We have considered the application of the Hirota bilinear method of the soliton theory to the problem of solving the Ernst equation in general relativity. As a concrete example, we have investigated the Tomimatsu-Sato (TS) solutions. We have found (i) the explicit form of the bilinear relations relevant to the TS solutions and (ii) that the TS solutions can be compactly expressed by the pfaffians whose elements are expressed by the Legendre functions. The TS solutions comply with the soliton conjecture that high-dimensional solitons are always expressed by special functions.

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Critical behavior associated with the helical or noncollinear ordering for isotropic n>3-component spins is studied near d=2 dimensions based on an O(n)×O(2) nonlinear σ model and the renormalization-group ε=d−2 expansion. A chiral fixed point is found for general n characterized by the critical exponents that are consistent with the previous 1/n expansion calculation. For n=3, it is argued that because of the nontrivial global topology of the order-parameter space, Π₁(SO(3))=Z₂, and the possible existence of a finite-temperature topological transition at d=2, the standard ε=d−2 expansion technique is not applicable.

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Dipolar interaction in two-dimensional space, (p_i·p_j)r⁻²−2(p_i·r)(p_j·r)r⁻⁴, is investigated upon uniaxial dipoles on the square lattice. Fourier transform D(q) of this interaction is analyzed and expressed in terms of rapidly convergent series. In the uniaxial dipole system, D(q) is shown to have a minimum value at q=π⁄a(1, 0). An outline of the phase diagram of this uniaxial dipole system, which also has the short-range interaction, is obtained from the mean field approximation and the Monte Carlo simulation.

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In order to determine whether or not the two events with the charge of Z=14 and the mass number of A≅370 recently observed in cosmic rays are super-hypernuclei (or strange quark matter) as claimed, the charge-to-mass-number ratio (Z⁄A) of the super-hypernuclei is investigated in the quark-shell model. Although a small Z⁄A ratio is always preferable for super-hypernuclei, such a small charge of 3∼30 may be realized as Z\lesssim\sqrt2⁄3A^1⁄2 if the nuclei are created spontaneously from bulk strange quark matter due to the Coulomb attraction.

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From the data of a 3D numerically simulated isotropic turbulence, it is found that the statistics of longitudinal velocity difference in distancer r is different from that of the velocity scale derived from dissipation averaged over a domain of scale r, and then intermittency exponents can hardly be related with exponents of structure functions. The probability distributions in both statistics are comparatively studied from the viewpoint of scale-similarity and modelling to involve multifractality.

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Thermal expansion of mixed-valence compound CeNi has been measured under hydrostatic pressure up to 15 kbar. It is found that the thermal expansion coefficient α(T) is strongly anisotropic, reflecting the noncubic (orthorhombic) crystal structure and is affected largely by applying pressure because of an instability of 4f electrons in this compound. A contribution to α from the valence instability, α_I, is estimated. The results are discussed briefly on the basis of the theory presented by Müller-Hartmann.

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The X-ray diffraction pattern of Langmuir-Blodgett films formed with alternately deposited Cd stearate and Cd behenate exhibits anomalous shifts in the diffraction angles when they have the deposition order with dimerized Cd layers. The magnitude of the reciprocal vector of the n-th order is represented by G_n=nG_a−(−1)ⁿg_n, where G_a is for averaged unit vector and g_n is the shift that changes gradually with the index of diffraction and the multiplicity of the layers.

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We investigate effects of the repulsive interaction U_pd between holes on the nearest-neighbor Cu- and O-sites in the d-p model, a model suitable to describe the CuO₂ plane in high-temperature superconductors. It is found that the condition for a metal-insulator (M-I) transition to occur at the half-filled case is modified. Furthermore, the charge susceptibility is found to be enhanced by U_pd, except for the region around the critical point of the M-I transition; it indeed diverges at a certain value of U_pd. Possible relevance of the enhanced charge susceptibility to the mechanism of the high T_c superconductivity is discussed.

