Showing papers in "Journal of the Physical Society of Japan in 1973"
TL;DR: In this paper, it was shown that the N -soliton collision in the Modified Korteweg-de Vries equation is essentially the same as that in the k-means soliton collision.
Abstract: It is shown that the Modified Korteweg-de Vries equation can be solved exactly by the “inverse scattering method.” As the special case, the N -soliton solution is obtained explicitly. It is found that N -soliton collision in the Modified Korteweg-de Vries equation is essentially the same as that in the Korteweg-de Vries equation; N -soliton collision is described as the successive collisions of two solitons and there is no effect of multiparticle collisions. Moreover, it is shown that the Modified Korteweg-de Vries equation has new families of the solution.
449 citations
TL;DR: In this paper, the effect of spin fluctuations on itinerant electron ferromagnetism was extended to include the ferromagnetic phase and the correction to the Hartree-Fock free energy as a function of magnetization was expressed in terms of the transversal dynamical susceptibilities.
Abstract: The theory of the effect of spin fluctuations on itinerant electron ferromagnetism, which we have developed previously, is extended to include the ferromagnetic phase. The correction to the Hartree-Fock free energy as a function of magnetization is expressed in terms of the transversal dynamical susceptibilities and is actually calculated by using a modified random phase approximation for the dynamical susceptibilities; the random phase approximation is modified so as to give a consistent static limit throughout the whole temperature range covering both below and above the Curie point. As a result, the magnetization at low temperatures shows a T 3/2 dependence due to the spin wave excitations, the Curie temperature is generally lowered from the Stoner (Hartree-Fock) value and the magnetic susceptibility above the Curie temperature shows an approximate Curie-Weiss behavior.
307 citations
TL;DR: In this article, a tensor operator method is employed in order to take account of the individual characters of the energy levels involved in the transition and the typical transition probability is also made on the lowest-order parity-allowed processes in nearest neighbour ions.
Abstract: Calculations made of the rates for several processes involving interactions between rare earth ions in crystals, such as resonance energy transfer, cooperative excitation transfer and cooperative optical transitions These processes are assumed to originate from the electric multipole interactions between the ions concerned A tensor operator method is employed in order to take account of the individual characters of the energy levels involved in the transition Evaluation of the typical transition probability is also made on the lowest-order parity-allowed processes in nearest neighbour ions The rates for the resonance transfer and cooperative transfer processes thus estimated are much smaller than those obtained by Miyakawa and Dexter
238 citations
TL;DR: In this paper, a simple expression for the magnetoresistance of the antiferromagnetic metals due to the electron-spin scattering by the s -d interaction is obtained using the molecular field approximation for the spin system.
Abstract: A simple expression for the magnetoresistance of the antiferromagnetic metals due to the electron-spin scattering by the s - d interaction is obtained using the molecular field approximation for the spin system The expression includes the ferromagnetic case It is shown that in the antiferromagnetic case the positive magnetoresistance appears below the transition point, in contrast to the negative-magnetoresistance in the case of the para or ferromagnetic case In the ferromagnetic case the negative magnetoresistance shows a deep and finite valley at the transition point, which is consistant with the experiments of the ferromagnetic rare-earth metals such as Gd and Tb
178 citations
TL;DR: In this article, the angular distribution of scattered light (or the particle scattering factor) of the stiff chain polymers is calculated by assuming an appropriate Fourier transform of the distribution function of this polymer chain.
Abstract: The angular distribution of scattered light (or the particle scattering factor) of the stiff chain polymers is calculated by assuming an appropriate Fourier transform of the distribution function of this polymer chain. For very small and very large scattering angles the result is respectively reduced to the forms of the Debye's scattering factor for random coil chain and to that for rigid rod molecule. By assuming that the polymer chain expansion by intramolecular forces is uniform, but the contour length is kept as constant the excluded volume effect on the angular distribution is calculated. The result shows that the transition point of scattering curve which gives a boundary between random coil- and rigid rod-scatterings is inversely proportional to the square of molecular expansion coefficient. This is in qualitative agreement with the recent experimental results by Wada and other. An approximate distribution function which gives the correct second and fourth moments of the chain end to end distance i...
