Showing papers in "Progress of Theoretical Physics in 1998"

Super-horizon scale dynamics of multi-scalar inflation

Abstract: We consider the dynamics of a multi-component scalar field on super-horizon scales in the context of inflationary cosmology. We present a method to solve the perturbation equations on super- horizon scales, i.e., in the long wavelength limit, by using only the knowledge of spatially homogeneous background solutions. In doing so, we clarify the relation between the perturbation equations in the long wavelength limit and the background equations. Then as a natural extension of our formalism, we provide a strategy to study super-horizon scale perturbations beyond the standard linear perturbation theory. Namely we reformulate our method so as to take into account the nonlinear dynamics of the scalar field.

Relativistic equation of state of nuclear matter for supernova explosion

Abstract: We construct the equation of state (EOS) of nuclear matter at finite temperature and density with various proton fractions within the relativistic mean field (RMF) theory for use in supernova simulations. We consider nuclei, alpha-particles, protons and neutrons in equilibrium at densities smaller than about PB '" 10 14 . 2 g/cm 3 by minimizing the free energy of the nuclear matter. The calculation is based on the RMF theory with the parameter set TM1, which has been demonstrated to provide good accounts of the ground state and excited state properties of finite nuclei. We tabulate the outcome for various densities in terms of the pressure, free energy, entropy, etc. at a sufficiently large number of mesh points in the density range PB = 10 5 . 1 '" 10 15 .4 g/cm 3 , the temperature range T = a '" 100 MeV and the proton fraction range Yp = a '" 0.56 to be used for supernova simulations.

From nagaoka's ferromagnetism to flat-band ferromagnetism and beyond : an introduction to ferromagnetism in the hubbard model

Abstract: This is a self-contained review about ferromagnetism in the Hubbard model, which should be accessible to readers with various backgrounds who are new to the field. We describe Nagaoka's ferromagnetism and flat-band ferromagnetism in detail, giving all necessary backgrounds as well as complete (but elementary) mathematical proofs. By studying an intermediate model called long-range hopping model, we also demonstrate that there is indeed a deep relation between these two seemingly different approaches to ferromagnetism. We further discuss some attempts to go beyond these approaches. We briefly discuss recent rigorous example of ferromagnetism in the Hubbard model which has neither infinitely large parameters nor completely flat bands. We give preliminary discussions about possible experimental realizations of the (nearly-)flat-band ferromagnetism. Finally we focus on some theoretical attempts to understand metallic ferromagnetism. We discuss three artificial one-dimensional models in which the existence of metallic ferromagnetism can be easily proved.

Space-time structures from iib matrix model

Abstract: We derive a long distance effective action for space-time coordinates from a IIB matrix model. It provides us an effective tool to study the structures of space-time. We prove the finiteness of the theory for finite $N$ to all orders of the perturbation theory. Space-time is shown to be inseparable and its dimensionality is dynamically determined. The IIB matrix model contains a mechanism to ensure the vanishing cosmological constant which does not rely on the manifest supersymmetry. We discuss possible mechanisms to obtain realistic dimensionality and gauge groups from the IIB matrix model.

The Luminosity Distance, the Equation of State, and the Geometry of the Universe

Abstract: The second derivative of the luminosity distance with respect to the redshift is written in terms of the deceleration parameter $q_0$. We point out that the third derivative contains the information regarding the sound speed of cosmic matter as well as the curvature of the universe. We restrict physically possible parameter ranges of the coefficients. It is found that there is a relation between the coefficients in a flat universe model with matter such that $c_{s0}(1+w_{\rm x0})=0$ ($c_{s0}$ is the total sound speed of the matter component and $w_{\rm x0}$=$p_{\rm x0}/\rho_{\rm x0}$).

Perturbations of kerr-de sitter black holes and heun's equations

Abstract: It is well known that the perturbation equations of massless fields for the Kerr-de Sitter geometry can be written in the form of separable equations. The equations have five definite singularities so that the analysis has been expected to be difficult. We show that these equations can be transformed to Heun's equations, for which we are able to use known technique for the analysis of the solutions. We reproduce results known previously for the Kerr geometry and de Sitter geometry in the confluent limits of the Heun's functions. Our analysis applies can be extended to Kerr-Newman-de Sitter geometry for massless fields with spin 0 and 1/2.