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The electrical resistivity, magnetic susceptibility and specific heat of a ternary intermetallic compound CeNi₂Al₅ have been measured. It is found that CeNi₂Al₅ is a new dense Kondo compound with the Néel temperature of 2.6 K. The temperature dependence of the resistivity has a broad peak at 4.0 K, reflecting the coherence of the Kondo scattering. The ground state of the Ce ions is determined to be a doublet from the result that the entropy equals Rln2 when we include the area of a tail extended by the short-range order. A spin-flip is observed in high magnetic field, and a magnetic phase diagram is roughly estimated.

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We calculate the spatial distribution of the electron density and the dispersion curves of the subband structure for the quantum wire patterned from the GaAs/AlGaAs heterostructure within the framework of the Hartree-Fock approximation. It is shown that electrons move to the part underneath the modulation-doped layer as the strength of the Coulomb interaction is increased, and that the pattern behaviour of the dispersion curve below the Fermi energy depends strongly on the strength of the Coulomb interaction and on the total electron number.

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A mechanism of superconductivity coming from the doping of mobile fermions into the spin dimerized insulator such as spin Peierls state, valence bond glass, Heisenberg spins with next nearest neighbor exchange coupling and the Haldane gap state is discussed. The doping of fermions with narrow band into a Mott insulator with a spin gap results in the superconducting long range order in two- and three-dimensions, while results in the power law divergence of the pairing susceptibility with Tomonaga-Luttinger liquid character of charge in one-dimension. An example of numerical calculation in one-dimension is shown. The possible relevance of this mechanism to high-temperature superconductivity, where dynamical coupling of lattice distortion to spin may play a crucial role, is discussed. A relevant model Hamiltonian with spin-phonon coupling and dynamical spin-Peierls fluctuation is proposed.

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Magnon-magnon interactions in a d-dimensional version of the simple cubic antiferromagnet with anisotropic nearest-neighbor exchange interaction and uniaxial anisotropy energy are studied to show the existence of a stationary self-localized magnon mode appearing below the magnon frequency band. This is an intrinsic nonlinear mode corresponding to a local large-angle, low-frequency precessional motion of spins, quantum states of which are characterized by the indefiniteness of the number of relevant magnons. The formulation of the problem is made by employing the Dyson-Maleev transformation and a coherent-state ansatz. Approximate analytical expressions for the eigenfrequency and profile functions of the stationary self-localized mode are obtained in the strong-localization limit for arbitrary d.

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Neutron diffraction study revealed that a powdered CuFeO₂, a quasi-two-dimensional antiferromagnet on a triangular lattice (AFT), has two successive magnetic phase transitions at low temperatures. In the high-temperature phase below T_N1=16 K, it has a monoclinic magnetic unit cell with five spins in a layer (\sqrt7a×\sqrt7a×2c, γ=141.78°). At T_N2=10 K, it shows a discontinuous transition and enters the low-temperature phase with an orthorhombic magnetic unit cell with four spins in a layer (\sqrt3a×2a×2c). In both magnetic structures, spins are collinear and parallel to the c axis.

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High-frequency diffraction by a strip was previously analyzed approximately by the Geometrical Theory of Diffraction (GTD), but the GTD solution has an essential difficulty that it is valid only in the limited range of incidence and observation angles. To overcome this difficulty, in this paper, plane wave diffraction by a strip is reconsidered using the Wiener-Hopf technique and the complete high-frequency asymptotic solution is obtained, which is uniformly valid everywhere in space and has no restrictions on incidence and observation angles. Further asymptotic expansion is also carried out to derive the non-uniform asymptotic solution, which is compared with the previous GTD solution. As a result, some discrepancies are recognized.

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Recoupling of angular momenta in representation theories of quantum group U_qsl(2) is investigated in relationship to braiding operation.

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Reduction relations for shell-model matrix elements of general operators in normal products (e.g. general many-body operators) are investigated in the framework of the seniority scheme of identical particles. A novel relation for Clebsch-Gordan (CG) coefficients is exploited to remove from reduction factors all the CG coefficients that result from Wigner-Eckart theorem in the quasi-spin space. Reduction factors in the final step have very simple dependence on the number of particles.

