Showing papers in "Progress of Theoretical Physics in 1992"

Statistical Mechanics of Population: The Lattice Lotka-Volterra Model

Abstract: To derive the consequence of heritable traits of individual organisms upon the feature of their populations, the lattice Lotka-Volterra model is studied which is defined as a Markov process of the state of the lattice space. A lattice site is either vacant or occupied by an individual of a certain type or species. Transition rates of the process are given in terms of parameters representing the trait of an individual such as intrinsic birth and death and migration rate of each type. Density is a variable defined as a probability that a site is occupied by a certain type. Under a given state of a site the conditional probability of its nearest neighbor site being occupied by a certain type is termed environs density of the site. Mutual exclusion of individuals is already taken into account by the basic assumption of the lattice model

Antisymmetrized Version of Molecular Dynamics with Two-Nucleon Collisions and Its Application to Heavy Ion Reactions

Abstract: Two-nucleon collision process is incorporated into the antisymmetrized version of the molecular dynamics by utilizing the technique and the concept developed in the time-dependent cluster model. This newly formulated method of microscopic simulation of the heavy ion reaction can describe quantum mechanical features such as shell effects, since it treats the time development of the system wave function. We also propose a new prescription by which we can avoid the spurious zero-point energies of center-of-massmotion of fragment wave packets. The fragment production cross sections of the 12C+12C reaction at 28.7 MeV /nucleon are analyzed by this new method. It is shown that the basic feature of the data including the large cross section of a-particle is reproduced well by the·theory. Furthermore we show that the data are reproduced very well when we take into account the statistical cascade decays of the produced fragments, which verifies the great usefulness of the new microscopic simulation framework.

Target Space Duality as a Symmetry of String Field Theory

Abstract: Toroidal backgrounds for bosonic strings are used to understand target space duality as a symmetry of string field theory and to study explicitly issues in background independence. Our starting point is the notion that the string field coordinates X(a) and the momenta pea) are background independent objects whose field algebra is always the same; backgrounds correspond to inequivalent representations of this algebra. We propose classical string field solutions relating any two toroidal backgrounds and discuss the space where these solutions are defined. String field theories formulated around dual backgrounds are shown to be related by a homogeneous field redefinition, and are therefore equivalent, if and only if their string field coupling constants are identical. Using this discrete equivalence of backgrounds and the classical solutions we find discrete symmetry transformations of the string field leaving the string action invariant. These symmetries, which are spontaneously broken for generic backgrounds, are shown to generate the full group of duality symmetries, and in general are seen to arise from the string field gauge group.

Order Function and Macroscopic Mutual Entrainment in Uniformly Coupled Limit-Cycle Oscillators

Abstract: A concept of order function is proposed to develop a general self-consistent theory of mutual entrainment in large populations of limit-cycle oscillators such that each element is uniformly coupled to every other. The onset of entrainment is revealed to be a bifurcation of the order function in functional space. Numerical evidence for the theory is also presented

Collective Behaviors in Spatially Extended Systems with Local Interactions and Synchronous Updating

Abstract: Assessing the extent to which dynamical systems with many degrees of freedom can be described within a thermodynamics formalism is a problem that currently attracts much attention. In this context, synchronously updated regular lattices of identical, chaotic elements with local interactions are promising models for which statistical mechanics may be hoped to provide some insights. This article presents a large class of cellular automata rules and coupled map lattices of the above type in space dimensions d=2 to 6. Such simple models can be approached by a mean-field approximation which usually reduces the dynamics to that of a map governing the evolution of some extensive density. While this approxima­ tion is exact in the d== limit, where macroscopic variables must display the time· dependent behavior of the mean·field map, basic intuition from equilibrium statistical mechanics rules out any such behavior in a low·dimensional system, since it would involve the collective motion of locally disordered elements. The models studied are chosen to be as close as possible to mean-field conditions, i.e., rather high space dimension, large connectivity, and equal·weight coupling between sites. While the mean·field evolution is never observed, a new type of non·trivial collective behavior is found, at odds with the predictions of equilibrium statistical mechanics. Both in the cellular automata models and in the coupled map lattices, macroscopic variables frequently display a non·transient, time· dependent, low·dimensional dynamics emerging out of local disorder. Striking examples are period 3 cycles in two-state cellular automata and a Hopf bifurcation for a d=5 lattice of coupled logistic maps. An extensive account of the phenomenology is given, including a catalog of behaviors, classification tables for the cellular automata rules, and bifurcation diagrams for the coupled map lattices. The observed underlying' dynamics is accompanied by an intrinsic quasi·Gaussian noise (stem, ming from the local disorder) which disappears in the infinite-size limit. The collective behaviors constitute a robust phenomenon, resisting external noise, small changes in the local dynamics, and modifi,cations of the initial and boundary conditions. Synchronous updating, high space dimension and the regularity of connections are shown to be crucial ingredients in the subtle build-up of correlations giving rise to the collective motion. The discussion stresses the need for a theoretical understanding that neither equilibrium statistical mechanics nor higher-order mean·field approxima· tions are able to provide.

