Showing papers in "Progress of Theoretical Physics in 1984"

Period-Doubling of Kink-Antikink Patterns, Quasiperiodicity in Antiferro-Like Structures and Spatial Intermittency in Coupled Logistic Lattice*) -- Towards a Prelude of a "Field Theory of Chaos"--

Abstract: On etudie des caracteristiques qualitatives d'un reseau a une dimension d'applications logistiques couplees. On trouve des configurations duales-antiduales de cycles 2 n -periodiques avec leurs bifurcations a dedoublement de periode

Renormalization of Supersymmetry Breaking Parameters Revisited

Abstract: On considere les equations du groupe de renormalisation dans le modele de jauge minimal SU(3)×SU(2)×U(1) a supersymetrie brisee doucement

Multi-Vortex Solutions of a Two-Dimensional Nonlinear Wave Equation

Abstract: On propose une equation d'onde non lineaire permettant des tourbillons topologiques qui est analogue a 2 dimensions d'espace de la chaine de spin de Heisenberg isotrope continue

A Coupled Base-Rotator Model for Structure and Dynamics of DNA Local Fluctuations in Helical Twist Angles and Topological Solitons

Abstract: Structure and dynamics of DNA are studied by using a model dynamical system in which each base in the system, coupled with its complementary base and nearest neighbours in the same strand by the hydrogen·bonding and the stacking energy, respectively, is allowed to rotate in a plane perpendicular to the helical axis. The potential energy of the base system is taken to be composed of two parts, intra·strand .base·base interaction energy and inter-strand one; in which base-sequence variation of interaction constants is neglected. When the intra-strand interactions are much larger than the inter-strand ones, a continuum approximation can be used, and the model system admits various topological solitons propagating along the helical axis. By studying numerically nonlinear difference equations determined from the extrema of a potential function of the model system in its simplified yet nontrivial case, it is shown that there exist fairly large local fluctuations in helical twist angles from one base pair to the next characterized by commensurate, incommensurate and chaotic phases, in addition to the conventional, idealized B-form.

Comments on the Dense Kondo State

Abstract: On discute du comportement de Kondo dense observe dans Ce, sur alliages et composes en tenant compte du couplage spin-orbite et du deplacement du champ cristallin. En utilisant une expression pour la temperature de Kondo sous champ cristallin on eclaircit la raison pour laquelle l'effet Kondo predomine dans l'interaction RKKY

Naked singularities in the Vaidya spacetime

Abstract: On etudie la propriete d'une singularite formee par l'effondrement spherique du rayonnement pur a partir de l'infini passe nul en temps de la congruence des geodesiques nulles dans l'espace temps de Vaidya

Stability Theory of Synchronized Motion in Coupled-Oscillator Systems. III Mapping Model for Continuous System

Abstract: By starting with a reaction-diffusion equation a mapping model for the continuous system is proposed The transition from the uniform state to the non-uniform one occurs at the same value of the diffusion constant for the mapping model as for the original reaction-diffusion equation if the transition exists The mapping model is further studied by adopting the logistic model in one-dimensional space with a periodic boundary condition Equal time spectra in wave number space and power spectra for several values of wave numbers are numerically obtained A comparison of the numerical results of the equal time spectra with a simple theory is made to give a satisfactory agreement for large wave numbers

A Model for Cooper Pairing. in Heavy Fermion Superconductor

Abstract: Cooper pair fonnation in the heavy fennion system is discussed on the basis of a tight-binding model for the Kondo lattice system. The attractive interaction between heavy fennions stems from the coupling with phonons, which arises through the modulations of the transfer to the nearest neighbor site and the single-particle level of the heavy fennion owing to the lattice vibrations. The interaction relevant to the Cooper pair fcinnation is written in the fonn of the superposition of separable fonns with SO, d- and p-like symmetries. A comparison among the transition temperatures for various types of Cooper pairing shows that the singlet pairing is always favorable compared to the triplet one, and that, of singlet pairings, the d-like one is most favorable in the weak coupling case and so is the s-like one in the strong coupling case. The manner in which the d- and s-components mix together below Tc is discussed in the Ginzburg-Landau region, from which it is shown that the possible type of pairing is purely s-like one or d-like one with s-like admixtures, depending whether the highest Tc occurs for s-like or d-like pairing. This implies that the low lying excitations can be nearly gapless for appropriate values of parameters characterizing the model.

