The spatial correlation functions of a director field are obtained analytically in a two-dimensional XY system consisting of randomly distributed topological defects. For a system containing point defects with the strength (the winding number) S, the correlation function is expressed as C(r)=exp [−ρr² {a+(1⁄2)·πS² log (R⁄r)}] for a large R, where R, ρ and a are the system size, the defect density and a constant, respectively. For a system with randomly distributed defect pairs of ±S separated by the distance l₀, the correlation function behaves at large distance as a power law, i.e., C(r)∝r^−πρ_pμ2, where ρ_p and μ are the density of defect pairs and the dipole moment defined as μ=l₀S, respectively.

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The ion mobility of He⁺ in He gas has been measured at 4.4 K and 85.7 K using a selected ion drift tube apparatus which has a cryogenic system. The thermal transpiration effect on pressure measurement was found to be very large and important at such a very low temperature. The pressure correction was made according to a semiempirical method proposed by Poulter et al. The reduced mobility, when plotted against effective temperature, agrees well with other experiments at high temperatures. As the effective temperature is decreased, the reduced mobility increases and reaches the Langevin limit at about 18 K, and then appears to decrease below that temperature. This may be the first evidence of what Dickinson predicted theoretically though further, more precise measurements are required.

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Following the idea proposed previously that describes the phenomena observed in the outer region of the turbulent boundary layer in terms of a one-dimensional map generating the intermittent chaos, we attempt to analyze the problem with the use of statistical mechanical methodology applied frequently to dynamical systems. From the binary sequences constructed by processing measured data of instantaneous streamwise velocities, we obtain the singularity spectrum or the fluctuation of the dynamical scaling indices. In particular, the Kolmogorov entropy is given quantitatively as a function of the distance from the wall. The difference from random motions is emphasized.

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Notable amplification of ion acoustic solitons through reflection of beam ions is observed in a plasma. Further, it is also confirmed that the soliton amplification is always associated with a detectable deformation of the beam energy distribution.

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We have measured the de Haas-van Alphen effect in the antiferromagnetic compound GdIn₃. The Fermi surface of GdIn₃ is almost the same as that of the non-f reference compound LaIn₃. The cyclotron masses of GdIn₃ are also close to those of LaIn₃. These results indicate that the 4f electrons in GdIn₃ are well localized and that mass enhancement due to the electron-magnon interaction is extremely small.

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The magnetotransport phenomenon is investigated in α-type crystals of (BEDT–TTF)₂I₃ which are metallized by applying quasi-hydrostatic pressures. At liquid helium temperatures, a fairly large magnetoresistance which rises in very low field and saturates above 0.5 T is observed. The effect of the magnetic field of 1.2 T is found to be recognizable at temperatures above 50 K. Our interpretation of the phenomenon is that the metal-insulator transition which has been suppressed by the pressure arises again, aided by the magnetic field.

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The effects of circular bends on ballistic transport in a quantum wire with hard-wall confinement potential are investigated. By means of the channel-matching method, the scattering matrix is calculated as a function of the Fermi energy. We discuss the dependence of scattering probabilities on the external magnetic field, bending radius, and bending angle. It is shown that the coupling of channels is different for right-turn and left-turn bends in the magnetic field. Furthermore, there appear to be extremely narrow dips in conductance just below the threshold energies for the next channel.

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We report on the anisotropy of magnetization, electrical resistivity and upper critical magnetic fields (H_C2) of UPd₂Al₃. The magnetization curve in the antiferromagnetically ordered state shows large anisotropy, indicating that the sublattice moments lie in the basal hexagonal plane. The value of −(dH_C2⁄dT) at T_C is estimated to be about 36 (kOe/K) for the magnetic field parallel and perpendicular to the hexagonal c-axis, and the upper critical field seems to be rather isotropic.