140 citations
TL;DR: In this paper, the emission, excitation and reflection spectra at 300, 80 and 15 K were obtained, and the parameters, F 0, G, ζ and R th, were calculated with the aid of the theories known in alkali halides.
Abstract: The emission, excitation and reflection spectra at 300, 80 and 15 K were obtained. The blue emission at 442 mµ was observed for CaS:Sb 3+ as well as the well-known yellow-green emission at 540 mµ. In the excitation or reflection spectra, A , B and C bands were found for all phosphors of Ca(S:Se):Sb 3+ investigated. These positions are 392, 345 and 321 mµ for CaS:Sb 3+ , and 428, 376 and 345 mµ for CaSe:Sb 3+ at 80 K. From these peak positions, parameters, F 0 , G , ζ and R th , were calculated with the aid of the theories known in alkali halides. The values of ζ decrease from 0.34 to 0.32 eV as the fraction of CaSe is increased. R th is about 6.8 for all the phosphors of Ca(S:Sb):Sb 3+ investigated.
129 citations
TL;DR: In this article, an analytical model for the spectra due to excitation of a core electron in metal with an incomplete shell was proposed. But the model assumes that the incomplete shell is treated as a nondegenerate localized state interacting with conduction band through the s − d mixing.
Abstract: Analytic features of the spectra due to excitation of a core electron in metal with an incomplete shell are studied with a simple model. The incomplete shell (denoted by d state, representatively) is treated as a nondegenerate localized state interacting with conduction band through the s – d mixing. It is assumed that in the initial state of the absorption the unoccupied d level is well above the Fermi energy e F while in the final states the d level of the excited atom is lowered down to e d due to the core hole left behind. When e d > e F , the singular absorption edge appears at \(\tilde{\varepsilon}_{\text{F}}\) as expected, with an antiresonance around \(\tilde{\varepsilon}_{d}\). When e d < e F , the singular absorption edge appears at \(\tilde{\varepsilon}_{d}\), the Fermi level threshold being blurred out by the life time effect of the d hole. Emission spectra are also calculated. The results are compared qualitatively with experimental data.
116 citations
TL;DR: In this paper, a high voltage electron microscope was used to study defect formation in gold by the irradiation of 2.0∼2.5 MeV electrons with high voltage.
Abstract: Defect formation in gold by the irradiation of 2.0∼2.5 MeV electrons was studied with a high voltage electron microscope. The formation of dislocation loops by the aggregation of interstitials generally precedes the formation of the defects by vacancies. Permanent sinks, such as specimen surfaces and dislocations, prevent the formation of interstitial type of defects and enhance the formation of vacancy clustered defects. A rapid formation of the vacancy type defects and the simultaneous shrinkage of interstitial type loops after the cessation of the irradiation are observed. Kinetics analysis of the point defect behaviour, standing on the random migration of interstitials and vacancies, explains all the observed various phenomena as the competition processes between two kinds of point defects under various circumstances. The irradiation intensity dependence of the density of interstitial type defects shows that the di-interstitials are their stable nucleus.
115 citations
TL;DR: In this article, exact N -soliton solutions have been obtained for the nonlinear lumped self-dual network equations, where N is the number of nodes in the network.
Abstract: Exact N -soliton solutions have been obtained for the nonlinear lumped self-dual network equations
115 citations
TL;DR: In this paper, the relation between a nonlinear (exponential) lattice, the Boussinesq equation and the Korteweg-de Vries equation is clarified and the exact solutions for the two-soliton state are given in each case for both the head-on and the overtaking collisions.
Abstract: Relations between a nonlinear (exponential) lattice, the Boussinesq equation and the Korteweg-de Vries equation are clarified and therefrom the exact solutions for the two-soliton state are given in each case for both the head-on and the overtaking collisions.