Calogero-Moser Models. I: A New Formulation

Abstract: A new formulation of Calogero-Moser models based on root systems and their Weyl group is presented. The general construction of the Lax pairs applicable to all models based on the simply-laced algebras (ADE) are given for two types which we call ‘root’ and ‘minimal’. The root type Lax pair is new; the matrices used in its construction bear a resemblance to the adjoint representation of the associated Lie algebra, and exist for all models, but they do not contain elements associated with the zero weights corresponding to the Cartan subalgebra. The root type provides a simple method of constructing sufficiently many number of conserved quantities for all models, including the one based on E8, whose integrability had been an unsolved problem for more than twenty years. The minimal types provide a unified description of all known examples of Calogero-Moser Lax pairs and add some more. In both cases, the root type and the minimal type, the formulation works for all of the four choices of potentials: the rational, trigonometric, hyperbolic and elliptic.

Rapidly Converging Truncation Scheme of the Exact Renormalization Group

Abstract: The truncation scheme dependence of the exact renormalization group equations is inves­ tigated for scalar field theories in three dimensions. The exponents are numerically estimated to the next-to-leading order of the derivative expansion. It is found that the convergence property in various truncations in the number of powers of the fields is remarkably improved if the expansion is made around the minimum of the effective potential. It is also shown that this truncation scheme is suitable for evaluation of infrared effective potentials. The phys­ ical interpretation of this improvement is discussed by considering O(N} symmetric scalar theories in the large N limit.

General Relativistic Effects of Gravity in Quantum Mechanics A Case of Ultra-Relativistic, Spin 1/2 Particles

Abstract: We present a general relativistic framework for studying gravitational effects in quantum mechanical phenomena. We concentrate our attention on the case of ultra-relativistic, spin-1/2 particles propagating in Kerr spacetime. The two-component Weyl equation with general relativistic corrections is obtained in the case of a slowly rotating, weak gravitational field. Our approach is also applied to neutrino oscillations in the presence of a gravitational field. The relative phase of two different mass eigenstates is calculated in radial propagation, and the result is compared with those of previous works.

Resonance and Continuum Components of the Strength Function

Abstract: It is shown that the strength function can be expressed in a sum of the contributions from bound, resonance and continuum terms and the role of each term can be investigated complementarily by using the complex scaling method (CSM). The mechanism of the Coulomb breakup reaction of Be is analyzed and we confirm the fact that the breakup is direct but not through resonances. The present method is also applied to other systems and its usefulness is discussed.

The Thermal Evolution of the Postshock Layer in Pregalactic Clouds

Abstract: We re-examine the thermal evolution of the postshock layer in primordial gas clouds. Comparing the time scales, we find that the evolutionary paths of postshock regions in primordial gas clouds can be basically understood in terms of the diagram drawn in the ion­ ization degree vs temperature plane. The results obtained from the diagram are independent of the density in the case that we do not include photodissociation and photoionization. We also argue that the diagram is not only relevant to the case of the steady postshock flow, but also to the isochorically cooling gas. The thermal evolution of primordial gas clouds has been investigated by many authors. 15),24),3),17),9),20),29) Almost all of those studies have been concerned with the formation of various kinds of galaxies, or primordial stars. In those papers, galaxies are assumed to grow out of small density perturbations present in the early universe. Because of the coldness of the growing density perturbations, the formed clouds, which are the progenitors of galaxies, experience strong shock heating at the bouncing epoch. Shock heating is also expected in the hierarchical clustering scenario of structure formation. In this case, shocks are expected in the collision between two clouds which are trapped in the gravitational potential well associated with the larger structure. In any case, shock heating is expected in the era of galaxy formation. The spatial structure and the thermal evolution of the postshock layer in primordial gas clouds were investigated by many authors. 8), 26), 27),14),23),10),1),30) In those studies the common and most important point is the over production of hydrogen molecules. For example, in Shapiro and Kang 23) (hereafter SK), the thermal evolution of steady postshock flow is investigated. They found that the postshock flow cools down so fast that the recombination process cannot catch up with the cooling. As a result, the ionization degree remains high (Ye rv 10- 3 ), even when the temperature has dropped below 10 4 K. Feeded these "relic" electrons, hydrogen molecules form through the processes

Baryon Mass and Phase Transitions in Large N Gauge Theory

Abstract: We calculate the baryon mass in N=4 large $N$ gauge theory by means of AdS/CFT correspondence and show that it is a truly bound state, at least in some situations. We find that a phase transition occurs at a critical temperature. Furthermore, we find there are bound states of W-bosons in the Higgs phase, where the gauge group is broken to SU(N_1)xSU(N_2).

Exact Results in Nc=2 IIB Matrix Model

Abstract: We investigate N_c=2 case of IIB matrix model, which is exactly soluble. We calculate the partition function exactly and obtain a finite result without introducing any cut-off. We also evaluate some correlation functions consisting of Wilson loops.

Indicators of reconnection processes and transition to global chaos in nontwist maps

Abstract: Reconnection processes of twin-chains are systematically studied in the quadratic twist map. By using the reversibility and symmetry of the mapping, the location of the indicator points is theoretically determined in the phase space. The indicator points enable us to obtain useful information about the reconnect ion processes and the transition to global chaos. We succeed in deriving the general conditions for the reconnection thresholds. In addition, a new type of reconnect ion process which generates shearless curves is studied. In the past decades, enormous effort has been dedicated to the study of two­ dimensional area-preserving maps with the twist condition,l) but very few studies have been made of nontwist maps. Recent studies on nontwist maps have revealed that rich properties are generated by violating the twist condition. 2) - 6) In a previous paper, 6) we studied the properties of the quadratic twist map and numerically determined the critical boundary in the two-dimensional parame­ ter space, where the transition to global chaos occurs. The critical boundary has many sharp singular structures, and their locations seem to have a one-to-one corre­ spondence with those of the reconnect ion thresholds. The relationship between the transition to global chaos and the reconnect ion processes was first pointed out by Howard and Hohs,2) but it has not yet been thoroughly investigated. In order to investigate the detailed structure of the critical boundary, one needs accurate information regarding the reconnection processes. In this paper, we study the details of the reconnect ion processes in the quadratie twist map and propose a theoretieal method to determine the reconnection thresholds. We show that the reversibility and symmetry of the mapping guarantee the existence of the "indicator points" in the phase space. These enable us to study the reconnect ion processes sys­ tematieally. For twin-chains of period one and period two, the reconnect ion thresh­ olds have already been determined, either exactly or approximately. 2), 3) The method presented here reproduces results which have been previously obtained, and it pro­ vides general conditions for the reconnect ion thresholds. The quadratie twist map (QTM) is defined by

The Competition between the 0- and π-Phase Shift in the Pb-Sr2RuO4-Pb Junction

Abstract: Recent measurements of the Josephson effect between two Ph-films via Sr2Ru04 show a very anomalous temperature dependence of the maximal supercurrent. In this article we show that this result is consistent with the assumption of (spin-triplet) odd-parity pairing. Using a generalized Ginzburg-Landau theory for the specific geometry of the experimental device, it is shown that there are two contributions to the Josephson current. One is due to a proximity-induced s-wave component in Sr2 Ru04, and the other is due to the intrinsic odd­ parity order parameter. These two components have opposite sign and lead to a competition below the onset of superconductivity in Sr2Ru04 yielding the anomalous properties. Two possible test experiments for this kind of scenario are proposed. 53

USp(2k) Matrix Model: F Theory Connection

Abstract: We present a zero-dimensional matrix model based on USp(2k) with supermultiplets in symmetric, antisymmetric and fundamental representations. The four-dimensional com­ pactification of this model naturally captures the exact results of Sen 1) in F theory. Eight dynamical and eight kinematical supercharges are found, as required for critical string inter­ pretation. The classical vacuum has ten coordinates and is equipped with orbifold structure. We clarify the issue of spacetime dimensions which F theory represented by this matrix model produces.

Canonical structure of locally homogeneous systems on compact closed 3-manifolds of types e3, nil and sol

Abstract: In this paper we investigate the canonical structure of diffeomorphism invariant phase spaces for spatially locally homogeneous spacetimes with 3-dimensional compact closed spaces. After giving a general algorithm to express the diffeomorphisminvariant phase space and the canonical structure of a locally homogeneous system in terms of those of a homogeneous system on a covering space and a moduli space, we completely determine the canonical structures and the Hamiltonians of locally homogeneous pure gravity systems on orientable compact closed 3-spaces of the Thurstontype E 3 , Nil and Sol for all possible space topologies and invariance groups. We point out that in many cases the canonical structure becomes degenerate in the moduli sectors, which implies that the locally homogeneous systems are not canonically closed in general in the full diffeomorphism-invariant phase space of generic spacetimes with compact closed spaces.

Gravitino Overproduction through Moduli Decay

Abstract: We derive cosmological constraints on the masses of generic scalar fields which decay only through gravitationally suppressed interactions into unstable gravitinos and ordinary particles in the supersymmetric standard model. For the gravitino mass 100 GeV -1 TeV, the scalar masses should be larger than 100 TeV to insure the validity of big-bang nucleosynthesis if no late-time entropy production dilutes the gravitino density.

Galilei covariance and (4,1)-de sitter space

Abstract: A vector space G is introduced such that the Galilei transformations are considered linear mappings in this manifold. The covariant structure of the Galilei Group (Y. Takahashi, Fortschr. Phys. 36 (1988) 63; 36 (1988) 83) is derived and the tensor analysis is developed. It is shown that the Euclidean space is embedded the (4,1) de Sitter space through in G. This is an interesting and useful aspect, in particular, for the analysis carried out for the Lie algebra of the generators of linear transformations in G.

Supersymmetry-Breaking Models of Inflation

Abstract: We consider dynamical models of supersymmetry breaking which naturally incorporate cosmological inflation. The inflaton plays an inevitable role in dynamical SUSY breaking, and the hierarchical scales of inflation and SUSY breaking are simultaneously realized through a single type of dynamics.

Angular Diameter Distances in Clumpy Friedmann Universes

Abstract: Solving null-geodesic equations, behavior of angular diameter distances is studied in inhomogeneous cosmological models, which are given by performing N-body simulations with the CDM spectrum. The distances depend on the separation angle of ray pairs, the mass and the radius of particles cosisting of galaxies and dark matter balls, and cosmological model parameters. The calculated distances are compared with the Dyer- Roeder distance, and after many ray-shooting, the average, dispersion and distribution of the clumpiness parameter are derived.

Renormalization Group Flow near the Superconformal Points in N=2 Supersymmetric Gauge Theories

Abstract: The behavior of the beta-function of the low-energy effective coupling is determined near the superconformal points in moduli space for two cases, the N = 2 supersymmetric SU(2) QCD with several massive matter hypermultiplets and the SU(3) Yang-Mills theory. The renormalization group flow is unambiguously fixed by looking at limited types of deformation near the superconformal points. It is pointed out that the scaling dimension of the beta­ function is controlled by the scaling behavior of moduli parameters, and the relation between them is explicitly worked out. Our scaling dimensions for the beta-functions are consistent in part with the results obtained recently by Bilal and Ferrari using a different method for the SU(2) QCD.

The Information Loss Problem of Black Hole and the First Order Phase Transition in String Theory

Abstract: In recent years, Susskind, Thorlacius and Uglum have proposed a model for strings near a black hole horizon in order to represent the quantum mechanical entropy of the black hole and to resolve the information loss problem. However, this model is insufficient because they did not consider the metric modification due to massive strings and did not explain how to carry information from inside of the horizon to the outside world. In this paper, we present a possible, intuitive model for the time development of a black hole in order to solve the information loss problem. In this model, we assume that a first order phase transition occurs near the Hagedorn temperature and the string gas changes to hypothetical matter with vanishing entropy and energy which we call `the Planck solid'. We also study the background geometry of black holes in this picture and find out that there is no singularity within the model.

Non-Linear Vorticity-Density Coupling in Lagrangian Dynamics

Abstract: We present a general Lagrangian formalism that allows for the treatment of vorticity. We give solutions for the rotational perturbations up to third-order in a flat background universe. We show how the vorticity affects the evolution of the density fluctuation in high-density regions.

A Maximum Mass-to-Size Ratio in Scalar-Tensor Theories of Gravity

Abstract: We derive a modified Buchdahl inequality for scalar-tensor theories of gravity. In general relativity, Buchdahl has shown that the maximum value of the mass-to-size ratio, $2M/R$, is 8/9 for static and spherically symmetric stars under some physically reasonable assumptions. We formally apply Buchdahl's method to scalar-tensor theories and obtain theory-independent inequalities. After discussing the mass definition in scalar-tensor theories, these inequalities are related to a theory-dependent maximum mass-to-size ratio. We show that its value can exceed not only Buchdahl's limit, 8/9, but also unity, which we call {\it the black hole limit}, in contrast to general relativity. Next, we numerically examine the validity of the assumptions made in deriving the inequalities and the applicability of our analytic results. We find that the assumptions are mostly satisfied and that the mass-to-size ratio exceeds both Buchdahl's limit and the black hole limit. However, we also find that this ratio never exceeds Buchdahl's limit when we impose the further condition, $\rho-3p\ge0$, on the density, $\rho$, and pressure, $p$, of the matter.

Topological Appearance of Event Horizon: What Is the Topology of the Event Horizon That We Can See?

Abstract: The topology of the event horizon (TOEH) is usually believed to be a sphere. Nevertheless, some numerical simulations of gravitational collapse with a toroidal event horizon or the collision of event horizons are reported. Considering the indifferentiability of the event horizon (EH), we see that such non-trivial TOEHs are caused by the set of endpoints (the crease set) of the EH. The two-dimensional (one-dimensional) crease set is related to the toroidal EH (the coalescence of the EH). Furthermore, examining the stability of the structure of the endpoints, it becomes clear that the spherical TOEH is unstable under linear perturbation. On the other hand, a discussion based on catastrophe theory reveals that the TOEH with handles is stable and generic. Also, the relation between the TOEH and the hoop conjecture is discussed. It is shown that the Kastor-Traschen solution is regarded as a good example of the hoop conjecture by the discussion of its TOEH. We further conjecture that a non-trivial TOEH can be smoothed out by rough observation in its mass scale.

Sterile Neutrinos in a Grand Unified Model

Abstract: Recent experimental results indicating the existence of neutrino oscillations may strongly suggest that at least one more light neutrino species is required in order to reconcile the existing data In simple GUT frameworks, this fact seems not to preserve the parallelism between quarks and leptons In this paper, we investigate an 80(10) grand unified model with a pair of extra generations in addition to the known three generations Using the GUT relations, the obtained neutrino mass matrix naturally indicates that one of the 8U(2)L singlet (sterile) neutrinos is very light and has a large mixing with the muon neutrino This can explain the atmospheric neutrino anomaly, and the existence of the hot dark matter neutrino is also indicated The solar neutrino problem can be solved by considering the mixing with the muon neutrino consistently with quark mixing, namely, the Cabibbo angle

Quantum Analysis and Nonequilibrium Response

Abstract: The quantum derivatives of $e^{-A}, A^{-1}$ and $\log A$, which play a basic role in quantum statistical physics, are derived and their convergence is proven for an unbounded positive operator $A$ in a Hilbert space. Using the quantum analysis based on these quantum derivatives, a basic equation for the entropy operator in nonequilibrium systems is derived, and Zubarev's theory is extended to infinite order with respect to a perturbation. Using the first-order term of this general perturbational expansion of the entropy operator, Kubo's linear response is rederived and expressed in terms of the inner derivation $\delta_{{\cal H}}$ for the relevant Hamiltonian ${\cal H}$. Some remarks on the conductivity $\sigma (\omega)$ are given.