Scenarios Leading to Chaos in a Forced Lotka-Volterra Model

Abstract: A predator·prey ecosystem is proposed to investigate roads to chaos in a differential system. In this model, Malthusian rate of prey is driven by a periodic external force. Feigenbaum scenarios and a torus to chaos with frequency locking as 1 ... torus'" 5'" chaos'" 4'" chaos'" 3'" chaos'" 5'" chaos'" 4'" 2 are obser· ved numerically and their scaling properties and multi· basins are investigated.

Oscillation and Doubling of Torus

Abstract: On etudie deux caracteristiques de l'instabilite du tore le long de la direction d'amplitude en utilisant diverses applications a 2 dimensions

Theory of Phase Transitions in Mixed Crystals Rb1−x(NH4)xH2PO4

Abstract: Discussion de ces transitions dans l'approximation d'amas, sur la base d'un modele de pseudospin pour le systeme protonique. Obtention theorique du diagramme de phase et comparaison a l'experience: bon accord

Entropy Production in the Inflationary Universe

Abstract: Entropy production mechanism during the vacuum energy dominated stage of the inflationary universe is considered. We propose a therrnalization mechanism of vacuum energy due to Higgs particles produced by the temporal change. of the background classical Higgs field which subsequently decay into other particles. Then the dissipation coefficient associated with the classical Higgs field is evaluated for an specific decay process and implications of the result are discussed.

Stable Distribution and Lévy Process in Fractal Turbulence

Abstract: On montre que la distribution en vitesse de la turbulence fractale dans R 3 est la distribution stable avec l'exposant caracteristique D/2, ou D est la dimension fractale de la turbulence

A Self-Consistent Mean-Field Approach to the Dynamical Symmetry Breaking: The Effective Potential of the Nambu and Jona-Lasinio Model

Abstract: The dynamical symmetry breaking phenomena in the Nambu and Jona·Lasinio model are reexamined in the framework of a self· consistent mean·field (SCMF) theory. First, we formulate the SCMF theory in a lucid manner based on a successful decomposition of the Lagrangian into semiclassical and residual interaction parts by imposing a condition that "the dangerous term" in Bogoliubov's sense should vanish. Then, we show that the difference of the energy density between the super and normal phases, the correct expression of which the original authors failed to give, can be readily obtained by applying the SCMF theory. Furthermore, it is shown that the expression thus obtained is identical to that of the effective potential (E. P.) given by the path· integral method with an auxiliary field up to the one loop order in the loop expansion, then one finds a new and simple way to get the E. P. Some numerical results of the E. P. and the dynamically generated mass of fermion are also shown. As another demonstration of the powerfulness of the SCMF theory, we derive, in the Appendix, the energy density of the D(N ).¢4 model including the higher order corrections in the sense of large N expansion.

Non-Linear Realization in Supersymmetric Theories. II

Abstract: On etudie la realisation non lineaire dans les theories supersymetriques N=1 a groupe de symetrie global G se brisant en son sous-groupe H. On definit un sous-groupe Ĥ de G c , le complexifie de G, de facon qu'il laisse invariant le point minimal du potentiel effectif invariant

Anisotropic Spinodal Decomposition under Shear Flow

Abstract: . When a critical fluid is brought into the unstable region in the presence of shear flow, growing fluctuations are greatly elongated in the flow direction, giving rise to strongly anisotropic light scattering. In the strong shear case the linear growth theory becomes applicable in a sizable time region 0 < t;:S te , in which the characteristic size along the flow direction grows as Dt/x, 1/x being the correlation length perpendicular to the flow in the strong shear case. For t;;:; te the characteristic size in the perpendicular "directions starts to increase. By applying a computational method of Langer, Bar·on and Miller, it is found to increase as t a ' with a';::;O.2, whereas the characteristic size in the flow direction continues to increase roughly as t.

Does Accidental Degeneracy Imply a Symmetry Group

Abstract: The question whether an accidental degeneracy in quantum mechanical system always implies the internal symmetry group of the system is probed by means of the simple 'model of the three·dimensional harmonic oscillator with a constant spin-orbit potential: H = (1/ 2)(p2+ r2)+ ;\6' L. For the fixed values of ;\ = += 1, this model has an interesting degeneracy of remarkable regularity; in particular, the ground state is infinitely degenerate, consisting of all the nodeless j = 1 ± 1/ 2 states. In order to systematically seek the symmetry group, we first investigate the full dynamical group of the system. To our surprise, we find that the· dynamical group of our system for .an arbitrary value of ;\ is the graded 5p(6R) - a supergroup extension of the dynamical group 5P(6R) of the three-dimensional harmonic oscillator. We find the graded 5U(3) as its subgroup, which is a supergroup extension of the well-known symmetry group 5U(3) of the harmonic oscillator. It is further shown that there exists a natural group chain, gr5P(6R)~5P(2R) XgrO(3), which corresponds to the group chain 5p(6R)~5p(2R)X 0(3), where x denotes the direct­ product. Next, we examine whether any subgroup of the full dynamical group constitutes the symmetry group of the system responsible for the accidental degeneracy. It is shown that there is no such a symmetry group in the system and that, instead of the symmetry group, there exists a special, simple algebraic structure which is essentially responsible for the accidental degeneracy.