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Multilayered thin films of iron and lithium fluoride (LiF) were prepared using ultrahigh-vacuum deposition with two independently controlled E-guns as heat sources. Mössbauer spectra corresponding to metallic Fe atoms and Fe³⁺ ions were observed in these films. The magnetization curve at 4.2 K was shifted with a magnetic field cooling from room temperature where absolute values of Hc’s for + magnetic field and − magnetic field were different. This suggests that exchange anisotropy due to magnetic exchange coupling between ferromagnetic and antiferromagnetic parts exists in the film.

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The Haldane state is investigated in the S=1⁄2 antiferromagnetic (AF) ladder model for open chains with the help of a nonlocal unitary transformation. It is shown that the transformation works well, as in the case of S=1 AF models, so that it transforms the model into a ferromagnetic model with Z₂×Z₂ symmetry, and four degenerate Haldane states are obtained by a variational calculation in a molecular field approximation. The S=1⁄2 edge states are examined in these Haldane states.

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The low-temperature magnetic property of the gap-type Kondo lattice compound CeNiSn has been investigated down to 0.08 K by the ¹¹⁹Sn nuclear magnetic resonance (NMR) technique. The temperature dependence of ¹¹⁹Sn nuclear-spin-lattice relaxation rate (1⁄T₁) down to 0.4 K was well interpreted by a model that the quasi-particle density of states has a V-shaped structure of the pseudogap proportional to the energy in the vicinity of the Fermi level. Below 0.13 K, however, (1⁄T₁) is found to decrease exponentially as exp (−Δ⁄k_BT) due to the appearance of the energy gap of Δ=0.25 K. The NMR spectrum starts to broaden below 0.13 K, signifying that there develops a static magnetic correlation with a magnetic moment estimated to be as small as 10⁻³ μ_B/Ce atom. It is suggested that the pseudogap state is changed into the “spin gap” state induced by the development of the static magnetic correlation.

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We have examined chaotic oscillation patterns of a Millipore membrane infiltrated with dioleyl phosphate and an azobenzene derivative under visible or UV irradiation. As a result, the amplitude of the oscillation was larger and the correlation dimension was smaller under UV irradiation. This result suggests that some of many nonlinear oscillators of the membrane could oscillate coherently under UV irradiation. We believe that it is the first experimental result which can be explained by the globally coupled map model.

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The conservation laws of the integrable modified Sawada-Kotera equation are studied. They fail to be satisfied in such a collision process that solitons change their identity from regular solitons to singular solitons through the interaction. We overcome this difficulty by expressing soliton solution in the complex t-plane.

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When a low dimensional space has a curvature, there is an effective potential in the Schrödinger equation as a geometrical correction. In this paper, we have shown that a confined space in three dimensional space can be regarded as a curved low (one or two) dimensional space when the thickness of the space multiplied by the Weingarten map of each space is sufficiently smaller than unity. Under the condition, we have also evaluated the effective potential using the path integral method.

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We derive low-temperature expansions of the internal energy, the specific heat and so on for the antiferromagnetic Ising model on a triangular lattice by using the expression obtained by Stephenson. We propose to use ΔT=exp (−2βJ) as the reduced temperature variable near the critical temperature. We then conclude the values of the critical exponents α, ν, γ, δ and Δ as α=0, ν=1, γ=3⁄2, δ=7 and Δ=7⁄4.

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The osmotic pressure is discussed for the one-dimensional solution of molecules having hard cores and attractions of infinite range and of infinitesimal strength. The volumes of the solution and of the pure solvent kept in contact with the solution through a semipermeable membrane (permitting the passage of the solvent only), the total number of solvent molecules, the number of molecules of each solute and the temperature in equilibrium are assumed to be known. The expansion of the osmotic pressure, in terms of the relative molarities of the solutes, is obtained to the fourth order. The present theory is regarded as an approximate theory of osmotic pressure of a three-dimensional solution, and can also give the number of solvent molecules spontaneously flowing into the solution through the semipermeable membrane till the equilibrium is attained.

