Electron motion in an oblique magnetosonic wave is studied by means of a one-dimensional, relativistic, electromagnetic particle code with full ion and electron dynamics. It is found that high-energy electrons can be produced; electrons with Lorentz factors γ > 100 have been observed in the simulations. They are reflected and then trapped by the wave. This phenomenon occurs in a large-amplitude oblique shock in a strong magnetic field such that ω_ce >~ ω_pe. The acceleration mechanism is given, and the dependence of γ on plasma parameters, such as the propagation angle, is discussed.

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Heterogeneous coexistence of high- and low-temperature phases has been observed around structural phase transitions. We find that such intermediate states result from a cubic coupling term of the form e₁ψ² in the free energy, with which the dilation strain e₁ can modify the effective temperature for the order parameter (tetragonal strain) ψ. We show that e₁ is asymmetrically induced in the high- and low-temperature phases, leading to elastic stabilization of tetragonally strained domains coherently embedded in the disordered matrix.

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The structure and dynamics of the alkyl chains are investigated by ²H-NMR for specifically deuterated samples of an antiferroelectric chiral smectic liquid crystal MHPOBC. The ²H-NMR spectrum for the chiral alkyl chain exhibits very small quadrupolar splittings, and the methylenes close to the chiral center give double splittings ascribable to two different quadrupolar splittings for each methylene unit. The unusual nature of the chiral chain is revealed; the chain is bent from the molecular long axis, and is asymmetrically hindered.

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The quantum statistics of a three-dimensional vortex filament under an applied superflow in superfluid ⁴He is investigated by the use of path integral techniques. The free energy evaluated in the saddle point approximation around a static vortex decreases abruptly at a certain critical value of the applied superflow velocity. This critical behavior is consistent with the experimental result of vortex nucleation by a moving ion. The dissipation effects are also discussed within the context of the damped harmonic oscillator approximation.

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Roles of Coulomb interaction, orbital degeneracy and Jahn-Teller couplingin double-exchange models are examined for perovskite Mn oxides.We study the undoped insulatoras well as metal-insulator transitions by hole doping, and especiallystrong incoherence of ferromagnetic metal.We derive models whereall the spins are fully polarized in two-dimensional planesas indicated by experimental results, and investigate their ground-state propertiesby the quantum Monte Carlo method.At half filling where the number of e_g electronsis one per site on average, the Coulomb interaction opensa Mott gap and induces a staggered orbital ordering.The opening of the gap is, however, substantially slower than the mean-field resultsif the Jahn-Teller coupling is absent.The synergy between the strong correlation and the Jahn-Teller couplinglargely enhances the charge gap amplitude and reproducesrealistic amplitudes and stabilization energyof the Jahn-Teller distortion.Doping of carriers destroysthe orbital ordering stabilized by the Coulomb interaction.The short-ranged orbital correlation is critically enhanced in metalstoward the metal-insulator transition, which should be related to the strong incoherence of charge dynamicsobserved in experiments.Our model, moreover, exhibits a uniform ordering of d_x²_-y² orbitals over a wide region of dopingin agreement with experimental indications.

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The density of states (DOS) in open chaotic billiards is studied semiclassically in the presence of Coulomb interaction. The exchange and Hartree corrections to the DOS as a function of energy ε relative to the Fermi energy are calculated at zero temperature including higher-order interaction effects. It is shown that the DOS decreases with increasing |ε | in the low-energy regime and begins to increase around |ε |≈ t_B^-1, where t_B is the classical escape time. For t_B^-1<< |ε |, a logarithmic increase of the DOS is shown to appear. This anomalous ε -dependence is due to competition between the exchange and Hartree corrections.

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With regard to the Shubnikov-de Haas oscillations in Sr₂RuO₄, an unusual enhancement was found in oscillatory components with frequencies F_{β ± α}=F_β ± F_α for a particular orientation of the crystal in the magnetic field, where F_α and F_β are the oscillatory frequencies for the two-dimensional Fermi surface branches, α and β, respectively. The orientation is given by the so-called Yamaji angles corresponding to the maxima in the angle-dependent magnetoresistance oscillation, where the carriers inthe slightly warped cylindrical Fermi surface behave as if they were in a two-dimensional system. The results can be understood in terms of the chemical potential oscillation effect as predicted by Nakano for de Haas-van Alphen oscillations.

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We studied the two-dimensional assembling process of nanometer-size Co clusters on substrates in terms of the percolation theory. We demonstrate the nonuniversal behavior of the electrical conductivity depending strongly on the cluster size, d: the conductivity critical exponent increases from 1.1 to 1.8 with increasing d from 6 to 13, nm. The soft-percolation model, which takes into account the wide distribution of connectivity between clusters, is a candidate to explain this nonuniversality.

