the BBS. Furthermore the BBS is also regarded as a limit (crystallization) of an integrable lattice model. Recent topics, and a periodic BBS in particular are also reviewed.

We investigate asymptotic behaviour of fundamental cycle of periodic box-ball systems (PBBSs) when the system size N goes to infinity. According to integrable nature of the PBBS, the trajectory is confined to qualitatively smaller number of states than that of the total states. We prove that, although the maximum fundamental cycle is of order of exp[rootN], almost all fundamental cycle is less than exp[(Iog N)(2)].

We investigate a box-ball system with periodic boundary conditions. Since the box-ball system is a deterministic dynamical system that takes only a finite number of states, it will exhibit periodic motion. We determine its fundamental cycle for a given initial state.

An initial-value problem of the periodic discrete Toda equation is solved by the inverse scattering method. Using this result, we demonstrate a method for solving an initial-value problem of a periodic box-ball system which is one of the typical soliton cellular automata. In the method, ultradiscretization and its inverse process play an essential role. The explicit solution to. the case of genus one is also presented.

Recursive polynomial expansion method is an efficient scheme to evaluate Green functions for large systems without direct diagonalization of the Hamiltonian. It is based on a polynomial expansion of the Green function, and has many advantages compared with other methods. However, there are little reports on its error estimations. In this paper, the cut-off error of the method is estimated analytically, which results from the truncation of expansion at finite orders. It is found that the error is inversely proportional to the number of expansion order N except for the singular points for the system with point spectrum. For the system with continuous spectrum, the error is inversely proportional to N-3/2 and decreases much faster in terms of the expansion order. (C) 2002 Elsevier Science B.V. All rights reserved.

We study the discrete transformations that are associated with the auto-Backlund of the (continuous) P-V equation. We show that several two-parameter discrete Painleve equations can be obtained as contiguity relations of P-V. Among them we find the asymmetric d-P-II equation which is a well-known form of discrete P-III. The relation between the ternary P-I (previously obtained through the discrete dressing approach) and P-V is also established. A new discrete Painleve equation is also derived.

We propose a box and ball system with a periodic boundary condition periodic box and ball system (pBBS). The time evolution rule of the pBBS is represented as a Boolean recurrence formula, an inverse ultradiscretization of which is shown to be equivalent to the algorithm of the calculus for the 2Nth root. The relations to the pBBS of the combinatorial R matrix of U-q' (A(N)((1))) are also discussed.

It is proved that almost all energy eigenstates of a certain isolated system have the following property: quantum expectation values of all local observables are equal to these statistical expectation values. Temperature is uniquely determined by energy density. (C) 2001 Elsevier Science B.V. All rights reserved.

Conserved quantities of box and ball system(BBS) are presented from the hungry Toda molecule equation, an inverse ultra-discrete limit of the BBS.

We construct a difference equation which preserves any time evolution pattern of the rule 90 elementary cellular automaton. We also demonstrate that such difference equations can be obtained for any elementary cellular automata.

We propose a general method to construct a partial difference equation which preserves any time evolution patterns of a cellular automaton. The method is based on inverse ultradiscretization with filter functions.

A soliton cellular automaton associated with crystals of symmetric tensor representations of the quantum affine algebra U-q'(A(M)((1))) is introduced. It is a crystal theoretic formulation of the generalized box-ball system in which capacities of boxes and carriers are arbitrary and inhomogeneous. Scattering matrices of two solitons coincide with the combinatorial R matrices of U-q'(A(M-1)((1))). A piecewise linear evolution equation of the automaton is identified with an ultradiscrete limit of the nonautonomous discrete Kadomtsev-Petviashivili equation. A class of N soliton solutions is obtained through the ultradiscretization of soliton solutions of the latter. (C) 2001 American Institute of Physics.

Cellular automate, which are realized by dynamics of several kinds of balls in an infinite array of boxes, are investigated. They show soliton patterns even in the case when each box has arbitrary capacity. The analytical expression for the soliton patterns are obtained using ultradiscretization of the nonautonomous discrete KP equation.

It is explained how a description of integrable systems using fermion operators leads in a natural way to the notions of Darboux and binary Darboux transformations. This approach is illustrated for a nonautonomous version of the discrete KP (dKP) equation. As an application of this technique, solutions - some of which are expressed in terms of special functions - are discussed. The ultra-discrete limit is then performed to obtain a nonautonomous ultra-discrete system with particularly interesting soliton behaviour. (C) 1999 Elsevier Science Ltd. All rights reserved.