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Correlation functions of real symmetric random matrix ensembles are expressed by correponding skew orthogonal polynomials. The skew orthogonal polynomials related to classical orthogonal polynomials are presented in a compact way and the correlation functions in the thermodynamic limit are exactly evaluated in several special cases. The local correlation functions in these cases are identical to those of the Gaussian ensemble.

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The geometrical fractal property of films formed by random deposition has been studied. In this paper we study the fractal property of the resistance of films in the eary stage of deposition. The films are grown by depositing particles of unit squares on segments divided into unit length (cells). First we define the fractal dimension for the resistance; then we compute the resistances by the finite-element method. It is shown that the resistance of large clusters has a fractal dimension of 1.14.

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The exact expression of the free energy is obtained for the free fermion model on a lattice with a multiple number of sublattices. Compact exact expressions are presented, in particular, for two-sublattice systems. Vdovichenko’s method is used in the derivation. Some remarks are given to justify the Vdovichenko’s method for the free fermion model.

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The high-spin states up to the vicinity of the second backbends of the Er isotopes are studied in the IBA-plus-two-fermion-pairs model. It was found that the energy levels of the quasi-β, quasi-γ bands as well as the yrast state can be reproduced reasonably well. The second backbends can be interpreted as the band crossings of the two-fermion-pair rotational band with the ground state bands. The B(E2) values were calculated and compared with the available experimental data. The drops of the B(E2) values at the backbends can be reproduced. The calculated moments of inertia and B(E2) values change too sharply as compared with the experimental values. Possible improvements of the model are discussed.

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To account for the experimental fact that the X-ray diffraction indicates the triple peaks near the transition point in the smectic phases, we propose here a double-kink soliton model as a φ⁶-system, extending the previous φ⁴-model. The present model indicates a variety of layer structure depending on a phenomenological parameter. The layer structure derived by this model seems to be qualitatively consistent with the experimentally found one.

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In Hasegawa-Mima equation, steady drift wave solutions representing a localized (solitary) vortex in the shear flow are examined by a singularity-free expansion method, in which total flow is expanded around the shear flow. It is shown that singular terms, caused by the “resonance” between the traveling velocity of the vortex and the shear flow, appear in the expansion of the two-dimensional nonlinear equation for the vortex moving steadily. If a singularity-free condition is imposed on a certain order coefficient of the expanded equation, the lower-order coefficients are uniformly bounded while the higher-order coefficients vanish. Analyzing the exactly truncated equation, we obtain piecewise continuous solutions of Larichev-Reznik’s type and also show the existence of a smooth monopole of solitary vortex in the shear flow in the whole plane.

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It is shown that the acceleration by the net inverse bremsstrahlung of laser light is a classical phenomenon in which high-energy electrons, whose momentum and energy are modulated by the laser light, strictly obey the momentum and energy conservation laws and the time-reversal invariance of the transition probability. Net inverse bremsstrahlung acceleration of high-energy electrons traveling in strong laser light and plasma waves is investigated using the relativistic quantum kinetics based on the Dirac equation. The quantum kinetics treats the classical phenomenon exhibited by high-energy electrons through the correspondence principle. The dc force in the laser light direction by the net inverse bremsstrahlung is independent of the spread of the electron beam energy, and increases with the electron beam energy. The dc force also increases with the laser intensity if the potential amplitude of the laser wave is smaller than the electron rest energy.

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Two types of Thue-Morse lattices of the 7th and the 10th orders have been grown by molecular-beam-epitaxy. Though the lattice has no periodicity, many sharp peaks are observed in Raman measurements. The observed all peaks are specified by (2k+1)⁄3·2^p with integers k and p. The frequency and scattering intensity of folded LA phonon modes can be explained by the elastic and photoelastic continuum model. The correlation of lattice arrangements becomes weak with increasing the order of the Thue-Morse lattices. These imply that the Thue-Morse lattice locates between quasi-periodic and random lattices.