Chaotic wandering and search in a cycle-memory neural network

Abstract: Numerical investigation of a single layer recurrent neural network model in which the synaptic connection matrix is formed by summing direct products of succesive patterns in cyclic sequeences shows that chaotic wandering dynamics can occur with the reduction of a connectivity parameter. The structure in these dynamics is discussed from the viewpoint of search among stored memory patterns

Neutrino Emitting Modes of Double Beta Decay

Abstract: Four types of nuclear double beta decays accompanied with emission of two neutrinos are compared: (1) capture of double atomic electrons, (2) capture of one atomic electron and emission of one positron, (3) emission of two positrons and (4) emission of two electrons. Under the assumption that a charge distribution is uniform inside nucleus, bound state solutions of the Dirac equation are given analytically by using transcendental functions. Practically, both captures of the K and L_I electrons are taken into account.

Quantum mechanics of a particle on a curved surface. Comparison of three different approaches

Abstract: When quantum mechanical motion of a particle constrained to a curved surface in the Euclidean space is considered, three different approaches may be adopted to describe the system. One is the confining approach which enforces a particle to stay in the surface by a physical confining potential. Both of the others follow Dirac's general prescription to treat a constrained system, but employ different constraints, namely the usual and the conservative constraints, respectively. The three approaches lead to results which do not in general agree with each other, though they give the same classical equation of motion

False vacuum decay with gravity: Negative mode problem

Abstract: Motivated by work of Lavrelashvili, Rubakov and Tinyakov (LRT), who claim that the WKB approximation would break down even at energy scale far below the Planck one, the decay of false vacuum under the presence of gravity is carefully investigated. First we approach the issue from a different point of view, namely, by solving the Wheeler-DeWitt equation under the boundary condition appropriate for the false vacuum decay. The resulting wave function shows no sign of the break-down of the WKB approximation. Then, based on the canonical Hamiltonian form of the Euclidean path integral, we develop a method to analyze the number of negative modes around the Euclidean bounce solution describing the tunneling process and evaluate it in some limiting cases. Again, we find a strong evidence that LRT's claim is superficial.

Where Is the Σb

Abstract: The masses of s-wave bottom baryons are discussed in a semirelativistic quark model, on the basis of a quark-distance relation. We stress that the Σ b is heavier than Ξ' b (b[su], b[sd]) containing the antisymmetric su(or sd) subsystem. We conclude that the two candidates for Λ b with very different masses are different states; Basile et al.'s result 5425 +175 −75 MeV is Λ b (b([du]), but Arenton et al.'s result ∼5750 MeV is Ξ' 0 b (b[su])

Quantum Mechanics of a Particle Confined to a Twisted Ring

Abstract: We derive an effective Hamiltonian for a particle confined to a thin tube which is gently twisted and curved to form a closed loop. The Hamiltonian describes the effect of both the curvature and the torsion of the loop correctly to the second order. Applied to the case of a tube of circular cross section, it reveals complete analogy with the Aharonov-Bohm effect. We also discuss eigenmodes for Mobius-like rings formed by a tube of non-circular cross section