108 citations
TL;DR: In this article, the method of derivative-expansion with multiple scales is applied in a generalized from to the analysis of weak nonlinear dispersive waves, and a nonlinear Schrodinger equation is derived from the condition that the perturbation expansion be free from secular terms.
Abstract: The method of derivative-expansion with multiple scales is applied in a generalized from to the analysis of weak nonlinear dispersive waves. It is shown that in a certain case a nonlinear Schrodinger equation, which describes a nonlinear slow amplitude modulation of wave trains, can be derived from the condition that the perturbation expansion be free from secular terms. A reduction to the Korteweg-de Vries equation for long waves is also discussed.
TL;DR: In this paper, a galvanic cell is used to detect the electrochemical potential of Ag +, since the interdiffusion of Cu + into AgI is nearly forbidden except near Cu 2 Se.
Abstract: The phase diagram is studied by X-ray and thermal analyses. The high temperature phase (α) is the solid solution of b.c.c. or f.c.c. in which Ag + , Cu + and electron are mobile. The galvanic cell Ag|AgI|specimen|Pt is available to controle the excess or deficit Ag density and to detect the electrochemical potential of Ag + , since the interdiffusion of Cu + into AgI is nearly forbidden except near Cu 2 Se. With the help of the cell and utilizing the weight-difference between Ag and Cu, the polarization and the interdiffusion are measured and interpreted with the diffusion theory. The electronic and ionic conductivities are measured with varying temperature and x . Further the various properties of α(Ag, Cu) 2 Se such as the conductivity, Hall coefficient, thermoelectric power, thermal conductivity etc. are measured and compared with the theory, indicating that the energy gap decreases with increasing x .
TL;DR: The magnetic properties of the insulating Heisenberg ferromagnet K 2 CuF 4 have been studied by neutron diffraction as discussed by the authors, where a strong paramagnetic diffuse scattering of the form of ridge was observed near T c =6.25 K supporting the two-dimensional nature of this compound.
Abstract: The magnetic properties of the insulating Heisenberg ferromagnet K 2 CuF 4 have been studied by neutron diffraction. A strong paramagnetic diffuse scattering of the form of ridge was observed near T c =6.25 K supporting the two-dimensional nature of this compound. From the asphericity of this scattering, the ratio of the exchange constants both in the weakest and the strongest directions was determined as J '/ J =0.00066. Below T c , ferromagnetism appears with the spin aligned parallel to the c -plane. As K 2 CuF 4 has no Ising-like symmetry, though the crystal structure is the same to that of K 2 NiF 4 , marked contrast appears. for instance, it behaves as a typical simple three-dimensional ferromagnet like M s ( T )∝(1- C T 3/2 ) up to T / T c ∼0.86, β=0.33 and 2ν=1.35.
TL;DR: In this article, an approximate method of studying interactions between two solitary waves which propagate in opposite directions is presented, where the solution is described by s superposition of two solitary wave which are governed by their respective Korteveg-de Vries equation.
Abstract: An approximate method of studying interactions between two solitary waves which propagate in opposite directions is presented In the first approximation, the solution is described by s superposition of two solitary waves which are governed by their respective Korteveg-de Vries equation The second order approximation gives a small correction where the two waves overlap one another The method is extended to the system, in which there exist n “quasi-simple” waves (the simple waves under the effects of higher derivative terms, such as dispersions of dissipations) The possibility that n “quasi-simple” waves can be superposed to describe nonlinear systems is studied Applications to ion acoustic waves in collisionless plasmas and shallow water waves are discussed
TL;DR: In this paper, a computer simulation of the step-wise reactions among vacancies up to large vacancy clusters is contrived to analyze the clustering process in an exhausting system as quenched-in vacancies and the variations of the progress of vacancy clustering with aging temperature and with the size of stable nucleus are investigated.