A soliton cellular automaton, which represents movement of a finite number of balls in an array of boxes, is investigated. Its dynamics is described by an ultra-discrete equation obtained from an extended Toda molecule equation. The rules for soliton interactions and factorization property of the scattering matrices (Yang-Baxter relation) are proved by means of inverse ultra-discretization. The conserved quantities are also presented and used for another proof of the solitonical nature.

Squeezed states of light are theoretically investigated in a system with a locally placed two-photon absorption medium. We assume that the two-photon absorption process is caused by elementary excitations in the medium (such as biexcitons). Many eigenmodes of photons and those of the elementary excitations are taken into account because of the locality of the absorber. Multi-mode Wigner functions are defined and used for representation of the density operator of the electromagnetic field. The Wigner functions exhibit multi-variable Gaussian distribution and the quantum states of photons are multi-mode quadrature squeezed states. We also discuss effects on squeezing due to detuning of the incident light, the size of the medium, the position of a photo-detector, and damping rates of photons and the elementary excitations.

A direct connection between a soliton cellular automaton (SCA) and an ultra-discrete analogue of the Toda molecule equation (uTM equation) is clarified. A solution to the SCA is presented by means of that to the uTM equation. A sorting algorithm based on this connection is also constructed. (C) 1999 Elsevier Science B.V. All rights reserved.

The (charged) free fermion formulation of the N-component KP hierarchies is used for the description of quadrilateral lattices in terms of multicomponent KP eigenfunction potentials. Tan functions for these hierarchies are explicitly calculated, giving rise to Grammian and Casorati determinant solutions to the (discretized) Darboux or Laplace equations describing the lattices. An example of localized tau functions and eigenfunction potentials is given. (C) 1999 Published by Elsevier Science B.V.

The static strength of a quasi-isotropically reinforced random chopped glass/polypropylene composite is studied theoretically and experimentally. In the previous paper((1)), a fracture model is proposed which simulates probabilistically the damage accumulation process On the basis of the percolation theory, the model can estimate the static strength of the FRPP as the critical point on condition that the fiber volume fraction is 30%wt. In this paper, by applying the model, the strengths of a discontinuous fiber composite are predicted as a function of the volume fraction of glass fiber. By comparing with the experimental data, the validity of the model is confirmed in terms of the fiber volume fraction.

One of the well-known convergence acceleration methods, the epsilon-algorithm is investigated from the viewpoint of the Toda molecule equation. It is shown that the error caused by the algorithm is evaluated by means of solutions for the equation. The acceleration algorithm based on the discrete Toda molecule equation is also presented.

A one-dimensional Frenkel excitonic chain confined in a two-dimensional microcavity is described by the spin-1/2 Haldane-Shastry model with anisotropy. Dispersion relations, long-range string states, and nonlinear optical properties are discussed. [S0163-1829(98)02524-7].

An ultra-discrete version of the Toda molecule equation is presented. The solution and conserved quantities for the equation are also discussed. (C) 1998 Elsevier Science B.V.

Starting from the free fermion description of the one-component KP hierarchy, we establish a connection between this approach and the theory of Darboux and binary Darboux transformations. Certain difference identities-allowing for the treatment of both continuous as well as discrete evolution equations-turn out to be crucial: first to show that any solution of the associated (adjoint) linear problems can always be expressed as a superposition of KP (adjoint) wavefunctions and then to interpret Darboux (and binary Darboux) transformations as Backlund transformations in the fermion language.

A method for constructing special function solutions of nonlinear integrable equations is given. It is based on Darboux transformations and the integral representation of special functions. Some explicit examples including the q-hypergeometric function are presented. (C) 1997 Published by Elsevier Science B.V.

It is shown how Darboux and binary Darboux transformations for a nonautonomous discrete KP equation can be obtained from fermion analysis. This equation is obtained by considering a generalized Miwa transformation; it is also shown to be linked to the discrete KP equation by a special gauge transformation. The Darboux and binary Darboux transformations are used to discuss general classes of solutions in the form of Casorati- and Gramm-type determinants. N-soliton solutions are discussed as well. (C) 1997 American Institute of Physics.

We investigate the nature of particular solutions to the ultradiscrete Painleve equations. We start by analysing the autonomous limit and show that the equations possess an explicit invariant which leads naturally to the ultradiscrete analogue of elliptic functions. For the ultradiscrete Painleve equations II and III we present special solutions reminiscent of the Casorati determinant ones which exist in the continuous and discrete cases. Finally we analyse the discrete Painleve equation I and show tow it contains both the continuous and the ultradiscrete ones as particular limits.

A deautonomized version of the two-dimensional Toda lattice equation is presented. Its ultra-discrete analogue and soliton solutions are also discussed. (C) 1997 Published by Elsevier Science B.V.