Theoretical Approach to Treatment of Non-Newtonian Forces*)

Abstract: We consider the set of gravitational and unified field theories that predict the deviation on Newton's law. The main attention is paid to mechanisms of new forces origin and particles which can be regarded as the mediators of new type of interaction. The all known to us theories are divided into eight classes and relation and discrepancy between them are discussed

Symmetry in the Nucleon-Nucleon Interaction and the Model of Moscow Potential

Abstract: An attempt to understand better the modern situation with short range baryon-baryon (by example of nucleon-nucleon) interaction is undertaken. The article covers five main ingredients of the whole problem: (i) visual demonstration of the inadequacy of modern models for short-range N-N interaction, (ii) the general property of the Wigner supermultiplet symmetry of interaction potentials for composite particles, (iii) a short outline of the main results of realistic six-quark microscopic calculations for nucleon-nucleon interaction and the results based on the Moscow model for N-N interaction

Neural network model carrying phase information with application to collective dynamics

Abstract: A network of periodically bursting model neurons is proposed. Its unique feature is a complex representation of the cell variables and also of the synaptic matrix. In the strong-coupling limit, the model recovers the traditional neural network model of simple on-off units, while in the weak­ coupling limit it reduces to the network of smooth phase oscillators. In the special case of all-to-all excitatory coupling, some numerical and analytical evidence is provided for the occurrence of global phase locking. More complicated collective behavior such as clustering is also discovered numeri­ cally. Stimulus-evoked collective oscillations as observed in the cat primary visual cortex are explained within the present framework. Recent electrophysiological studies revealed that neuronal responses with oscil­ latory modulation of the spiking frequency occur in various parts of mammalian brain.l),2) It has hence been suggested that multiple sensory inputs with some mutual similarity could be linked through the 'phase locking of this sort of neural oscillations, and that such linking could be crucial to the early stage neural information process­ ing. 3 ) Unfortunately, however, traditional neural network models composed of the· simple McCulloch-Pitts elements or of their continuous analogues do not seem to provide a suitable framework for testing the above hypothesis nor for evaluating the computational power of oscillatory neural networks in generaL This is because such models ignore from the outset the basic fact that a single neural cell itself can behave as an oscillator and hence carry phase information_ It is not only meant here that cell membranes are capable of generating a periodic train of action potentials_ More importantly, they are known to exhibit quite commonly the periodic bursting, Le_, alternation between the period of rapid spiking and that of quiescence_ 4 ),5) This second form of neural oscillation is of our main concern in the present paperRecent~y, some researchers studied oscillator networks in relation to sensory

Supersymmetric Gauged Wess-Zumino-Witten Models

Abstract: We construct the gauged Wess-Zumino-Witten models which have the N=2 superconformal symmetry and study the classical aspects of these models

Origin of Core-Halo Structure in One-Dimensional Self-Gavitating System

Abstract: The relaxation process of self-gravitating systems is examined by using one-dimensional numeri­ cal simulation. We get the asymptotic distribution function which disagrees with that proposed by Lynden-Bell. Our distribution function has two peaks in low and high energy regions and a valley in the medium energy region. This characteristic core-halo structure in phase space has been observed in many simulations. Vir e clarify the dynamical mechanism which generates this 'core-halo' structure. The essence of this mechanism is that the elements of the system are accelerated (or decelerated) very effectively by the evolving gravitational potential in a specific energy region, reflecting the initial conditions. Some classes of stellar systems,such as elliptical galaxies, seem to have already settled down to their final equilibrium configuration. This is strongly suggested from the fact that most elliptical galaxies show the universal luminosity profile which is characterized by R1!4-l aw.*} Moreover, most giant elliptical galaxies have little rotation and a random stellar velocity. The velocity dispersion of the stars in the inner few kiloparsecs is also universally correlated with luminosity according to the Faber-Jackson law. 2 ) Therefore, there must be a common relaxation mechanism which guarantees this universality. The ordinary relaxation mechanism due to the two-body gravitational interaction (binary encounter) has been the only well­ established relaxation process in an elliptical galaxy which has poor gas. However, the relaxation time scale is too long (more than 10 15 yrs) to relax an elliptical galaxy within the age of the Universe. Hence we believe that there must be another relaxa­ tion mechanism which is more rapid and more effective for a self-gravitating system. 25 years ago, Lynden-Bell proposed a new relaxation mechanism due to the variation of the mean potential. 3 ) The relaxation time scale is far shorter than that by binary encounters. This new mechanism was expected to solve the above­ mentioned problem. The evolution of self-gravitating systems is generally described by Boltzmann equation and Poisson equation,