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All salient features of paramagnetic MnSi under high pressures, i.e., a broad gigantic susceptibility maximum, a pronounced steep peak of the field-dependent differential susceptibility, and the nonquadratic temperature dependence of the electrical resistivity, can be explained on the basis of the Fermi liquid model in terms of the logarithmic dependence of the free energy and the density of states function with respect to temperature, magnetization and quasiparticle energy.

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We performed specific heat measurements of CoS₂ in a magnetic field of 0 T ≤ H ≤ 5 T over a broad temperature range (30 K < T < 250 K)by means of ac-calorimetory.The magnetic phase transition was significantly rounded toward the high-temperature sidewithout considerable change in the total magnetic entropy, while the field variation obeyed the Maxwell relation.We also found a magnetic equation of state for C_H(T), which includes critical indices α, β and δ determined from the previous zero-field measurements.

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The phase transition under pressure up to 1, GPa in a relaxor-Pb(In_1/2Nb_1/2)O₃ (PIN) single crystal was investigated by X-ray diffraction. With increasing applied pressure, the integrated intensity of the (3 2 0) Bragg reflection increases and that of the (3 2 0) diffuse scattering disappears, implying that the phase transition occurs from the relaxor phase to the normal ferroelectric phase.

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Neugebauer-Kramer solutions on a flat background are extracted from other series of exact solutions to Ernst equation by imposing asymptotic flatness and reality of metrics. Because of this result, we partially verify the conjecture that Neugebauer's solutions are most comprehensive in physically meaningful solutions to Ernst equation.

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We study the lattice W(A₂⁽²⁾) algebra, which is a reduction ofthe lattice W₃ algebra.We give the integrals of motions, and define the integrabledifferential-difference equations.We also discuss on the relationship with the affine Toda field theoryand the q-deformed W algebra.

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We present new expressions to a pair of Bäcklundtransformations for the modified Volterra lattice equation. We derive a superposition formula to generate multi-soliton solutions.In an appropriate continuum limit, the Bäcklund transformationscoincide with those for the modified Korteweg-de Vries equation.

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We study the quantum group symmetry of theZ_N symmetric lattice field theory, which is viewed asa discretization of the sl (N) affine Toda field theory.We reveal the quantum group structure, and construct explicitlythe quantum local integrals of motion by use of the quantumdilogarithm function.

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A coupled map lattice model is proposed as a mean-field typemodel for the diffusion-limited aggregation. The fractal dimension is estimated numerically for several dimensions, which is consistent with the formula D=(d²+1)/(d+1).

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Emission cross sections for CH⁺(A¹Π-X¹Σ⁺) produced by single electron impact of CH₄ are estimated at 100 and 400, eV by subtracting the calculated band intensities for CH(A²Δ-X²Π) from the experimentally measured band spectra. Vibrational and rotational temperatures are analyzed for CH molecule in the A²Δ state by fitting calculated band intensities assuming the Boltzman distributions in the upper electronic state to experimental ones at 17, 28, 100 and 400, eV. Rotational population distribution at 17, eV is quite different from others.

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The phase relaxation of the resonance fluorescence from sodium vapor was studied by measuring the contrast of interference between the delayed fluorescence pulses. It is shown that the phase relaxation time can be measured by a conventional cw mode-locked pico-second pulsed laser without any sophisticated apparatus to actively lock the phases of exciting laser pulses. Using a modified Michelson type interferometer, and a homemade software based on FFT algorithm, we obtained a phase correlation time as 300 ps with good S/N ratio. A local minimum observed in the decay curve is attributed to the ground state hyperfine splittingand the temperature dependence of the phase relaxation time is explained by the change in the spread of atomic velocity distribution with temperature (Doppler broadening mechanism). Analytical calculation indicates that when the laser bandwidth is much broader than the linewidth of the fluorescence, as in the present case, the envelope of the interfering fluorescence signal can be represented by Fourier transform of the absorption spectra. The analysis based on this approximation are in good agreement with the results obtained in the experiment.

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The flow instability has been examined in a polymer liquid extruded from a die, especially periodic spurt observed under constant piston moving. A stick-slip model of a group of microscopic springs has been presented toexplain the macroscopic slip which is supposed to occur during theinstability. The constitutive relationship of the slip velocity and theapplied force has been derived and the coupling of the slip dynamics and thecompressibility of the melt in the reservoir has been considered. Thesteady state solution, the linear stability analysis, and the numericalcalculation suggested the followings. 1) The flow curve is basicallyN-shaped. 2) The range of the negative slope in the flow curve can beunstable. 3) In the unstable range, limit cycle appears around an unstablesteady state. 4) The controlling parameter of the stability is the meltdepth in the reservoir, which determines the compliance of the whole system.Experimental examination of the periodic spurt of polyethylene has confirmedthose theoretical predictions. The results clearly suggest that theinstability should be treated as a bifurcation of the dynamical system.