Equilibrium of Two Rotating Charged Black Holes and the Dirac String

Abstract: On etudie le probleme a 2 corps pour des trous noirs charges en rotation en fonction de la solution stationnaire axisymetrique electrovide obtenue a partir de la transformation de Ernst de la famille 2-Kerr-NUT

Theory of Diffusion and Intermittency in Chaotic Systems

Abstract: On etudie la dynamique statistique de A t obeissant a A t+1 =B(x t )A t , ou B est une fonction de x t genere par une application chaotique a 1 dimension x t+1 =f(x t ). On montre que A t a 2 aspects complementaires; diffusion et intermittence

Characteristics of Collapse of Rotating Isothermal Clouds

Abstract: In order to solve the long-standing "centrifugal bounce or runaway" problem and also the problem of subsequent dynamical evolution, the collapse of rotating isothermal clouds has· been investigated by axisymmetric two-dimensional simulations and also by one-dimensional analysis as well as simulations in a thin disk approximation. For the initial condition, we have considered flattened configurations besides a uniform sphere. The results show that the collapse of the inner region follows a series of similar disk-like configurations nearly independent of initial and boundary conditions: The angular velocity and the column density of the disk are both proportional to (ac 2 + (U'2 )-'/2, and the equatorial density to (ac 2 + (U'2 )-', where ac is the core radius decreasing with time and (U' is the distance from the rotation axis. This similarity law arises from a competition between gravity and pressure in the core, contrary to the previous belief that centrifugal force would playa more significant role than pressure. The above form of column density shows that an axisymmetric disk cloud does undergo runaway collapse as long as it is isothermal, as was found in the simulations of Norman et al. The inner region is not very flattened (its axial ratio or flatness being about 6); hence, it is unlikely that the inner region will be subject to ring formation during the isothermal collapse. However, as for the outer envelope, whether it becomes gravitationally unstable to ring formation depends on its initial condition, i.e., the magnitudes of initial flatness and also density fluctuation. It is also shown that the above mentioned central runaway occurs only when the gas is isothermal. However, the runaway is actually stopped because the core becomes opaque and the gas is no more isothermal. It is found that the departure from isothermality gives rise to a bounce of the core and that, if the cloud is very flattened, it becomes unstable to ring formation, but otherwise it oscillates around an equilibrium state.

Gauge Dependence of the Grabvitational Conformal Anomaly for the Electromagnetic Field

Abstract: The conformal anomaly for the electromagnetic field in the background gravitational field is obtained in the general covariant gauge with a gauge parameter. We have used the path integral method of Fujikawa with the zeta-regularization. The gauge dependence is observed in the coefficient of the DR term in the' anomaly; various contradicting values have been assigned to the coefficient of this term in the previous calculations on the basis of different regularization schemes in the Feynman gauge. We empha­ size that at the cost of the classical conformal invariance those terms can be eliminated altogether by adding a finite counterterm proportional to ,;g R2 to the Lagrangian. A calculational scheme with regularized Green functions was also examined, and it gives rise to the same results for the anomaly in the conventional Faddeev-Popov formalism as well as in the B-field formalism. The regularization of Green functions introduces an auxiliary mass parameter for each field and the W ard-Takahashi identities impose a condition among those mass parameters. In the framework of the zeta-function regularization, the gauge dependence of the DR term in the anomaly thus appears to be inevitable.

On the Spin-Spin Correlation Function in the Ising Square Lattice and the Zero Field Susceptibility

Abstract: On obtient la fonction de correlation spin-spin X(m,n) dans le reseau carre d'Ising sous forme d'un developpement en serie different du developpement bien connu

Kaluza-Klein Inflation

Abstract: Dynamical evolution of the Kaluza-Klein space-time is studied using higher dimensional Einstein equation with dust matter. The difference of the topology between the usual space and the internal space gives rise to the segregation of these subspaces. Furthermore the contraction of the internal space causes the inflation of the usual space. From the standard big-bang model of the uni­ verse we obtain excellent results, the explanation of 3K background radiation and of primodial helium abundance in the universe. This model has, however, fundamental problems, so-called "Horizon problem" and "Flatness problem". -These problems originate from two basic assump­ tions: