Showing papers in "Progress of Theoretical Physics in 1974"

A Method for Finding N-Soliton Solutions of the K.d.V. Equation and K.d.V.-Like Equation

Abstract: To find N-soliton solutions of the K.d.V. equation, a method which can be also applicable to the so-called K.d.V.-like equation is presented. This equation belongs to another series than the class of equations solvable bv inverse scattering method for Schrodinger equation.

Connection of Dual Models to Electrodynamics and Gravidynamics

Abstract: It is shown that the Virasoro-Shapiro model contains Einstein's theory of gravity as a zero-slope limit. It is also shown that the conventional dual model contains the scalar electrodynamics as a zero-slope limit. The connection between the generating functionals for the scattering matrices of these dual models and the corresponding field theories is demonstrated.

New Universality of Critical Exponents

Abstract: Here is proposed a new (or weak) universality that reduced critical exponents r=r/v, fi=[j/v', 1=£1/v, ¢= (2-a,) /11, etc., as well as r; and iJ are independent of the details of the system Hamiltonian. Two concepts of scaling laws and universality1l have been main motives for recent investigations of critical phenomena. The scaling law has been confirmed in many examples. We find, however, several counter-examples against the ordinary universality which claims that critical exponents themselves depend only upon such fundamental parameters as dimensionality d, symmetry (or the degree of freedom n) and potential-range parameter a. One of such typical counter-examples will be the eight-vertex modeFl in which critical exponents vary continuously as the strength of interaction changes. Here we propose a new concept of universality which covers "apparently" exceptional cases such as the eight-vertex model. The old universality is concerned with critical exponents defined by the power of the singularities of physical quantities with respect to the temperature difference from the critical point Tc. However, does the temperature difference have an absolute meaning in critical phenomena? There exist many examples indicating that it is not the case, as will be shown later. Instead of the temperature difference itself, the inverse correlation length tC plays an essential role in critical phenomena. Thus, our new proposal is that critical exponents defined through IC instead of the variable TTc should be universal. That is, our new universality claims that reduced critical exponents

Spontaneous breaking of chiral symmetry in a vector-gluon model

Abstract: Solutions of the self-consistent equation for fermion propagator in a vector-gluon model are fully examined. The equation is characterized by a set of parameters, i.e., the coupling constant g, the bare mass of the fermion mo and the cutoff A. It is proved that with a suitable gauge chosen, the equation without ~utoff has solutions ·only in the case mo=O, It is then shown that, if g'/4n Bn, the "normal-state" solution for the equation without cutoff, even if it existed, should necessarily have an unphysical singularity. This fact implies that the "normal-state" solution becomes unstable for a su.fficiently large value of g'. § l. Introduction The. reason for success of low energy theorems obtained by current algebra and PCAC-treatment may be well understood in terms of chiral symmetry in which the pseudoscalar mesons play a special role among hadtons as the Nambu­ Goldstone (NG) bosons1l transforming nonlinearly under chiral transformation. On the other hand, in the composite hadron models based on SU(3) or SU(6), it is clear that there is no vital distinction between pseudoscalar mesons and others such as vector- and tensor-mesons. It is therefore worth expecting that the pseudoscalar NG bosons can also be interpreted as the bound states in con­ formity with the viewpoint of the composite model. . This homogeneity and· heterogeneity ot the pseudoscalar mesons to other mesons should rather be in­ vestigated by comparing their internal structure with composite particles· . . In this respect it would be meaningful to study a model in which spontaneous breaking of chiral symmetry is realized by a composite NG boson: The Nambu­ Jona-Lasinio model2l is known as such an example. However, the use of chain approximation and the momentum cutoff inevitable for the local four-fermion

Irreversible Circulation of Fluctuation

Abstract: Irreversible circulation of fluctuation around the steady state, or cyclic balance, is useful in describing coupled degrees of freedom at off-equilibrium situation. When it entails instability, a macroscopic orbital revolution may appear, which is characteristic to far from equilibrium situation.

Irreversible Circulation and Orbital Revolution Hard Mode Instability in Far-from-Equilibrium Situation

Abstract: The need and the use of the concept\" of cyclic balance and irreversible circulation are demonstrated by a chemically reacting system with two ind~pendent degrees of ,freedom.· Under the presence of auto-catalytic channel, the reaction network may lead to instabilities. at a certain threshold for the controllable major reactant.. Attention is concentrated on the hard mode instability in particular, which leads to an orbital revolution. of the distribution function. By looking at the evolution of fluctuation as well as the drift, one finds that the irreversible circulation becomes singular at the marginal situation. The resulting limit cycle is just a macroscopic manifestation of the dynamically directed property which is latent in the fluctuation below threshold. The state beyond 'the threshold is analyzed with PrigogineLefever-Nicolis model. Emphasis is placed' on the fact· tha't temporal .oscillation is ·a new type of order which appears only far from equilibrium.

Higher Order Gravitational Potential for Many-Body System

Abstract: Gravitational potential for many-body system is obtained up to post-post-Newtonian order of approximation from the metric tensor derived previously, which is Minkowskian at spatial infinity. The calculation is based on the Lagrangian of Fokker type. The transverse­ traceless part of the metric tensor contributes to the potential of post-post-Newtonian order, even to the G3-static part. The fact that the G3-static potential includes the contribution from the transverse-traceless part is the manifestation of non-linear nature of the theory of gravity. The gravitational potential obtained here coincides with that calculated in the canonical formalism, but does not coincide with that obtained in the conventional formalism of quantized theory.

Effect of Magnetic Field on Sound Propagation near Magnetic Phase Transition Temperatures

Abstract: The anomalous ultrasonic attenuation and velocity variation caused by the critical fluctuation of spins near the Curie and N~el temperatures are theoretically investigated and found to be stronglY:. affected by an application of magnetic field. In the random phase approximation, the attenuation coefficient is expressed in terms of a sum of the two terms; a cross term of the static spin polarizatlpn and th~ two-spin correlation function, and a product of the -tw.O~spin correlation functions. In the :tnagnetic field, the former term has a positive contribution. to the attel\\uation, since this term has a finite value only when the static spin polarization exists. The'-latter term decreases in the field, owing to the suppression of spin thermal fluctu;ations due to the magnetic field. The magnitude of the contributions from these terms depends upon temperature, the strength of magnetic field and the nature of the exchange interaction in magnetic materials. The theory explains various types of the field dependence of the attenuation observed in magnetic materials including MnP, Dy and MnF2• A new attenuation peak found recently by Hirahara et al. in the paramagnetic phase of MnP under a magJ~etic field is explained on the basis of the present theory.