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Two conditional averages for the longitudinal velocity increment u_r are considered: h(u_r) is the average of the difference of the Laplacian of the velocity field with the u_r value fixed, while g(u_r) is the corresponding oneof the square of the difference of the velocity gradient.The fitting formulae for h and g are derived for the 512³ data of the direct numerical simulation.The computed PDF is characterized as(1) the Gaussian distribution for smaller amplitudes, (2) the exponential distribution for larger ones, and (3) the stretched exponential distribution for intermediate ones due to a factor in front of the exponential function.

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The neoclassical transport theory in a presence of temperature anisotropy is investigated in the low to the intermediate collision frequency regimes for a large aspect-ratio tokamak plasma.The standard procedure for an isotropic plasma in the plateau regime is extended to an anisotropic plasma, and the neoclassical transport coefficients in this regime are explicitly calculated.By interpolating the results in the plateau regime and the previously obtained ones in the banana regime, the expressions for the neoclassical transport coefficients which are continuously valid from the banana to the plateau regimes are presented.

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We have calculated spectra of impurity Ar ions including contribution from the satellite lines in high density hydrogen plasmas. The doubly excited states are assumed to be in Local-Thermal-Equilibrium (LTE) with respect to the singly excited ions in the next ionization stage. The disappearance of bound states due to pressure ionization is found to be very important in determining the populations of the doubly excited states. The emission lines of H-like and He-like Ar ions are broadened and enhanced by the unresolved satellite lines from the states with a spectator electron with principal quantum number n=3-- 6 for ion densities higher than 10²³ cm^-3 and electron temperature in the range of 0.5-- 1.0 keV.

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The atomic structure of liquid Te_1-xI_x mixtures with x=0.2, 0.4, 0.5, 0.6, 0.7, 0.8 and 0.9, has been measured in the temperature range from 525 to 873, K. Distinct changes in the structure factors have been observed in the concentration ranges from x=0.2 to 0.4 and from 0.8 to 0.9. The structural changes in Te-I mixtures mainly reflect the variation in the number-number correlation function. The metal-nonmetal transition in this system is closely related to the change in topology of the melt. The iodine-iodine correlation mainly contributes to the first peak region in the radial distribution function of liquid Te_0.1I_0.9.

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For a one-dimensional discrete model of a crystal the solution of the form of a moving domain wall in an odd-periodic commensurate structure was derived in the continuum approximation. The energy of the commensurate odd-periodicstructure, the width and the energy of domain wall were expressed in termsof the amplitudes of harmonics of carrying commensurate structure. With theuse of the result by Ishibashi, the relation between domain wall solutionsin odd-periodic and even-periodic commensurate structures was established.The applicability and the accuracy of the solutions were also discussed.The obtained solutions were found to be more accurate and general thanthose by other authors.

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The sevenfold phase of Betaine Calcium Chloride Dihydrate (q_c/c^*= 2/7)is analyzed in the framework of the conventional phenomenological model for the type I commensurate phase. Parameters of the potential are determined from a set of selected experimental data. Quantitative results are obtained for various physical properties, including therelaxation frequency of the (“pseudo”) phason gap and the mobility of the domain wallsin the commensurate phase, the thickness and mutual distance of the phase solitons in the incommensurate phase, field- temperature phase diagram and the amplitude of the order parameter.

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A new promise method to derive experimentally the diffusion constants of cation and anion in molten salts, which is based on the time-dependentdecaying of the charge polarization in them, has been presented.The application was carried for molten AgI. The determineddiffusion constants of cation and anionare reasonably agreed in comparison with the resultsby computer simulation.AC conductivity in molten salts is theoreticallydiscussed in terms of a simplified Langevin equationand an application is also carried out for molten AgI.From these, the average value of the deviation fromthe Nernst-Einstein relation weighing by the diffusion constantsof cation and anion is obtained as a function of temperature, indicating a large amount of collective motionof the same kinds of ions under the external field.

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A free-electron gas confined to a thin toroid is studied. Due to the cylindrical symmetry, the longitudinal angular momentum (L) is conserved in the electron-electron interactions. The Coulomb matrix elements, which satisfy the conservation of the transverse angular momentum (J), are much larger than the others. Therefore, the electronic excitations are well described by L and J. The L- and J-decoupled plasmons are investigated by evaluating the dielectric function within the random-phase approximation (RPA). They, respectively, correspond to the coherent plasma oscillations along the longitudinal and transverse directions. For the (L, , J=0) plasmons, the RPA results are almost the same with those of the Tomonaga model.