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We study the dimensional dependence in the critical behaviour of a system of bulk hadronic matter described by the exponentially rising density of hadronic levels ρ(m)∼cm^a exp (bm), adopting the statistical bootstrap model. We calculate the critical exponents for such system both in the grand canonical and microcanonical ensembles. In a particular case when a+d⁄2<−2, we show that quantum statistical effects change effectively the parameter b leading to the renormalization of the critical temperature.

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Excitation energy spectra of one-kink, kink-antikink and breather modes in the sine lattice equation characterized by the sine-second difference sin (u_n+1−u_n)−sin (u_n−u_n−1) and the on-site term sin (2u_n) are calculated, where u_n is a lattice-field variable associated with an n-th site of a one-dimensional lattice. It is shown that each of these three types of excitations has a one-to-one correspondence to that of the sine-Gordon equation in the case of a weak on-site potential. By exploiting such a correspondence, the ideal-gas phenomenology of kinks is formulated to obtain thermodynamic quantities such as free energy, internal energy, specific heat and pair correlation functions of the u_n’s in the sine lattice.

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The double chain Heisenberg antiferromagnet with anisotropy is studied using the mapping onto the coupled anisotropic nonlinear σ model. This model consists of two anisotropic antiferromagnetic quantum Heisenberg chains with half-integer spin coupled with each other via the ferromagnetic interchain coupling J′. For small J′, our analysis suggests that J′ is an irrelevant parameter and consequently the two chains behave independently and no gap is generated. On the other hand, for large enough J′, the two chains behave as a single Heisenberg chain with integer spin which has a gap in the excitation spectrum. The expected behavior in the isotropic limit is also discussed.

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In the theory of random matrices, the eigenvalue statistics of Hamiltonian ensembles is reduced to one-dimensional classical statistical mechanics of logarithmically interacting particles. Corresponding to one-body external potentials, there may be infinite number of ensembles related to orthogonal polynomials. Gaussian ensembles, which are related to the Hermite polynomials, are usually adopted. We choose general classical orthogonal polynomials and get a wider class of statistical ensembles. The partition functions for these ensembles are given by Selberg’s integral formula. We discuss the thermodynamic limit of this formula and evaluate the free energies, the internal energies, the entropies and the specific heats.

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Nonlinear Alfvén waves in a compressible viscous fluid with thermal and electrical conductivities in the presence of an external magnetic field are investigated by using a nonlinear perturbation method. In the lowest order of perturbation, it is found that the system of equations for the Alfvén waves can be reduced to a nonlinear integro-differential equation. It is shown that in the case of steady propagation this equation has solutions representing the Alfvén shock waves.

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The crystal structure of the ferromagnetic copper oxide La_2−xBa_1+xCuO₅ (x=0.2) has been refined by Rietveld analysis of TOF neutron powder diffraction data taken at room temperature. It is tetragonal with space group P4/mbm, and its lattice parameters are a=0.68652(1) nm and c=0.58698(1) nm. La³⁺ and Ba²⁺ ions form LaO₈ and BaO₁₀ polyhedra, respectively. The La site is 11% occupied by excess Ba atoms, and 2.5% of the Ba site are substituted by La atoms. No deficiencies could be detected in a Cu site or two O sites.

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Hubbard-Beeby theory is applied to investigate collective motions in a superionic conductor α-AgI. By making use of the results of a computer simulation obtained by Vashishta and Rahman and Fukumoto et al., longitudinal optical modes are studied. A polarization term in model potentials may play a role in softening of optical modes. Results are discussed in comparison with low excitation modes, which have been measured in many kinds of superionic conductors by neutron inelastic scattering experiments.

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Structural phase transition of K₃D(SO₄)₂ was studied by X-ray scattering experiments, and new reflections were observed below T_c=85 K. The space groups are A2⁄a (Z=4) above T_c and P2₁⁄a (Z=4) below T_c. The postulated structure of the low temperature phase has an antipolar character. Temperature dependence of lattice parameters was also investigated, whose anomaly below T_c was marginally small. The deviation from the curve calculated by the Debye approximation was utilized to estimate the nature of the order parameter. Similar experiments in K₃H(SO₄)₂ have not shown any evidence of the phase transition.

