Showing papers in "Progress of Theoretical Physics in 1987"

Local and Grobal Self-Entrainments in Oscillator Lattices

Abstract: By computer simulations of an active rotator model, it is found that 1-, 2and 3-dimensional oscillator lattices with distributed natural frequencies exhibit peculiar clustering patterns due to local entrainment. A simple theory suggests that some of such self-entrained clusters mayor may not develop into macroscopic size depending on system dimension, and this fact consistently explains our numerically obtained order parameter curves.

Memory Dynamics in Asynchronous Neural Networks

Abstract: A model which can perform learning, formation of memory without teacher for successive memory recalls is presented. The philosophical background of the study is summarized. The investigated network consists of two sets both composed of asynchronously firing model neurons. One set of neurons is responsible for the field effect, and the other is introduced as an input/ output module. The field effect is given in the form of the system's self·response. It is shown that positive and negative global feedbacks by the field effect play an essential role in the successive recall of stored patterns. The possibility that these proposed mechanisms are implemented in the brain is discussed. We obtained a quasi-deterministic law on the level of a macrovariable concerning a random successive recall of memory representations by taking a Lorenz·plot of this macrovariable. We show that this macroscopic order is deterministic chaos steming from collapse of tori and this type of chaos can be an effective gadget for memory traces. § 1. General introduction -philosophical background of the study

Integrals of a Lotka-Volterra System of Odd Number of Variables

Abstract: On introduit un systeme de Lotka-Volterra a (s+1) quantites conservees et (2s+1) variables. Dans le systeme chaque espece interagit avec les 2s autres especes. On represente explicitement les quantites conservees

General Structure of Non-Equilibrium Thermo Field Dynamics

Abstract: Non-equilibrium thermo field dynamics (NETFD) is constructed in a compact form upon several basic requirements (axioms) without referring to the existence of the reservoir. The dissipation is involved in NETFD through the axioms, preserving most properties of the usual quantum field theory, e.g., the operator formalism, the time-ordered formulation of the Green’s functions, the Feynman diagram method in real time. NETFD with this general and compact form appear to be fundamental in physics.

Grain Formation through Nucleation Process in Astrophysical Environments. II: Nucleation and Grain Growth Accompanied by Chemical Reaction

Abstract: On formule le processus de nucleation homogene et de croissance de grains pour un mineral satisfaisant la relation stœchiometrique. Application a la condensation de mineraux refractaires dans un gaz refroidi de composition solaire. Discussion de formations de grains dans l'environnement astrophysique

Character Formula of C≪1 Unitary Representation of N=2 Superconformal Algebra

Abstract: The character formula of c≪1 unitary representation of N=2 superconformal algebra is obtained. As a corollary of our formula, we can easily express Waterson's bosonic construction of the algebra in character form.

Fragmentation of Isothermal Sheet-Like Clouds. II— Full Nonlinear Numerical Simulations —

Abstract: Calcul des processus de fragmentation d'un feuillet de gaz isotherme s'etendant indefiniment dans les directions x et y par une simulation numerique 3D afin d'analyser les effets non lineaires sur la croissance des perturbations

Statistical-Thermodynamics Formalism of Self-Similarity

Abstract: The self-similarity in dynamical and stochastic systems is formulated from a statistical­ thermodynamical standpoint. The global structures of the self-similarity are found to be determined by one generating function which plays a role similar to the Helmholtz free energy in the equilibrium statistical mechanics. The interrelations among fractal measure theories developed for, e.g., general­ ized fractal dimensions of strange sets and velocity structure functions in turbulence are clarified from a unified point of view.

Quantization of Conductivity Induced by Topological Structure of Energy-Momentum Space in Generalized QED3

Abstract: On etudie une structure topologique d'application definie par un propagateur dans l'espace energie-impulsion de l'electrodynamique quantique generalisee a 3 dimensions. En utilisant une identite de Ward-Takahashi on relie un tenseur de conductibilite a un invariant topologique

Mass and Spin of Exact Solutions of the Poincaré Gauge Theory

Abstract: Recently, in the framework of the Poincare gauge theory (PGT), I) the question of the total energy and spin of an isolated system has been discussed in some detail, assuming that the spacetime around the system is asymptotically flat. 2 ) In the present paper we would like to relax the assumption of asymptotic flatness, and asymptotical· ly only require a spacetime of constant curvature, because exact solutions of the PGT typically approach a de Sitter space for increasing radial coordinate r.3) The underlying spacetime of the PGT is a Riemann-Cartan spacetime with torsion and curvatures:

Solitons in Interaction

Abstract: Several new nonlinear systems are given which are completely integrable. These systems can be considered as flows describing the self-interaction of single solitons in multisoliton fields. The construction of action variables, recursion operators, bi-hamiltonian formulation and the like is performed for these nonlinear systems. Furthermore virtual solitons are introduced and it is shown that 2-solitons in general may be understood as the superposition of two pairs of interacting solitons exchanging one virtual soliton and that the interacting soliton itself can be considered as the result of a collision of a wave with a virtual soliton. In a sense, virtual solitons only pop up during the time that solitons interact with each other. In case of the KdV the details of decomposition into interact­ ing and virtual sQlitons are plotted, and a qualitative analysis of interaction is given. A brief discussion is appended, how to describe multisolitons by their "trajectories".

