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Showing papers in "Progress of Theoretical Physics in 1988"


Journal ArticleDOI
TL;DR: In this paper, two kinds of external fields are applied to the system: (1) periodic force and (2) random noises, and some effects of the external fields on the mutual entrainment are studied by analyses for steady macroscopic rotation and also by numerical simulations.
Abstract: Systems of many limit cycle oscillators are studied by using a phase description of the oscillation. Each oscillator interacts with all the other oscillators uniformly and is subject to external field. Two kinds of external fields are applied to the system: (1) periodic force and (2) random noises. Some effects of the external fields on the mutual entrainment are studied by analyses for steady macroscopic rotation and also by numerical simulations.

292 citations


Journal ArticleDOI
TL;DR: On considere des systemes non lineaires discrets and on etend le formalisme quasi continu pour inclure des effets discrets d'ordre eleve as discussed by the authors.
Abstract: On considere des systemes non lineaires discrets et on etend le formalisme quasi continu pour inclure des effets discrets d'ordre eleve

161 citations




Journal ArticleDOI
TL;DR: In this article, a systeme modele for des oscillateurs cycle limite distribues sur un reseau cubique a d dimensions is described, where the oscillateurs are divided into two groups.
Abstract: On etudie un systeme modele pour des oscillateurs cycle limite distribues sur un reseau cubique a d dimensions

98 citations


Journal ArticleDOI
Hideo Kodama1
TL;DR: In this paper, the authors apply Ashtekar's canonical formalism to the Bianchi cosmology and show that the constraints and the dynamical equations can be expressed explicitly in terms of the canonical variables, which depend only on time.
Abstract: Recently Ashtekar found a new canonical formalism of general relativity in which the constraints and the dynamical equations are all written formally as polynomials of canonical variables. In this paper we apply his formalism to the Bianchi cosmology and write down the constraints and the dynamical equations explicitly in terms of Ashtekar-type canonical variables which depend only on time. In particular we prove that for the vacuum Bianchi IX model the gauge freedom is decoupled from the dynamics and the canonical variables reduce to three diagonal components of the metric and their Ashtekar-type conjugate momentum, preserving the polynomial nature of the equations. Further we discuss the quantization of this model and show that the quantized hamiltonian constraint takes a quite simple and beautiful form. To illustrate the tractability of this equation, we present an explicit non-trivial solution to it. § 1. Introduction Recently Ashtekar proposed a new canonical formalism of general relativity.1),2) Iri his formalism the constraint equations and the dynamical equations become polynomials when they are expressed in terms of the new complex canonical vari­ ables, the Ashtekar variables_ Hence the severe nonlinearity, which has been thought to be an inevitable nature of general relativity and has bothered us so far, disappears. In spite of this fascinating aspect, Ashtekar's formalism has various problems yet to be solved. First the role of the newly introduced gauge freedom which corre­ sponds to rotation of triad is not clear. Second the complex nature of the canonical variables brings about new problems when one tries to quantize the theory, such as the structure of state space, interpretation and the correspondence with the Wheeler-DeWitt theory based on the conventional ADM formalism. In order to solve these problems and also to check the power of the formalism, it is desirable to see how the Ashtekar formalism works in simple systems. From this point of view, in the present paper, we examine how the canonical dynamics of spatially homogeneous spacetime is described in terms of the Ashtekar variables. In particular, as an application we study the vacuum Bianchi IX model in detail. We show that in this model the gauge freedom is decoupled from the dynamics and the canonical variables reduce to the three diagonal components of the spatial metric and their Ashtekar-type conjugate momentum, preserving the polynomial nature of the equations. This implies that there is a direct correspond­ ence between the Ashtekar formalism and the ADM formalism in this case. Further we show that when the theory is quantized it leads to an equation for the wavefunc­ tion which is much more tractable than the Wheeler-DeWitt equation in the conven­ tional ADM formalism. In order to illustrate the tractability of the equation, we give an example of non-trivial exact solutions, though it is unphysical. The relation

98 citations



Journal ArticleDOI
Hideo Fukutome1
TL;DR: In this paper, a new theory for large quantum fluctuations in a Fermion many-body system that cannot be described by fluctuations around the Hartree·Fock ground state but arises from resonance of different correlation structures was developed.
Abstract: We develop a new general theory for large quantum fluctuations in a Fermion many·body system that cannot be described by fluctuations around the Hartree·Fock ground state but arises from resonance of different correlation structures. We start with an exact coherent state representation of a Fermion system on a unitary group. We show that the Hamiltonian in the coherent state representation has a close connection with the Hartree·Fock energy functional. From this, we can derive a new approximation called the resonating Hartree·Fock approximation in which a state is approximated by a superposition of non· orthogonal Slater deterrp.inants with different correlation structures. We derive the variation equations to determine a resonating Hartree· Fock wavefunction. We show that the resonance between degenerate broken symmetry Slater determinants may partially recover the symmetry. We discuss how to choose trial Slater determinants in a resonating Hartree· Fock wavefunction. We suggest that resonance of Slater determinants representing localized defects, such as solitons, polarons and breathers, produced in the long range order of the HF ground state may be the most important content of large quantum fluctuations in condensed matter systems.

85 citations


Journal ArticleDOI
TL;DR: In this article, the phase transition involving hyster· esis was investigated in greater detail with particular attention to codimension·two bifurcation points, and unexpectedly rich bifurbcation structures were revealed.
Abstract: Bifurcation structures associated with the onset of macroscopic rhythms in a large population of active rotators are analyzed theoretically and numerically. The phase transition involving hyster· esis found numerically in a previous work are investigated in greater detail with particular attention to codimension·two bifurcation points. As a result, unexpectedly rich bifurcation structures are revealed. '

77 citations


Journal ArticleDOI
TL;DR: In this paper, a generalized formalism of the hidden local symmetry was proposed, in which any nonlinear sigma model based on the manifold C/H is gauge equivalent to a model possessing GglobalX Goeal symmetry.
Abstract: We present a generalized formalism of the hidden local symmetry in which any nonlinear sigma model based on the manifold C/H is gauge equivalent to a model possessing GglobalX Goeal symmetry, which is a natural extension of the well-known gauge equivalence between a C/H nonlinear sigma model and a CglObal X H'oea' "linear" model. As an application of this formalism, we reexamine a possibility that the Al mesons as well as the p mesons and their U(3) partners are dynamical gauge bosons of the hidden local symmetry, [U(3)L x U(3)RJ.oeal, in the U(3h x U(3)R/U(3)v nonlinear sigma model.

75 citations



Journal ArticleDOI
TL;DR: In this article, the Sato equation is introduced, and it is shown that the generalized Lax equation, the Zakharov-Shabat equation and the IST scheme can be derived from the sato equation.
Abstract: An .elementary introduction to Sato theory is given. Starting with an ordinary differential equation, introducing an infinite number of time variables, and imposing a certain time dependence on the solutions, we obtain the Sato equation which governs the time development of the variable coefficients. It is shown that the generalized Lax equation, the Zakharov-Shabat equation and the IST scheme are generated from the Sato equation. It is revealed that the r-function becomes the key function to express the solutions of the Sato equation. By using the results of the representation theory of groups, it is shown that the r-function is governed by the partial differential equations in the bilinear forms which are closely related to the PlUcker relations.




Journal ArticleDOI
TL;DR: In this paper, the authors investigated the superfluid transition of thin film adsorbed on porous materials with emphasis on the role of vortices and showed that the interaction among the vortice excited in the film is essentially one dimensional due to the quantum behavior of the flow.
Abstract: We investigate the superfluid transition of 'He thin film adsorbed on porous materials with emphasis on the role of vortices. Considering the multi· connectivity of the film, we show that the interaction among the vortices excited in the film is essentially one dimensional due to the quantum behavior of the flow. As a result, it is generally shown that the vortices do not dissociate at TA where the long range order (LRO) vanishes in contrast to the two dimensional case. We also study the mechanism of dissipation for applied AC flow with the frequency (J), noting that a finite dimension of the film, the pore size a, plays an important role. The crossover phenomena between the Kosterlitz- Thouless transition and the I! transition are predicted: The superfiuid onset is accompanied with the disappearance of the free vortices in large a or high (J) cases, whereas with the appearance of the LRO in small a or low (J) cases. Our theory qualitatively explains various experimental results with the torsion pendulum.


Journal ArticleDOI
TL;DR: On etudie des relations entre des algebres super-Virasoro and des systemes super-soliton aux niveaux classique et quantique.
Abstract: On etudie des relations entre des algebres super-Virasoro et des systemes super-soliton aux niveaux classique et quantique. On deduit explicitement plusieurs membres de l'ensemble infini de quantites conservees

Journal ArticleDOI
TL;DR: In this article, an exact formula for Hall coefficient including the many-body effects on the basis of the Fermi liquid theory was given by Eliashberg, and the result is given by (for simplicity, we give a static conductivity per spin)
Abstract: The systems in which electron-electron interactions cannot be neglected, such as heavy fermion systems!) and highTc oxide superconductors, are of current interest_ The former system exhibits the large T2-component of resistivity in its low temperature coherent regime. This behaviour is ascribed to electron-electron scattering with the Umklapp process_ Therefore, Hall coefficient should also be affected by manybody effects. Until now, many-body effects have been treated only within crude approximations. In metals, it seems dangerous to treat them on the basis of such approximate calculations as alloy analogy and Hubbard decoupling which neglect the momentum dependence of the self-energy. Moreover, we should include the vertex corrections originating from electron-electron interactions in order not to violate the Ward identity. These motivated us to seek an exact formula for Hall coefficient including the many-body effects on the basis of the Fermi liquid theory. Such a formula for conductivity was given by Eliashberg) in 1961. He collected all the terms which are, in the static limit, singular with respect to quasiparticle. damping, namely, divergent terms as the quasiparticle damping goes to zero. The result is given by (for simplicity, we give a static conductivity per spin)

Journal ArticleDOI
TL;DR: In this article, an attempt is made to clarify the realization of a classical distribution from quantum fltictuations of the order parameter in the inflationary universe, where it is shown that off-diagonal elements of p decreased as the phase transition proceeds.
Abstract: An attempt is made to clarify realization of a classical distribution from quantum fltictuations of the order parameter in the inflationary universe. We discuss destruction of quantum coherence associated with a state of the order parameter in models where it interacts with the enviroiunent. For that purpose, the time evolution of the reduced density matrix p, which is obtained by coarse· graining of the environment, is investigated. It is shown that off-diagonal elements of p decreased as the phase transition proceeds.

Journal ArticleDOI
TL;DR: In this article, it was shown that a fraction of the non-inflationary solutions in the Friedmann-Robertson-Walker (FRW) model is a generality of the inflationary solutions.
Abstract: Friedmann cosmological models with a massive minimally coupled scalar field are investigated by numerical methods. It is indicated that the majority of the solutions undergo the inflationary stage in flat and open models. In a closed model the ratio of the number of solutions without adequate inflation to the number of the total solutions are obtained numerically. I ) One oL the questions concerning this model is a generality of the inflationary solutions. We investigate this problem studying classical solutions of a homogeneous model with a massive scalar field. Among all solutions in this model some are inflationary and the others are not. If it is found that a fraction of the inflationary solutions (the ratio of the number of the inflationary solutions to the total number of solutions in some measure) is large enough, it becomes very reasonable to take such solutions for the model of our universe. For the flat Friedmann-Robertson-Walker (FRW) models, this problem was treated in the paper by Belinsky, Grishchuk, Zel'dovich and Khalatnikov. 2 ) Analyz­ ing the behavior of trajectories in the phase space of this dynamical system, they have shown that a fraction of the non-inflationary solution is the order of m/mp, mp and m being the Planck mass and a mass of the scalar field respectively. In fact, in order for the density fluctuation generated during the inflation to be small, the ratio m/mp is restricted to be smalI"such as m/mp~ 1O-5~ 10- 6 • 4 ) Therefore, at least for the flat FRW model, the overwhelming majority of the solutions are found to be inflationary. N ow, as for the open and closed FRW models, the problem was treated by the analytic method in the paper by Belinsky and Khalatnikov. 5 ) For the open model, the result is not so different from the flat model. However, for the closed model, the result is quite different: Due to the curvature effect, the expansion tends to turn into collapse. In the previous work, it was shown that the fra<;:tion of the non-inflationary solution is about 1/4 in some measure. In this paper, we investigate the evolution of the universe.modelsby an.explicit numerical computation of the phase space trajectories and have confirmed the.results of the previous work. The phase space for open and closed models is three dimen­ sional and the trajectories start from the two dimensional surface called "Quantum

Journal ArticleDOI
TL;DR: In this paper, a new microscopic model which takes into account both the static and dynamic triaxial deformations in the high-spin states of odd-A nuclei is developed, based on the rotating shell model and treats the quasiparticle-vibration couplings in the uniformly rotating frame of reference.
Abstract: _ A new microscopic model which takes into account both the static and dynamic triaxial deformations in the high·spin states of odd-A nuclei is developed. The model is based on the rotating shell model and treats the quasiparticle-vibration couplings in the uniformly rotating frame of reference. Effects of the static and dynamic triaxial deformations on the signature splitting of the quasiparticle energies and on the signature dependence of B(M1), B(E2; I -+ I -1) and B(E2; 1-+ I - 2) for the transitions within the unique·parity bands in odd-A nuclei are discussed. Numerical exam­ ples are presented for odd-Z nuclei 157Ho, l59Tm and 161, 165Lu, and for odd-N nuclei 161Dy,167Er and 16l,l63, l67 Yb to which experimental data for B(M1) and B(E2) are available.

