Showing papers in "Progress of Theoretical Physics in 1983"

Stability Theory of Synchronized Motion in Coupled-Oscillator Systems

Abstract: The general stability theory of the synchronized motions of the coupled· oscillator systems is developed with the use of the extended Lyapunov matrix approach. We give the explicit formula for a stability parameter of the synchronized state W unlfWhen the coupling strength is weakened, the coupled system may exhibit several types of non· synchronized motion. In particular, if W Unlf is chaotic, we always get a transition from chaotic Wunlf to a certain non· uniform state and finally the non·uniform chaos. Details associated with such transition are investigated for the coupled Lorenz model. As an application of the theory, we propose a new experimental method to directly measure the positive Lyapunov exponent of intrinsic chaos in reaction systems.

Grand Unified Theories Based on Local Supersymmetry

Abstract: General features are discussed of grand unified theories with local supersymmetry broken at high energies by the super-Higgs effect. The low-energy effective Lagrangian is a globally supersymmetric one with all the explicit soft breakings. It is argued that the energy splittings among the vacua due to gravitational effects must be small in order to be able to pick out the correct vacuum. Also discussed are the mechanisms of breaking SU(2) by the gravitational effects and of suppressing monopole production in the early universe.

Statistical Dynamics Generated by Fluctuations of Local Lyapunov Exponents

Abstract: Fluctuation-effect of local Lyapunov exponents on the distance between two nearby trajectories is studied from a statistical-mechanical point of view. It is shown that fluctuations of the logarithmic distance between two nearby trajectories are asymptotically described as the diffusion process, if the system is chaotic, obeying the normal distribution. The diffusion coefficient is proved to be invariant under conjugation. Onset behaviors of the diffusion near two typical transition points (the accumulation point of the Feigenbaum bifurcations and the Pomeau-Manneville intermittency transition) are briefly discussed.

Lagrangian Mechanics of Massless Particles With Spin

Abstract: On etudie la mecanique lagrangienne des particules sans masse a spin, basee sur l'interpretation que le spin correspond au deplacement dans des directions complexes

Fermi Liquid Theory of Dilute Submonolayer 3He on Thin 4He II Film Dimer Bound State and Cooper Pairs

Abstract: Discussion de l'apparition possible de la superfluidite dans un systeme de fermi dilue degenere, avec un etat lie dimere

Gravitational instabilities in a dust-gas layer and formation of planetesimals in the solar nebula

Abstract: Dust particles which are initially distributed homogeneously in the solar nebula aggregate and settle towards the equatorial plane. As a result, the solar nebula separate into three layers: an equatorial thin dust-gas layer and two residual gas layers. We study gravitational in­ stabilities in the dust-gas layer on the assumption of axial symmetry, taking account of motions perpendicular to as well as parallel to the equatorial plane and also making use of proper boundary conditions between the dust-gas layer and the gas layers. As far as radii of dust particles are sufficiently small (:S 1 cm at 1 au), a dust fluid and a gas fluid are firmly coupled owing to the drag force; consequently, they behave like one fluid. It is also found that the dust-gas layer behaves like an incompressible fluid owing to high pressure of the gas layers exerted on the dust-gas layer. Taking these conditions into account, a mode of gravitational instability accompanied with a motion perpendicular to the equatorial plane is newly found. If unstable wavelengths of the largest growing rate for non-axisymmetric and axisymmetric perturbations are the same, typical masses of planetesimals are 4 x 10 17

Transition from Torus to Chaos Accompanied by Frequency Lockings with Symmetry Breaking : In Connection with the Coupled-Logistic Map

Abstract: Transition from torus to chaos is studied using the coupled· logistic map. We observe the period-adding sequence, which obeys the critical phenomena of a one-dimensional mapping. The fixed Lyapunov exponent is also obtained. The locking that appears after the sequence breaks the symmetry of the system. Self-similar stripe structure of basins is also found. Various properties and a phase diagram of the map are given. The mechanism of the distortion of torus and transition to chaos is also discussed.

Light p-Shell Λ-Hypernuclei by the Microscopic Three-Cluster Model

Abstract: A systematic investigation of ^6_ΛHe, ^6_ΛLi, ^7_ΛLi ^8_ΛLi and ^9_ΛBe hypernuclei is carried out within the framework of the microscopic α+χ+Λ cluster-model dynamics (χ=n, p, d, t, or α). The positive and negative parity energy spectra are analysed in detail and are classified into several characteristic “bands” according to the underlying structures. The E2, E1 and M1 γ-ray transition probabilities and magnetic dipole moments are calculated. The intra-band B(E2)’s are obtained to be several times enhanced in comparison with the shell-model values. The level widths of the strong peaks observed at lower B_Λ are roughly evaluated on the basis of the calculated reduced width amplitudes. The existing data can be well explained by the present model. The cluster-model estimates of the effective neutron number Neff(θ=0°) for the (K^-, π^-) reaction are consistent with the experiments.

Double beta decay

Abstract: The double β decay is investigated by the use of the relativistic Coulomb wave function including the finite nuclear size effect. A general form of the V±A interactions is considered. It is shown that the decay rate is enhanced considerably in comparison with the case of the plane wave multiplied by the non-relativistic Fermi factor.