Simple BRS Gauge-Fixing

Abstract: It is pointed out that the BRS gauge-fixing procedure has wide applicability beyond what it is as the usual gauge-fixing method. The examples we discuss are the equivalence theorem, generalized field transformations and a natural derivation of the gaugeon formalism. We also propose a direct way of BRS gauge-fixing for open gauge theories

Cutoff Dependence of Self-Consistent Solutions in Unquenched QED3

Abstract: In the leading order of the liN expansion for the vacuum polarization, we obtain the chiral­ symmetry-breaking solutions of the Schwinger-Dyson equation in three-dimensional QED with N four-component Dirac fermions. Special attention is paid on the critical number of the fermion flavor Nc and the scaling law for the dynamical fermion mass. In this framework we introduce the infrared cutoff as well as the ultraviolet one. We show the relation between the vertex ansatz and the scaling law which is consistent with our numerical results that the scaling law is affected by the infrared cutoff. Especially in the case of the Pennington and Webb's vertex ansatz, the mean-field type scaling law and cutoff-dependent finite Nc are obtained in the large infrared cutoff, while the exponential type scaling and infinite Nc are given in the sufficiently small infrared cutoff. The connection with the Monte Carlo simulation is discussed.

Numerical Approach to One-Loop Integrals

Abstract: Two numerical methods are proposed for the calculation of one-loop scalar integrals. In the first method, the singularity is cancelled by the symmetrization of the integrand and the integration is done by a Monte-Carlo method. In the second one, after the transform of the integrand into a standard form, the integral is reduced into a regular numerical integral. These methods provide us practical tools to evaluate one-loop Feynman diagrams with desired numerical accuracy. They are extended to the integral with numerator and the treatment of the one-loop virtual correction to the cross section is also presented

A Charged Kerr Metric Solution in New General Relativity

Abstract: We give an exact solution of the gravitational and electromagnetic field equations with a charged rotating source in new general relativity. The solution has three parameters Q, h and a, and it gives a charged Kerr metric space-time. The parallel vector fields and the electromagnetic vector poten- " tial are axially symmetric. In this space-time, we cannot discriminate new general relativity "from general relativity, so far as scalar, the Dirac and the Yang-Mills fields and macroscopic bodies are used as probes. The space-time does not have singularities at all, although it has an "effective singularity". Two kinds of Reissner-Nordstrom metric solutions, one is our solution with h=O and the other is a solution given by Hayashi and Shirafuji, are physically equivalent with each other. Nevertheless, these are markedly different from each other with regard to the asymptotic behavior of the torsion tensor for r -+ 00 and the space-time singularities.

Fragment Mass Distribution in Intermediate Energy Heavy-Ion Collisions and the Reaction time Scale

Abstract: Quantum Molecular Dynamics method is combined with multi-step statistical decay calculation and they are applied to the investigation of fragment mass distribution and the reaction time scale in intermediate energy heavy-ion collisions. The fragment mass distributions in 14N(35 MeV /u)+ C , and 4°Ar(44 MeV/u)+ Al collisions are well reproduced by our framework. We discuss the time evolution of fragment mass yield and contribution of statistical decay process in these two systems.