Abstract: A method to perform a computer simulation of the step-wise reactions among vacancies up to large vacancy clusters is contrived to analyze the clustering process in an exhausting system as quenched-in vacancies. The variations of the progress of vacancy clustering with aging temperature and with the size of stable nucleus are investigated. Initial transient decrease of mobile vacancies with a rapid increase of small vancancy complexes establishes mutual quasi-equilibrium. Stationary stage of small vacancy complexes following the initial transient corresponds to the nucleation period of vacancy clustered defects. Factors which determine the size distribution of final clusters are discussed. Existence of a definite stable nucleus for a dislocation loop in aluminum is denied. Agreement of the computed results with experiment is obtained when small binding energies of a vacancy to vacancy clusters are postulated, i.e. , less than 0.2 eV up to the cluster of forty vacancies.
TL;DR: In this paper, the behavior of a gas in contact with its condensed phase is considered on the basis of a relaxation model of the linearized Boltzmann equation, and the temperature and density distributions of the gas in the Knudsen layer as well as so called slip boundary condition on the interface of the Gas and its Condensed phase are obtained.
Abstract: The behavior of a gas in contact with its condensed phase is considered on the basis of a relaxation model of the linearized Boltzmann equation. The temperature and density distributions of the gas in the Knudsen layer as well as so called slip boundary condition on the interface of the gas and its condensed phase are obtained.
TL;DR: In this paper, the path integral method applied to an electron interacting with acoustic as well as with optical modes of lattice vibrations is shown to cause the abrupt change, as coupling increases, of the polaron state from nearly free type to self-trapping type.
Abstract: With Feynman's path integral method applied to an electron interacting with acoustic as well as with optical modes of lattice vibrations, it is shown that the abrupt change, as coupling increases, of the polaron state from nearly free type to self-trapping type is caused by the short range interaction (deformation potential due to acoustic vibrations) but not by the long range interaction (electric polarization field due to optical vibrations), in agreement with previous argument. Whether or not one takes into account the discreteness of electron coordinate has no relevance to the very existence of the abrupt change, although the quasi-continuum model leads to underestimation of its magnitude. When the rigid lattice band width is not large compared to the average phonon energy, however, one can no more distinguish between the nearly free state and the self-trapping state in a clear-cut way.
TL;DR: In this paper, the motions of a vortex tube with an elliptic cross section and a vortex sheet of finite length in an inviscid, incompressible fluid are simulated by a number of discrete vortex filaments, each vortex moving under the action of the velocity field of all the other vortices.
Abstract: The motions of a vortex tube with an elliptic cross section and of a vortex sheet of finite length in an inviscid, incompressible fluid are simulated by a number of discrete vortex filaments, each vortex moving under the action of the velocity field of all the other vortices. By the use of this simulation, rotation of the vortex tube and rolling-up of the vortex sheet are investigated numerically as initial value problems. Comparison with exact solutions shows the validity of this method of approximation. In order to improve the results, an artificial viscosity is introduced to the equations of motion. This diminishes randomization of vortices inherent to the treatment without viscosity and thus leads to regular rolling-up of a vortex sheet.
TL;DR: In this article, the Ising of spin 1/2 with the nearest-neighbor interaction, in which nonmagnetic impurity atoms are dissolved, is investigated based on the identity =, decoupling approximation is introduced for treating the many-spin correlation functions.
Abstract: The Ising of spin 1/2 with the nearest-neighbor interaction, in which nonmagnetic impurity atoms are dissolved, is investigated. Based on the identity = , decoupling approximation is introduced for treating the many-spin correlation functions. The dependences of the critical temperature and of the spontaneous magnetization on the impurity concentration are calculated for two- and three-dimensional lattices. The results for the critical temperature and the critical concentration are better than the results of the results of the extended molecular-field approximations of Mamada and Takano, or of Oguchi and Obokata. Especially for the three-dimensional lattices the critical obtained agrees with that of Sykes and Essam, estimated from the series expansion.
TL;DR: In this article, the optical discernibility between domains connected by a second-order state shift is discussed. And the styles and directions of mechanical, electrical or combined forces effective on these secondorder state shifts are expounded with simple examples.