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The temperature dependence of the lattice constant and the diffraction intensity profiles of ultrafine bcc Cr particles with 750 Å in the average diameter were investigated by X-ray diffraction and least-squares pattern fitting methods in a wide temperature range from 88 K to 375 K. Coefficient of a thermal expansion differed by about 30% at T>T_N and 10% at 170 K<T<T_N respectively from the bulk data. New extra peak was observed below about 210 K at the low angle side of the observed 110, 211 and 310 reflection positions for the bcc Cr structure. The feature in the experimental results was discussed on the basis of a lattice expansion which was closely related to an enhancement of the magnitude of the magnetic moments relative to the maximum value of the spin density wave in bulk Cr.

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Low-temperature phase transitions in the solid solutions Rb₃H_1−xD_x(SO₄)₂ and Rb₃H_1−xD_x(SeO₄)₂ have been studied by dielectric measurements. The phase transitions, which do not exist in the hydrogen compounds (x=0), appear at deuterium contents above the critical contents, x_crit. The observed critical contents are about 0.22 and 0.04 for Rb₃H_1−xD_x(SO₄)₂ and Rb₃H_1−xD_x(SeO₄)₂, respectively. The relation T_c∝(x−x_crit)^1⁄2 between the transition temperature T_c and x holds over a wide range of x for Rb₃H_1−xD_x(SeO₄)₂, but in a rather limited range for Rb₃H_1−xD_x(SO₄)₂.

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Static and dynamic light scattering experiments have been performed to study the critical dynamics of fluctuations in a water-in-oil microemulsion system (DDAB/hexane/water). A transition from local to non-local dynamics was observed at a certain temperature above the critical point, where the diffusion coefficient deduced from the relaxation rate changes the sign of the slope in the plot against q² (q: wave number). This unusual behavior was explained by taking into account a new background term, in addition to the background term of Rouch et al. The experiment data were further found to agree excellently with the full mode-mode coupling theory including two background terms.

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Transmission spectra of third sound were measured in the Thue-Morse lattice. The structure of the experimental spectrum confirmed some of the theoretical predictions. The spectrum was compared with that for the periodic lattice and for the Fibonacci lattice. The present result supported the idea that the Thue-Morse lattice was more random than the quasi-periodic lattice, although both were generated by the automatic rules. The experimental method was described in some detail.

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Elementary excitations in the s-d model are calculated at finite temperatures with the use of the Bethe-ansatz solution. Our formulation of the spectra is based on Yang and Yang’s method which has been developed in the one-dimensional interacting boson system. We investigate the temperature dependence of the spin excitation spectra. It is shown that the narrow peak structure develops in the low energy region as the temperature is decreased. At low temperatures, the shape of the spectra is described well by the renormalized resonance level model.

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The average energy of positron annihilation radiation from Al has been determined by the Doppler-broadening summing technique with two detectors. Energy differences of annihilation radiation from the electron rest mass are 8.2±3.1 eV and 8.9±3.3 eV for the single and coincidence measurements, respectively. According to the analysis by using the electron binding energy, half of the intensity of the momentum distribution outside the Fermi momentum is due to high-momentum components of the conduction electrons. The contribution of the core electrons to the total annihilation is estimated to be 5∼6%, and the core enhancement factor is 1.2∼1.5. The average energy of annihilation radiation estimated with this contribution is consistent with the above measured values within the experimental accuracy.