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The spontaneous magnetization of the three-dimensional Ising model is studied numerically by the Monte Carlo method. The values of squared magnetizations for finite simple-cubic lattices are extrapolated to those of the infinite system to estimate the values of spontaneous magnetization. The extrapolation parameter is the inverse of the system size. By assuming that the spontaneous magnetization is a simple pole function near the critical point, the values of the critical point K_c and the exponent β of the spontaneous magnetization are estimated to be 0.221657(3) and 0.3205(6), respectively. If we assume that it is the form of simple pole function plus regular function, they are estimated to be 0.221651(4) and 0.3265(9), respectively. Therefore they are estimated to be 0.221654(6) and 0.324(4), respectively, from the mid values of these estimations.

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X-ray diffraction analysis under high pressure was performed for three icosahedral quasicrystals (Al–Li–Cu, Al–Ru–Cu and Al–Mn). Only the i-phase of an Al–Li–Cu alloy undergoes structural phase transformations: i-phase to an amorphous phase and then to a crystalline phase. The electrical resistance decreases almost to half at each transformation. Peak widths of diffraction lines for the i–Al–Li–Cu becomes broader with increasing pressure, in contrast to those of Al-transition metal systems.

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We studied the low temperature specific heat C of nonsuperconducting oxides (La_1−xSr_x)₂NiO_4+δ in a wide range of x up to 0.65, along with the lattice parameters at room temperature, electrical resistivity ρ and magnetic susceptibility χ. We observed the qualitative change in both ρ and χ at x=0.20∼0.25 corresponding to that in c⁄a, which is ascribed to the transition from the high-spin to low-spin state of Ni ions. The anomalous hump in C below 10 K was observed. It disappears gradually above x∼0.20 and coincides with the transition of the spin states. However, this hump is well described by a modified Schottky-type contribution and possibly originates from the presence of the two-level system due to a glassy magnetic state.

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The conformation defect in polythiophene and polyfuran has been studied based on their optimized geometries using the semi-empirical tight-binding SCF-CO (self-consistent crystal orbital) method. It has been demonstrated that the total energy, the ionization potential and the band gap energy increase with increasing torsion between rings for both polymers. From the viewpoint of the total energy, however, polyfuran is difficult to have the conformation defect in comparison with polythiophene. The π-conjugation length along the polymer chain is largely decreased due to the existence of the conformation defect in polythiophene substituted with alkyl side chain induced by the steric hindrance at high temperature but not in substituted polyfuran.

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The spin-polarized band calculation for Fe₄N has been performed with use of LMTO-ASA method in the frame of local spin density functional formalism. The calculated magnetic moments on the two unequal Fe sites are in good agreement with the experimental values reported previously. The N atom not only brings about these magnetic moments for the γ-phase Fe lattice through the magnetovolume effect, but also prevents the exchange-splitting by helping the hopping of the electrons. The down spin electrons are distributed more in face-centered Fe, FeII, than in cornered Fe, FeI. This gives the larger magnetic moment to FeI site. In addition, we have made a comparison of the charge density of an N atom in Fe₄N and the one of a free N atom within the atomic sphere. The result indicates that the N atoms in Fe₄N play a role of an acceptor for electrons.

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The two dimensional Hubbard model with repulsive interaction is studied in the t-matrix approximation, which is the valid approximation in low electron density. The particle-particle correlation function and the t-matrix are obtained analytically. By use of these analytical results it is shown that the t-matrix and hence the self-energy have no singularities in the upper half plane of the complex energy variable. The phase angle δ(2k_F+q, ω), with k_F being the Fermi wave vector, in the limit of q=0 and ω=0 is found to depend strongly on the ratio ω⁄q and is not always zero. The case of the attractive interaction is also briefly studied.

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Dark conductivities σ_d of undoped and dye-doped poly(N-vinylcarbazole) (PVK) films have been measured at 298, 276, and 208 K over a wide range of static electric field E=10⁴∼10⁶ V/cm. The observed field dependence of σ_d follows apparently the E^0.6-power law, rather than the E^1⁄2-power law of the well-known Poole-Frenkel (PF) type expression. Based on these experimental results, we have discussed the field-induced carrier generation processes from “ion pairs” (bound holes-charged acceptors) that are formed by an electron transfer between carbazole-rings and acceptors involved. Here we have taken into account the Onsager “dissociation-association” model to account for the observed electric field dependence of σ_d, in which the dissociation of the ion pairs is enhanced by an applied field.