Abstract: The ferroic state shifts higher by one order than the ferroelectric state shifts and the ferroelastic ones are considered. (Nonmagnetism is assumed.) The styles and directions of mechanical, electrical or combined forces effective on these second-order state shifts are expounded with simple examples. The orders of magnitude of the “coercive forces” for these state shifts are estimated. The optical discernibility between domains connected by such a state shift is discussed.
TL;DR: In this article, the spontaneous volume magnetostriction of Fe-Ni and Ni-Cu alloys at 0 K evaluated from their thermal expansion curves can be quantitatively explained on the basis of the collective electron model, using the density of states curve for nickel.
Abstract: Thermal expansion measurements were made on f.c.c. Fe-Ni and Ni-Cu alloys from liquid helium temperature up to 1000 K. The spontaneous volume magnetostriction of these alloys at 0 K evaluated from their thermal expansion curves can be quantitatively explained on the basis of the collective electron model, using the density of states curve for nickel. The lattice constants of these alloys at various temperatures evaluated from their thermal expansion curves deviate from Vegard's law in the Invar region. This deviation is discussed in connection with the magnetic state of the Invar alloy and with the origin of the Invar effects.
TL;DR: In this article, a general theory of spin-dependent phonon Raman scattering in magnetic crystals is developed, where the integrated Raman intensity as a function of temperature is expressed as S (T )=( n 0 + 1)| R + M | 2, where the first term represents the spin independent part and the second one the spin- dependent part which is proportional to the nearest neighbor spin correlation function.
Abstract: A general theory of the spin-dependent phonon Raman scattering in magnetic crystals is developed. The integrated Raman intensity as a function of temperature is expressed as S ( T )=( n 0 +1)| R + M | 2 , where the first term represents the spin-independent part and the second one the spin-dependent part which is proportional to the nearest neighbor spin correlation function . Three types of temperature variation of intensity are predicted in ferromagnetic and antiferromagnetic cases, depending on values of R / M . Two microscopic mechanisms, variation of the d electron transfer with lattice vibrations and that of the non-diagonal exchange, contribute to the spin-dependent part, and it is shown that the former is essentially important in producing the large temperature variation. The theory is applied to explaining the observed temperature variation of various Raman active phonon modes in CdCr 2 S 4 and the experimental results are explained successfully.
TL;DR: In this article, exact N -soliton solutions for the nonlinear lumped network equation have been obtained for the Korteweg-de Vries equation with functional forms similar to the functional forms of the N soliton solution.
Abstract: Exact N -soliton solutions have been obtained for the nonlinear lumped network equation, \(\frac{\partial^{2}}{\partial t^{2}}\log(1+V_{n}(t)){=}V_{n+1}(t)+V_{n-1}(t)-2V_{n}(t)\). The solutions have the same functional forms as the N -soliton solution of the Korteweg-de Vries equation.
TL;DR: In this paper, the H band has an asymmetric shape tailing to the low energy side and the peak energy, measured from the exciton band, varies linearly with temperature.
Abstract: Super-linear luminescences of cuprous halide crystals under the high density excitation by an N 2 -laser have been studied at temperatures above 100 K, where excitons and free charge carriers are considered to co-exist. A new emission, which is called H band, is found in CuCl, CuBr and CuI crystals. The H band has an asymmetric shape tailing to the low energy side. The peak energy, measured from the exciton band, varies linearly with temperature. By assuming that the emission is due to the interaction of exciton with free electron, the properties of the H band are explained and the effective masses of the electron and hole are obtained as m e =0.43 m o , m h =4.2 m o in CuCl, m e =0.28 m o , m h =1.4 m o in CuBr and m e =0.33 m o , m h =14 m o in CuI crystals.
TL;DR: In this article, the electroreflectance of Cd x Hg 1-x Te alloys for x from 0 to 0.70 and for x = 0.97 and x = 1 was measured by the electrolyte technique in the range of photon energy 0.5 to 6 eV at room temperature.