Gauge Invariant Scalar Perturbations in the New Inflationary Universe

Abstract: Etude de l'evolution temporelle des perturbations scalaires dans le nouvel univers inflationniste a l'aide d'une version etendue de la formulation invariante de jauge de Bardeen. On montre que suivant le contenu en matiere de l'espace-temps de fond, l'existence d'une etape a expansion exponentielle peut conduire soit a la naissance de perturbations de densite de grande amplitude soit a l'amplification de perturbations existantes

Elastic Scattering and Breakup of 6Li: A New Type of Dynamical Polarization Potential

Abstract: °Ca, respectively, are investigated on the basis of a microscopic coupled-channel (CC) method. The ground state and discretized breakup continuum states of 'Li are described by a totally antisymmetrized a-d cluster model. The CC potentials are given by doubly folding the M3Y effective nucleon-nucleon potential into the diagonal and transition densities of 'Li and the target density. The CC calculation with the bare normalization NR = 1.0 for the real potentials fits very well the experimental angular distributions of elastic scattering on account of large CC effects of the projectile breakup channels. The dynamical polarization potential due to the 'Li breakup is found to be strongly repulsive with a negligibly small imaginary part in the important surface region; this accounts for the strong reduction of the normalization factor, NR = 0.5 ~ 0.6, required in usual double-folding single-channel calculations. The breakup of 'Li into both the a-d resonant and non­ resonant states is found to occur in the extremely peripheral region much beyond the grazing distance and to proceed under a heavy interference between the one-step and multi-step breakup processes.

Doubling of Torus

Abstract: On trouve le doublement du tore dans des applications dissipatives a 3 et 4 dimensions. Dans ces modeles, le doublement apparait seulement un nombre fini de fois avant l'apparition du chaos

Phase Transition and Fractals

Abstract: A geometrical interpretation of critical phenomena, particularly of the scaling relations on critical exponents is given by the use of statistical fractal dimensionality. The relation between this geometrical interpretation and the finite size scaling theory is also discussed. The concept of connectivity dimensionality (or generalized fractal topological dimen· sionality) is introduced to discuss the relation between critical exponents and fractal dimen· sionalities of some explicit lattices.

Vortex, spin and triad for quantum mechanics of spinning particle. I General theory)

Abstract: On montre qu'une extension naturelle du formalisme hydrodynamique de la mecanique quantique pour une particule de Schrodinger pour inclure des ecoulements tourbillonnaires conduit au formalisme hydrodynamique de la mecanique quantique pour une particule a spin

Exciton Solitons in One-Dimensional Molecular Crystals

Abstract: Etude des vibrons couples non lineairement aux vibrations reticulaires dans des cristaux moleculaires 1D: les solitons vibroniques ainsi formes sont gouvernes par l'equation de Schrodinger non lineaire ou les solitons de Davydov, obeissant a la meme equation, sont plutot applicables aux excitons avec transfert par interactions d'echange

Theory of Electronic Structures and Lattice Distortions in Polyacetylene and Itinerant Peierls Systems. II Coulomb Interaction Dependences of the HF Ground State, Lattice Dimerization and 1Bu Excited State in Regular Trans-Polyacetylene

Abstract: We study the Coulomb interaction dependences of the HF ground state, lattice dimerization and I Bu excited state in regular trans-poly acetylene using the PPP hamiltonian model developed in a previous paper. The nature of the HF ground state is determined by the relative magnitudes of the on site and nearest neighbour parts and the screening of the longer range part of the effective Coulomb potential. The Coulomb interaction with relatively large nearest neighbour part and not too strongly screened longer range part induces lattice dimerization. The driving force of the Coulomb induced dimerization is the nearest neighbour exchange interaction. The lattice dimerization in polyacetylene is due to the Coulomb mechanism. The SSH model is implicitly taking into account the nearest neighbour exchange interac­ tion. The Franck-Condon band gap is mostly determined by the nearest neighbour exchange interaction. The IBu excited state is excitonic. The exciton binding energy is estimated for the effective Coulomb potential with the screened long range part. It is not large owing to very small effective mass of electron and hole. To explain the observed I Bu excitation energy, the short range part of the effective Coulomb potential must be screened by about half compared to the one in small conjugate molecules. The condition for splitting of the exciton into a zwitter­ ionic pair of charged solitons is discussed.

Pseudo Dirac Neutrino

Abstract: There is a growing interest in the neutrino masses. Theoretically, there is much freedom in neutrino mass patterns in contrast to quarks and charged leptons because neutrinos are in general considered Majorana particles. Experimentally, the v-oscillation!) and the /3/3 decay2),3) give serious constraints to neutrino masses and their mixing scheme. A special case where there are degeneracies of Majorana neutrino masses has recently been interesting. If the degeneracy happens as a consequence of the special symmetry in the mass matrix, a pair of degenerate Majorana neutrinos may form a Dirac neutrino. This Dirac neutrino is called the pseudo Dirac (PD) neutrino,4)-6) if the symmetry of the mass matrix is not the symmetry of the weak interaction. That is, the lepton number assigned to this Dirac neutrino is not conserved in the weak interaction and thus the mass degeneracy is removed by the higher order perturbation of the weak interaction. A PD neutrino has recently drawn special attention due to the tight neutrino mass bound obtained from the analysis of the /3/3 decay,2),3)