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⁸⁹Y NMR shifts in the high T_c superconductor YBa₂Cu₃O_6+x are compared with ¹⁷O NMR new data published by Yoshinari et al. and the orbital shift ⁸⁹K_orb is estimated to be 155 ppm. The nuclear spin lattice relaxation rate ⁸⁹(1⁄T₁T) for ⁸⁹Y is found to be proportional to ¹⁷(1⁄T₁T) for ¹⁷O at 2, 3 plane sites, which supports the single spin fluid model. The relation T₁TK_S=const. is realized for ⁸⁹Y nuclei in the oxygen depleted compounds YBa₂Cu₃O_6+x. It is found that the relation T₁TK_S=const. means that the energy width of dynamical spin susceptibility χ″(q, ω) with the wave vector q∼0, hΓ₀, is independent of temperature although the uniform susceptibility χ₀ strongly depends on temperature. It is also shown that the weight of the low q part of the spin excitation spectrum decreases with decreasing the hole concentration.

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An Ising system with axially long range antiferromagnetic interaction is discussed. A ferromagnetic nearest neighbor interaction exists in the plane perpendicular to the axis. This system exhibits a devil’s staircase phenomenon in the ground state; the magnetization changes in a rather strange way with external magnetic field. It is shown using a mean field approximation that, at finite temperatures, this system exhibits also a curious magnetization curve and some other interesting phenomena. However, the devil’s staircase structure is destroyed by thermal fluctuation. A finite temperature phase diagram, which is composed of many phases, is also given.

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Low-field DC magnetization measurements have been made on a random mixture Co_xMn_1−xTiO₃ with competing exchange interactions and competing anisotropies, and the magnetic phase diagram in the concentration (x)-temperature (T) plane has been determined from these results. Typical behavior characterizing a paramagnetic to spin glass transition is observed in an intermediate range of concentration. In the samples of the Co-rich and Mn-rich region, antiferromagnetic orderings take place. The magnetizations perpendicular to the spin axes of the respective antiferromagnetic orderings behave just as paramagnets even below the Néel temperature. At low temperatures, the Co-rich and Mn-rich samples with certain x reenter from the antiferromagnetic phase to the spin glass phase. In spite of the strong planar anisotropy of Co²⁺, the XY-like spin glass behavior has not been found, and the spin glass and reentrant transition in S_⁄⁄ and S_⊥ occur simultaneously, reasons for which are discussed.

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Magnetic susceptibility and nuclear magnetic resonance measurements have been made on quasicrystalline and crystalline phases of Al₆₂Mn₂₀Si₁₀Ru₈ and Al₆₈Mn₂₀Si₆Ru₆ alloys. The average value of local magnetic moment on Mn atoms and the spin-glass freezing temperature are not different so much between the two phases. However, static and dynamical properties of ²⁷Al NMR signals observed in the two phases are significantly different. These results suggest that most of the magnetic properties such as the formation of local magnetic moments and the magnitude of interactions between them are not closely related with the presence or absence of translational symmetry of the lattice; these properties might be related with local atomic configuration. A characteristic property of electrons in the present quasicrystals has been demonstrated by the transferred hyperfine interactions between Mn atoms and Al nuclei.

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The crossover of the two- and four-sublattice spin structures appeared in CoCl₂6(H₂O)_1−u(D₂O)_u is explained by introducing a weak interlayer exchange interaction and the fourth-order magnetic anisotropy. The magnetic phase diagram and the spin structure are well explained by the proposed model. The antiferromagnetic resonance has been investigated and the results are well explained by the crossover model.

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Absorption spectra are reported for PbI₂ clusters incorporated into zeolite FAU with various loading densities. There appear many absorption bands corresponding to one to five molecular clusters. With decreasing the cluster size, the spectra show the remarkable blue shift in qualitative agreement with the quantum confinement of the electron and the hole. The smaller clusters indicate the strong absorption in spite of the decrease in the molecular number. This result is ascribed to the quantum size effect on the exciton oscillator strength.

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