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We present a theory for the metallic phase of heavily doped polyacetylene. The Hartree-Fock (HF) ground state in this system is a charged soliton (S^±) lattice that has a nearly periodic long range order in the charge density as well as the one in lattice distortion. We take account of electronic correlation effects by considering superpolarons (SP’s) as local fluctuations in the electronic order parameter (OP). They are electrons and holes injected into a S^± lattice that make no lattice distortions but are selftrapped and make local defects in the electronic OP. They make intrachain quantum translation and interchain hopping through dopants. The formation energy of a SP pair is reduced by these quantum motions and become negative in a high doping regime. Therefore, the ground state in this regime is a S^± lattice with spontaneously produced SP’s. The SP’s may be regarded as Fermion quasi-particles. Since they partially occupy the translational bands of SP’s, metallic properties appear in this phase.

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Piezoresistance (PR) of p-type Si, consistent with experimental ones, has been obtained by numerically calculating the conductivity for the degenerate valence bands with and without stress. Small stress coefficients for total bands and even each band well fulfil the symmetry relationship for the PR coefficient in the cubic crystal. It is found that the mobility of each hole linearly changes with stress, while the carrier concentration change is of the second order in stress. This leads to a conclusion that the principal mechanism of PR in p-type Si is the stress proportional mobility change of holes, the carrier redistribution effect which is the mechanism for many valley semiconductors being ruled out. Experimental temperature dependence of a PR coefficient which exhibits (1⁄T)-like and saturation behaviors is also explained in terms of that of mobility change of holes. It has been suggested that deviation of energy dependent hole conductivity masses from bulk hole masses may be responsible for hole mobility change.

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A model calculation of the Hall factor for a metallic system with a small Fermi energy has revealed that it can lead to a significant temperature dependence of Hall coefficient even when a single parabolic band contributes to electrical conduction. The present result gives a natural explanation for the behavior of temperature dependence of the transport properties observed in GaAs/Al_xGa_1−xAs superlattices.

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We derive an expression of dynamical susceptibility in superconducting states from a generalized B.C.S. hamiltonian. We investigate the wave number dependence of static susceptibility with a d-wave superconducting gap in square lattice at T=0 K for several values of chemical potential. It is shown that the position of maximum of static susceptibility depends on the value of chemical potential.

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The Eliashberg equation is solved in both frequency and momentum variables to obtain the superconducting transition temperature T_c in the multivalley electron gas without phonons. Both the one-particle Green’s function and irreducible two-electron interaction are evaluated in the random-phase approximation which provides exact results in the limit of large valley degeneracy g_v and is known to give sufficiently accurate ones even for g_v as small as 3 or 4. Among s-, p-, and d-waves, the s-wave pairing is most stable for g_v≥2 with a fairly high T_c. For g_v>>1, our solution is reduced to “bipolaronic superconductivity”. We discuss implications of the present results to the exotic superconductors with relatively low carrier concentration.

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We reexamine harmonic fluctuation theory of Abrikosov flux lattice previously developed on the basis of Landau level expansion of the order parameter. We explicitly show that, as far as fluctuations of flux density are taken into account, the usual elastic theory is nicely derived in the case with fluctuations of lowest two Landau levels, and that superconducting long range order (or gauge invariant phase coherence) is absent in 3D flux lattice. It is pointed out that these results are also obtained according to other frameworks based on the elastic theory. The resulting expression of elastic free energy becomes complicated when other higher Landau levels are taken into account. Nevertheless we can show that the superconducting long range order is lost even in such a general case. The relevance of these results to high T_c superconductors is briefly discussed.

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The temperature dependence of birefringence Δn(T) of a triangular lattice antiferromagnet RbMnBr₃ has been measured together with comparative measurements of Δn’s of related compounds CsMgCl₃, CsMgBr₃, RbMgBr₃, CsMnI₃, CsMnBr₃. A structural phase transition of RbMnBr₃ at T_S2=220 K with symmetry-breaking in the hexagonal c-plane has been found. The low-temperature structure below T_S2 is suggested as orthorhombic, which can be the origin of an incommensurate spin structure of RbMnBr₃. Critical exponents of magnetic specific heat are determined as α′=0.22±0.06, α=0.42±0.16, which are in fair agreement with the values of the Z₂×S₁ universality class.

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Fe/Co multilayered films were prepared by ultrahigh vacuum deposition and the structure was studied by X-ray diffraction and transmission electron microscopy. It was found that hcp Co(101) is epitaxially grown on bcc Fe(110), when the nominal Co layer thickness was between 10 and 30 Å. The Mössbauer spectroscopy was applied to study the interface mixing and the thickness of interface alloy layer was estimated to be about 10 Å. The magnetostriction constant changes from negative to positive and the magnetoresistance increases with a decrease of compositional modulation period. These changes are attributed to the interface mixing.

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We have clarified the magnetic and electrical properties of U₇Ge, U₅Ge₃, U₃Ge₄ and UGe₂, measuring the electrical resistivity, thermoelectric power, Hall coefficient, magnetic susceptibility, magnetization and specific heat. U₇Ge and U₅Ge₃, which are Pauli paramagnetic compounds, become superconductive below 1.40 K and 0.99 K, respectively. The latter compounds U₃Ge₄ and UGe₂ indicate ferromagnetism. Anisotropic properties of UGe₂ are well reflected in the electrical resistivity, magnetic susceptibility and magnetization.

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Magnetic structures and magnetization processes of [Fe(27 Å)/Cr(12 Å)] multilayered films are investigated by polarized neutron diffraction, polarization analysis and ⁵⁷Fe Mössbauer spectroscopy. Transverse components of total magnetic moments of the ferromagnetic Fe layers, spaced by a Cr layer, to the applied field form an antiparallel long range order in the multilayers. The magnetization process of the total moment of the Fe layer is a uniform rotation of the Fe moment vector with keeping the magnitude constant except in a very low field region. The existence of non-zero magnetic moment is suggested in the Cr layer. The relationship between the antiferromagnetic alignment of the Fe layer moments and the change of the magnetoresistance in various applied fields is briefly discussed.

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We investigate low- and high-temperature properties of the ferromagnetic Ising model of infinite-spin. By using the cummulant expansion methods, we obtain low-temperature expansions of the free energy, the specific heat, the spontaneous magnetization, the zero-field susceptibility and so on, and high-temperature expansions of the free energy and the zero-field susceptibility. We compare the results with those obtained by Thompson for the system on the one-dimensional lattice, with those by using Monte Carlo simulations for the systems on the square lattice and on the simple cubic lattice and with those with the aid of the mean-field approximation.

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We have observed electron paramagnetic resonance of paired spin in Rb₂Co_0.3Mg_0.7F₄ at 220, 370, 693.6 and 762.2 GHz in pulsed magnetic fields and found that the g-value is different from that of single spin. It is considered that the anomalous g-value of paired spin comes from the mixing of the ground state with the excited state due to both λLS and strong exchange interaction. The detailed analysis is discussed.

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The permanent dipole of the NO₂ radical and the relative displacement between the ions are considered about the ferroelectricity in NaNO₂. In this case the possibility of the rotation of NO₂ can be explained as the mixed double rotations around the a-axis and the c-axis. The IC phase between the ferroelectric and paraelectric phases is considered to be constructed by the interaction between the 2D electron system on the c-domain surface of the crystal and the NO₂ dipole, whose long periodicity can be estimated by the magnitude of spontaneous polarization.

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Hydrogen-ordering in KH₂PO₄ (KDP)-type ferroelectric crystals is elucidated by making use of a double minima potential for hydrogen. The two lowest eigenvalues of this potential are obtained in an explicit form to correlate with the tunnelling energy and the H-site separation δ. The order parameter ⟨x⟩ and the transition temperature T_c are derived in the mean field theory, and the geometrical isotope effect is discussed. The T_c values are compared with those obtained by means of the recent neutron diffraction experiments performed by Nelmes et al. The relationship between T_c and δ obtained is different from the linear relation proposed by Ichikawa.

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The crystal structures of the monoclinic low-temperature phase (phase V) at 161 K and the threefold-modulated orthorhombic phase (phase VI) at 149 K of [N(CH₃)₄]₂ZnCl₄ are determined. The crystal structure of the threefold-modulated monoclinic phase (phase IV) at 223 K is also reexamined in order to investigate the structural relation to other phases. The modulation pattern of the fivefold-modulated orthorhombic phase (phase III) reported previously is interpreted to be constructed with that of phase IV. The structural changes on the phase transitions from the disordered phase (phase I) to phase V are described mainly by the rotations about the b- and c-axes and the translations along the a-axis of ZnCl₄ and one kind of N(CH₃)₄. On the phase transition from phase V to phase VI, the magnitudes of the displacements of each ions along the b- and c-axes become larger than those on other phase transitions.

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Domain walls in the commensurate phase of crystals which have a preceding incommensurate phase are discussed on the basis of the Landau-type energy written in terms of two order parameters. The contribution from the Lifshitz invariant to the domain wall energy is analyzed, using the variation method. Contours representing two possible types of domain walls and spatial modulation of the order parameters in them are presented.

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It has been reported that there exists Mn-related photoluminescence at 2.0 eV in addition to excitonic emission in Cd_1−xMn_xTe with x more than 0.3 grown by conventional methods. We have investigated dependence of these luminescence lines on substrate temperature, T_s, in MBE-grown Cd_0.6Mn_0.4Te crystals. A large broad line was observed at around 2.05 eV in samples grown at high T_s at about 400°C whereas a sharp line at around 2.17 eV evolved in samples grown at T_s=320–340°C. Both of these lines were seen in the case of T_s=380°C. Measurement of the magnetic field dependence of the peak positions up to 40 T revealed that the former assigned as Mn related luminescence shows no observable Zeeman shift. On the other hand, the later is assigned as the excitonic emission because of the large shift to lower energy in the magnetic field. The experimental results suggest that the Mn-related photoluminescence at 2.0 eV is affected strongly by crystal imperfections, probably the vacancy type defects. On the basis of these results, a possible optical processes of the Mn-related luminescence are discussed.

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Reflectivity spectrum of YbB₆ was measured in the energy region between 1 meV and 40 eV at 9 K and 300 K. Observed optical absorption structures in the energy region from 1 meV to 1 eV were decomposed into three parts. The first is a Drude part. The effective conduction electron number was evaluated to be about 0.9% per mole with weak temperature dependence. The second part consists of a weak absorption due to impurity centered 0.2 eV and strong interband transition between valence and conduction bands with the energy gap of about 0.5 eV. The last one is due to phonon absorption bands. By comparing with the theoretical phonon dispersion curve calculated by Takegahara et al., the absorption at about 13 meV was identified to be a T_1u-mode due to the relative motion of Yb and B₆ and the absorption at about 108 meV to a T_1u-mode due to an intra-molecular vibration of B₆.

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The irradiated Na₂TeO₃·5H₂O single crystal is investigated by ESR method. Three types of stable radicals are observed in this crystal at room temperature. Two of them are identified as TeO₃⁻ and another is assigned to TeO₂⁻ radical. The radical structure of a TeO₃⁻ is assumed to be a pyramidal structure, with slightly different structures of TeO₃⁻ being observed in the irradiated crystal. The TeO₂⁻ radical is created by hole trapping and subsequent Te–O bond rupture.

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The telegraph equation with a drift term to determine an asymmetric random walk is applied to the behavior of paramecia to accumulate at their optimal temperature in the presence of temperature gradient. From this equation, the following two points are clarified; 1, the stationary solution of the equation explains that the observed stationary distribution of the cells decreases exponentially from their optimal position, and 2, on a kind of paramecium that begins to accumulate at the optimal temperature after the treatment with riboflavin, the calculated transition time from a random distribution to the stationary distribution agrees with the observed transition time, 3 minutes.

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