Perturbations of the Cosmic Microwave Background Radiation and Structure Formations

Abstract: After the recent discovery of temperature fluctuations of the cosmic microwave background radiation by COBS, the study of the temperature fluctuations becomes more and more important for understanding formations of large scale structures of the universe. The treatments for the evolution of small density fluctuations of matters and radiation by gauge invariant formalism are summarized. And the expected values of temperature anisotropies in various cosmological models are shown. Both flat and open universe models with and without the cosmological constant are considered. As for open universe models, in particular, any work had never been done by the complete treatment on large scale anisotropies. However we could find the complete formula to handle large scale temperature anisotropies and here this formula is adopted

The Difference of Effective Hamiltonian in Two Methods in Quantum Mechanics on Submanifold

Abstract: The difference between the effective. Hamiltonians in two methods, the Dirac and Schroedinger equation method is analyzed. It is shown that the difference between quantum potentials is coming from the existence or vanishing of the uncertainty principle in the direction normal to a subspace embedded in a Euclidean space

Spacetime Probabilities in Nonrelativistic Quantum Mechanics

Abstract: We demonstrate the existene of spacetime probabilities in nonrelativistic quantum mechanics, that is, quantum mechanical probabilities for a set of alternatives which are associated, not with a surface of constant time, but with spacetime domains with nonzero spatial and temporal width in Newtonian spacetime. We use the criterion that quantum mechanical probabilities can be defined for a set of alternatives if and only if the interference between any two different alternatives vanishes. Although generalized quantum mechanics was formulated on the basis of this criterion, the actual existence of spacetime probabilities has not been known. In this paper we consider a rectangular spacetime domain Ω and introduce a set of spacetime alternative {Yes, No} : «Yes» is to find a particle in Ω and «No» is the complement to «Yes»

Gauge Field Theory of the Quantum Group SUq(2)

Abstract: The gauge field theory of the quantum group SU q (2) is formulated. The parallelism to the case of SU(2) is maintained with the help of the definition of the SU q (2) gauge transformations preserving some group-like properties, the differential calculus on SU q (2) developed by Woronowicz, and the q-deformed trace. The Lagrangian invariant under local SU q (2) transformations is obtained

Coalescence of Spinning Binary Neutron Stars of Equal Mass 3D Numerical Simulations

Abstract: We have performed numerical simulations of coalescence of binary neutron stars using a Newtonian hydrodynamics code including radiation reaction by gravitational waves. In order to examine the effect of spin, we start the simulations from two distinct types of the initial conditions. In the first case, to see the dependence of results on the initial separation of binary, a Roche solution of separation 27 km, each mass ~ 1.5 Mo and each radius ~ 9 km, respectively, is given as the initial condition. We found that the evolution sequence and the wave form of gravitational waves are essentially the same as those in the previous simulations in which computations are started when two neutron stars just contact. In the second case, we include spin of each star with -Q, where Q is Keplerian angular velocity of orbital motion, which is required from the conservation of the circula­ tion. We found that the wave pattern has high amplitude oscillation after coalescence contrary to the former case. This means that it will be possible to determine the spin of coalescing neutron stars from the observed wave form of gravitational waves. The maximum amplitude of gravitational waves is 3.4 x 1021 for a hypothetical event at the distance of 10 Mpc.

Can the Strongly Interacting Dark Matter Be a Heating Source of Jupiter

Abstract: We show that the strongly·interacting massive particle (SIMP) with mass of 3x10 6 -10 7 GeV is astrophysically interesting as a dark matter candidate in" the galactic halo. The annihilation of SIMPs inside Jupiter naturally explains the intrinsic heat flux irrespective of details of the planetary models. We discuss its effect in all Jovian planets as well as in the Sun and the Earth. We also comment that such a SIMP is accommodated in a class of hadronic axion models. The dark matter (for a recent review, see, e.g., Ref. 1)) giving a large fraction of the gravitational mass of the galaxy may be composed of elementary particles. These particles must be so weakly-interacting or so few and heavy that they are not conspicuous. Many dark-matter candidates have been proposed!) and the possibil­ ities of their experimental detection have been intensively studied. 2 ) Among them the strongly-interacting dark-matters 3 ) are very interesting since they may allow the direct detection in the dark-matter search experiments on the Earth. In fact, only small regions have been left open for the strongly-interacting massive particles h (SIMPs), one with mass of 10 5 -10 7 GeV and the other with mass above 1010 GeV. 3 ) Furthermore, the recent experiment by Caldwell et a1. 4 ) has excluded some portion of the window. However the SIMP with mass of 3 X 10 6 -10 7 Ge V is still allowed. *) In this paper we point out that for the window, SIMPs are trapped in the planets and can annihilate in their centers producing possible heating energies. We indeed find that our model may explain the mysteriously large intrinsic heat flux of Jupiter 5 ) within the three standard deviations irrespective of the detailed parameters of the planet as well as the annihilation cross section. However for other Jovian planets,6),7) one must require that the SIMP's annihilation has not yet reached the steady state, since otherwise it overproduces the heating energy. In this case the predicted heat fluxes depend on details of the densities and temperatures of the planet cores and the annihilation cross section. We also examine SIMP's annihilation effects in the Earth and the Sun. The final comment is devoted to stressing that this stable SIMP is naturally accommodated in a class of hadronic axion models. Our basic assumption is that the dark halo of our galaxy 'is a cloud of the SIMPs h with the mass density Ph=OA GeV fcm