Journal ArticleDOI
TL;DR: In this paper, the authors present various types of momentum distributions of the a particle using a TMS wave function generated with the Reid soft core V 8 model potential, which are well represented as a sum of Gaussian functions.
Abstract: We present various types of momentum distributions of the a particle using A TMS wave function generated with the Reid soft core V 8 model potential. Those are the momentum distributions of the single-nucleon, two-nucleon-cluster relative motion, two-nucleon-cluster center of mass, triton-proton relative motion and deuteron-deuteron relative motion. These momentum distributions are well represented as a sum of Gaussian functions. With these Gaussian expansions, the realistic momentum distributions of the a particle would become accessible to everyone.


Journal ArticleDOI
Terumitsu Morita1, Hiroki Hata1, Hazime Mori1, Takehiko Horita1, Koji Tomita1 
TL;DR: In this article, the scaling properties of chaos are studied from a dynamic viewpoint by taking invertible two-dimensional maps, and a fundamental role is played by an evolution equation for the probability of a small box along a chaotic orbit.
Abstract: Scaling properties of chaos are studied from a dynamic viewpoint by taking invertible two· dimensional maps. A fundamental role is played by an evolution equation for the probability of a small box along a chaotic orbit. A new relation between the partial dimen~ions of strange attractors in the expanding and contracting direction is derived in terms of the local expansion rates of nearby orbits. When the lacobians of the maps are constant, this relation can be written in terms of a potential rJJ(q) for the fluctuations of the local expansion rate in the expanding direction. For hyperbolic attractors, this potential rJJ(q) is related to the generalized entropies K(q) by rJJ(q)=(q -l)K(q), and the above relation reduces to a simple relation between the generalized dimensions and the generalized entropies. Furthermore, the generalized dimensions, the potential rJJ(q) and the probability densities are expressed in terms of the local expansion rates of unstable periodic orbits within the attractors, leading to a new method of studying chaos.



Journal ArticleDOI
TL;DR: In this paper, the authors investigated the wave function of a collapsing dust sphere and the interior of the associated black hole and found that the wave functions are meaningful only at WKB level due to the sharp boundary surface of the collapsing sphere.
Abstract: We investigate the wave function of a collapsing dust sphere and the interior of the associated black hole. We first consider the wave function of purely vacuum black hole interior and discuss the relation to the corresponding classical solutions. Because of the vacuum nature, a mass scale which characterizes the black hole mass can only be introduced into the wave function by hand. Then to put a mass scale into the wave function in a natural manner, we consider a dust collapse model whose classical counterpart can be exactly solved. As a result, we obtain the wave function of the black hole interior with mass determined by the dust mass. However, we find that the wave function is meaningful only at WKB level due to the sharp boundary surface of the dust sphere.

Journal ArticleDOI
Hiroki Hata1, Takehiko Horita1, Hazime Mori1, Terumitsu Morita1, Koji Tomita1 
TL;DR: In this paper, a weighted average of the coarse-grained local expansion rate along the local unstable manifold with a q-dependent weight is derived for chaotic attractors at the bifurcation points of band mergings and crises.
Abstract: Chaotic attractors at the bifurcation points of band mergings (or splittings), crises and saddle· node bifurcations have singular local structures which produce coherent large fluctuations of the coarse·grained local expansion rates of nearby orbits. Such local structures are studied in terms of a weighted average A(q), (-00< q< (0) of the coarse·grained local expansion rates along the local unstable manifold with a q·dependent weight. By taking invertible two·dimensional and noninverti· ble one·dimensional maps, it is shown that, as q is varied, A(q) exhibits discontinuous phase transi· tions at discrete values of q; qa, qp, .... Three types of such phase transitions are discussed. One is that caused by the homoc1inic tangencies with qa=2.0. The second is that due to the accumulation of homoc1inic tangency points at unstable periodic points with qp\"'\" -0.8. The third is that due to the intermittent hopping motions between two repellers with qT=LO. Different phases of the phase transitions represent different local structures. Thus the q-weighted average A(q) turns out to provide a useful means for characterizing singular local structures of chaotic attractors.