Abstract: The electroreflectance of Cd x Hg 1- x Te alloys for x from 0 to 0.70 and for x =0.97 and x =1 was measured by the electrolyte technique in the range of photon energy 0.5 to 6 eV at room temperature. The E 0 + Δ 0 , E 1 , E 1 + Δ 1 and E 0 ' transitions were investigated as a function of alloy composition. The transition energies at critical points show quadratic dependence on the alloy composition. The deviations from linearity are interpreted by using the dielectric two band method. The spin-orbit splitting Δ 0 at k =0 for HgTe was measured directly as 1.08±0.02 eV at room temperature.
TL;DR: In this paper, the high-temperature susceptibilities and specific heats have been extended up to the eighth and seventh order, respectively, for general spin by means of the method of Rushbrooke and Wood with the aid of high speed computers.
Abstract: With the honeycomb, square and triangular lattices the high-temperature susceptibilities and specific heats have been extended up to the eighth and seventh order, respectively, for general spin by means of the method of Rushbrooke and Wood with the aid of high-speed computers. Analyses of these coefficients by means of the ratio and Pade approximant methods seem to give evidences for non-divergence at finite temperatures of the high-temperature susceptibilities of the two-dimensional ferromagnetic Heisenberg spin systems contrary to the assertion of Stanley and Kaplan.
TL;DR: The theory of nonlinear wave modulation in a collisionless plasma is developed on the basis of the Vlasov description, with particular attention to the nonlinear Landau damping process associated with resonance effects at the group velocity of the wave.
Abstract: The theory of nonlinear wave modulation in a collisionless plasma is developed on the basis of the Vlasov description, with particular attention to the nonlinear Landau damping process associated with resonance effects at the group velocity of the wave. Contributions from resonance particles, moving at the group velocity, change the nonlinear Schrodinger equation, derived in previous investigations, into the following equation, \(i\frac{\partial}{\partial\tau}\phi+p\frac{\partial^{2}}{\partial\xi^{2}}\phi+q|\phi|^{2}\phi+s\frac{\mathfrak{B}}{\pi}\int\frac{|\phi(\xi',\tau)|^{2}}{\xi-\xi'}\mathrm{d}\xi'\phi{=}0\), where φ(ξ,τ) is the small but finite potential amplitude, and τ and ξ are stretched variables in the “reductive perturbation” theory. \(\mathfrak{B}\) denotes a Cauchy principal part. Besides giving rise to the nonlocal-nonlinear term, the contribution of these resonant particles reverse the sign of the nonlinear coupling coefficient, q , relative to the value calculated neglecting their effect.
TL;DR: In this article, the long-wavelength lattice vibrations in ammonium sulfate are analyzed group-theoretically, and symmetry coordinates of external modes belonging to the irreducible representation B 1 u, which is responsible for the phase transition from D 2 h to C 2 v, are obtained.
Abstract: Long-wavelength lattice vibrations in ammonium sulfate are analysed group-theoretically, and symmetry coordinates of external modes belonging to the irreducible representation B 1 u , which is responsible for the phase transition from D 2 h to C 2 v , are obtained. They are composed of two groups; one is made of the purely translational and polar modes, and the other is made of the purely librational and nonpolar modes. Some peculiar properties of ammonium sulfate, including, especially, the very small value of the Curie-Weiss constant, are explained phenomenologically by a model in which a normal mode with a large component of a librational nonpolar mode admixed with a small contribution of a translational polar mode becomes soft.
TL;DR: In this paper, a new solution of solitary pulses in three-wave interactions is obtained, which were not given in the previous paper, which was applied to the interaction among two Alfven waves and an ion-acoustic wave, which propagate along the external magnetic field.
Abstract: New solutions of solitary pulses in three-wave interactions are obtained, which were not given in the previous paper of this series. In those solutions, the wave of lower frequency has a shock-type envelope and behaves as a “pump” while the other two waves have the pulse-type ones. In addition, by considering two effects, linear translations of the waves and nonlinear interactions, a physical mechanism of formation of the solitary pulses is found. The theory is applied to the interaction among two Alfven waves and an ion-acoustic wave, which propagate along the external magnetic field,