Vector Charge Density Wave Model of Metallic and Trigonal Te

Abstract: High pressure metallic (m-) Te and pressure dependence of trigonal (t-)Te are studied by the vector charge density wave (VCDW) model, namely by coupled CDWs on vector p orbitals. Metallic Te comprising dimerized zigzag chains as well as semiconducting t-Te with helical chains can be described by VCDWs with the wave numbers (O, π/2, π/2) and (2π/3, 2π/3, 2π/3), respectively, on a simple cubic lattice. The VCDW model is improved to include all the first order change of the transfer interaction so that the effect of shear deformation can be taken into account

Statistics and Structures of Strong Turbulence in a Complex Ginzburg-Landau Equation

Abstract: One·dimensional complex Ginzburg·Landau equation with a quintic nonlinearity (QCGL) is studied numerically to reveal the asymptotic property of its strong turbulence. In the inviscid limit, the QCGL equation tends to the nonlinear Schrodinger (NLS) equation which has a singular solution self·similarly blowing up in a finite time. The probability distribution function (PDF) of fluctuation amplitudes is found to have an algebraic tail with exponent close to -8. This power law is described as the multiplication of the PDF of the amplitude of a singular solution of the NLS equation and that of maximum heights of bursts. The former is shown to have a -7 power law in terms of the scaling property of the NLS singular solution. The latter is found to have a -1 power law by numerical simulation. Significant deviations from Gaussian statistics make it difficult to understand the property of the fully developed turbulence. Non-Gaussianity observed in the proba­ bility distribution functions (PDFs) of the velocity gradients plays a fundamental role in the energy transfer. The nonzero skewness of the longitudinal velocity gradients induces the energy transfer toward small scales. The strong intermittency in the energy dissipation is reflected in the large flatness of the velocity gradients. 1 )-3) Recently several authors have discussed the structures of PDFs. 4 H) She et al. 4 ) showed by a Fourier-space band-filtering method that the flatness factors not only of the velocity derivatives but of the velocity fields are large when wave numbers involved are in the dissipation range. It is noteworthy that the PDFs of velocity gradients reconstructed with the Fourier modes in inertial range are close to Gaus­ sian. These results suggest the existence of small-scale coherent structures, e.g., strong bursts in energy dissipation. The structures may be related to the complex­ space singularities of the N avier-Stokes (NS) equations; in the inviscid limit, these singularities may appear in real-space in a finite time. Therefore it is plausible that the tail structures of the PDFs may be accounted for in terms of those coherent structures in the limit of high Reynolds number. Introducing a mapping closure model based on this idea, Kraichnan and She 5),6) tried to reproduce non-Gaussian PDF of the transverse velocity gradients obtained by direct numerical simulations at moderate Reynolds numbers. However, the charac­ teristics of coherent structures are not clarified in their heuristic model. Anyway singularities of the Euler equations including their existence have not been explained thoroughly yet in spite of accumulation of researches.7)-9) Our computational facilities are not powerful enough to simulate the NS equa­ tions at sufficiently high Reynolds numbers at which singularities may be visible if *) Present address: Faculty of Education, Kanazawa University, Kanazawa 920.