Relaxation Mode Theory of Hopping Conduction

Abstract: Non-local theory of hopping conduction of classical particles is developed on the basis of the perturbation theory, to obtain the conductivity formula which is expressed in terms of the dynamical correlation function. The relaxation mode theory is utilized to evaluate this conductivity formula in a one-dimensional double-well lattice and to apply it to the ultrasonic attenuation. It turns out that the Hutson-White type of ultrasonic attenuation formula, confirmed to be valid in semiconductors, holds even in the hopping conduction system

Ordering Dynamics of a Deeply Quenched Complex Field

Abstract: A statistical theory is presented for the ordering dynamics of a system with a complex order parameter quenched below the critical temperature. On the basis of a picture that string·like defects are formed in the early stage of the ordering process, the disappearing process of the defects is studied. We obtain the time evolution of the defect density and its two-point correlation function, which exhibits a scaling behavior, if the strings are initially convoluted and percolated. We also calculate the correlation function of the gradient of phase of the order parameter corresponding to the superfiuid velocity in 'He. The characteristic length in this system is found to behave as t1/ •

Theory of diffusion and intermittency in chaotic systems. III: New approach to temporal correlations

Abstract: On presente une approche de mecanique statistique de la correlation temporelle dans les series temporelles a une dimension engendrees par une dynamique chaotique

On Partial Dimensions and Spectra of Singularities of Strange Attractors

Abstract: New relations of thegenerClIized dimensions and entropies of strange attractors to the·fluctua· tions of divergence rates of nearby orbits and to the eigenvalues of the Jacobian matrices of unstable periodic points are obtained in order to derive the spectra of singularities from the dynamical viewpoints. A strange attractor often has a multifractal structure. The probability measure on such an attractor is highly concentrated in some regions and very rarefied in other regions. Repeated magnifications of a small piece of each region lead to a hierarchy of similar structures. Such a complicated structure of the probability measure can be described by the spectrum of scaling indices j(a),!) which can be obtained as follows. Cover the attractor with boxes and estimate the partition function r(q, r)=~i(Piq Il/), where li and Pi are the size and the probability of the ith box, respectively. As max(tJ~O, r goes to infinity for r>r(q) and to zero for r< r(q). This defines r(q) which are related to the generalized dimensions D(q) by r(q)=(q-1)D(q).2) The Legendre transformation of r(q),

Fermi Liquid Theory on the Basis of Periodic Anderson Hamiltonian with Orbital Degeneracy

Abstract: --~ The Fermi liquid theory on the basis of the periodic Anderson Hamiltonian is extended to the case with orbital degeneracy. The general expressions for T-linear term of specific heat, spin and orbital susceptibilities and T2-term of resistivity are derived. These results confirm that the general relations derived for the single orbital case hold also in the degenerate case, though they are given in matrix forms. For example, the T2-term of resistivity is proportional to the square of the mass enhancement factor, when the Coulomb repulsion is large enough to suppress the charge fluctuation of f-electrons. Moreover, it is shown that f-orbital degeneracy suppresses the magnetic instability and the Fermi liquid theory can be applied to a larger value of U compared with the single orbital case.

Fractal Configurations of the Two- and Three-Dimensional Ising Models at the Critical Point

Abstract: The fractal structure of the Ising model at the critical point Tc is studied in the present paper. The fractal dimensionality D of the total magnetization at Tc was estimated numerically as D = 1.86 ±O.Ol for the two-dimensional square lattice and D=2.46±O.Ol for the three-dimensional simple cubic lattice by Monte Carlo simulations. These values agree very well with the value D=1.875 obtained from the exact critical exponents and D=2.48 obtained from the known critical exponents, re­ ~pectively, through the relation D=d-fJ/v=(d+r/v)/2. This fractalness yields the hyperscaling relation dv=2fJ+r. It was also observed how the fractal nature of the relevant system disappears as the system deviates from the critical point. The dimensionality d of the relevant lattice is observed at temperatures lower than Tc and the random percolation value d/2 at higher temperatures.