In this paper, a lattice deformation model for the Hofstadter system is proposed to study the effects of lattice deformation on an electronic system coupled with a magnetic field. Uniform lattice deformation necessarily occurs in this model so that it causes the flux in a plaquette lock in to a rational value in a unit of a flux quantum. Then the Hall conductance, which is always integer times e(2)/(h) over bar, is also locked. In addition to the uniform lattice deformation, the Peierls instability induces nonuniform lattice deformation at some electron density. The conditions for the occurrence of nonuniform lattice deformation are also given in terms of elastic constants, electron density, and the applied magnetic field.

We show that the cellular automaton proposed by two of the authors (D.T. and J.M.) is obtained from the discrete Toda lattice equation through a special limiting procedure. Also by applying a similar kind of limiting procedure to the N-soliton solution of the discrete Toda lattice equation, we obtain the N-soliton solution for this cellular automaton.

In the previous paper we demonstrated novel multiexcitons in a neutral mixed-stack charge-transfer solid. The lowest multiexciton, the biexciton, has recently been of interest also in the context of quasi-one-dimensional organic materials that are different from the mixed-stack solids. The nature and strength of the optical transition from the exciton to the two-exciton states is of importance in understanding photoinduced absorption as well as two-photon absorption. We show that within the diverse theoretical models that describe these different classes of materials, the excited state absorption from the optical exciton to the two-exciton states changes in a fundamental way upon the formation of the biexciton. The identical nature of the exciton absorption within these models is a consequence of one dimensionality. (C) 1996 American Institute of Physics.

Optical excitation in a strongly neutral quasi-one-dimensional mixed-stack charge-transfer solid results in an exciton state, in which the electron and the hole are bound by electrostatic Coulomb interactions that are large, compared to the one-electron hopping. We present a joint theoretical-experimental demonstration of a new class of collective excitations, multiexcitons or exciton strings, consisting of a string of several (more than two) bound excitons, in a prototype neutral charge-transfer solid. The stability of the multiexciton states arise from the combined effects of one dimensionality and strong Coulomb interactions. Theoretically, we show that in narrow band one-dimensional semiconductors with long range Coulomb interactions, the occurrence of stable 2-exciton string (biexciton) necessarily implies stable higher multiexcitons. Experimentally, evidence for the multiexciton strings is demonstrated by femtosecond pump-probe spectroscopy of anthracene pyromellitic acid dianhydride. Excellent qualitative agreement is found between the calculated and the measured differential transmission spectra. Photoinduced absorptions to the 2-exciton string at low pump intensity and to the 3-exciton string at high pump intensity are observed, in agreement with the theory of excited state absorption. The 2-exciton string is confirmed also by a direct two-photon absorption measurement. The binding energies of the 2-exciton and the 3-exciton strings are obtained from the experimental data. The larger binding energy of the 3-exciton is in agreement with theory. (C) 1996 American Institute of Physics.

We show a direct connection between a cellular automaton and integrable nonlinear wave equations. We also present the N-soliton formula for the cellular automaton. Finally, we propose a general method for constructing such integrable cellular automata and their N-soliton solutions.

We develop a real-space method for exciton polaritons in a bounded medium with a tight-binding approximation. The creation and annihilation operators for photons are approximately constructed in a real-space representation. The quantum-mechanical derivation gives all necessary boundary conditions and complete solutions to the problem of reflection and transmission near the resonance of excitons. The present theory without the long-wavelength approximation covers the whole range of system size. In addition we calculate transient responses for short-pulse excitation. The results deeply reflect the spatial dispersion of exciton polaritons.

A quasiperiodic grating induces new surface plasmon modes and peculiar light emission. The energy spectrum of the plasmon mode is equivalent to that of a quasiperiodic electronic system with long range electron transfer. The angle-resolved emission spectra from tunnel junction show sharp peaks according to the quasiperiodicity.

Conformational disorder in a molecular chain leads to randomness of orientation of transition dipole moments which simultaneously induces randomness of exciton transfer. The optical absorption spectrum is sensitive to both of randomness and represents their correlation effect. The drastic change of the spectral profile near the critical point of helix-coil phase transition is also demonstrated.

The bound states of n Frenkel excitons (n = 2, 3,...), which are called excitonic n-strings, are theoretically shown to exist in contrast to a system of Wannier excitons. The electronic structure and nonlinear optical responses of these excitonic n-strings are clarified.

The theoretical calculation of the emission spectra of highly excited one-dimensional Frenkel exciton systems shows intensity dependent frequency shifts and system-size dependent fine structure. The system-size dependence of the emission intensity reflects the critical exponent of the equivalent quantum spin system.