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We numerically investigate the influence of classical percolation on the quantum Hall localization-delocalization transition. This is accomplished within the framework of the generalized Chalker--Coddington network model which allows us to control the number of classical saddle points by setting the width W of the saddle point distribution. It is found that increasing this width causes a new microscopic length scale to appear which depends on W and scales with the exponent X≈ 1.36 which indicates a close connection to the classical percolation length ξ and its exponent ν_p=4/3. Furthermore, the influence of an increase in W on the spectral statistics of the quasienergies of the network model is investigated. An effect similar to the increase of the potential correlation length in the Landau model is seen.

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Critical properties in photoemission spectra for the one-dimensional Mott insulator with orbital degeneracy are studied by exploiting the integrable t-J model, which is a supersymmetric generalization of the SU(n) degenerate spin model. We discuss the critical properties for the holon dispersion as well as the spinon dispersions, by applying the conformal field theory analysis to the exact finite-size energy spectrum. We study the effect of orbital-splitting on the spectra by evaluating the momentum-dependent critical exponents.

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The ground state properties of the one-dimensional Kondo lattice with an f² configuration at each siteare studied by the density matrix renormalization group method.At half-filling, competition between the Kondo exchange J and the antiferromagnetic intra f-shell exchange I leads to reduction of energy gaps for spin, quasi-particle and charge excitations. The attractive force among conduction electrons is induced by the competition and the bound state is formed. As J/I increases the f² singlet gives way to the Kondo singlet as the dominant local correlation.The remarkable change of the quasi-particle gap is driven by the change of the spin-1/2 excitation character from the itinerant one to the localized one. Possible metal-insulator transition is discussed which may occur asthe ratio J/I is varied by reference to mean-field results in the f² lattice system and the two impurity Kondo system.

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The B1s and P2p soft x-ray emission of BP has been measured using monochromatic synchrotron radiation as an excitation source. The band-gap energy was estimated to be about 2.1 eV which is in good agreement with other experiments. The emission bands which reflect the partial density of states in the valence band showed resonant aspects. The spectral profile was interpreted by a momentum conservation approach.

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The spatial inhomogeneities are expected to affect nucleation process in an essential way. These effects are studied theoretically by considering the case of the depinning of the charge density wave as a typical example. The threshold field of the depinning of the one-dimensional commensurate charge density wave with one impurity has been examined classically based on the phase Hamiltonian at absolute zero. It is found that the threshold field is lowered by a finite amount compared to that in the absence of an impurity.

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Angular dependence of magnetoresistivity, ρ _c(φ ), of a quasi-two-dimensional organic conductor, τ -(EDO-S, S-DMEDT-TTF)₂(AuBr₂)(AuBr₂)_y, (y-- 0.75), where EDO-S, S-DMEDT-TTF is ethylenedioxy-S, S-dimethylethylenedithio-tetrathiafulvalene, was measured for the magnetic field and the electrical current parallel and perpendicular to the most conducting ab plane. The magnetoresistance is negative in the semiconducting range below about 50, K. It was found that the period of ρ _c(φ ) changes from 90° at 5.0, T to 180° at 0.5, T and the principal axis of ρ _c(φ ) at 0.5, T depends on the field-orientation at 5.0, T. The change in the period and the principal axis of ρ _c(φ ) is discussed in terms of formation and reorientation of magnetic domains.

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We have measured the longitudinal magnetoresistance ρ _zz of graphite in high magnetic fields of up to -- 37, T at low temperatures down to -- 0.6, K. A dramatic increase in ρ _zz was newly found in the high-field-low-temperature region. We have also found prominent non-ohmicity in the current-voltage characteristic in ρ _zz over the relevant magnetic-field-temperature region. This non-ohmic behavior is reminiscent of sliding motion of a pinned charge-density wave or spin-density wave, the direction of which is mainly parallel to the c-axis. This magnetoresistance anomaly could be attributed to a magnetic-field-induced 2k_F-type instability due to the one-dimensionality caused by Landau quantization.

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Tunneling spectrum observation was carried out on a Pb(Tl)Te film grown by hot-wall epitaxy method. The observed spectrum characteristics on Ag--SiO_x--Pb(Tl)Te junctions reflect a series of discrete energy levels E_n below the conduction band edge E_c, besides the quasi localized Tl impurity states in the valence band. These discrete energy levels E_n are well expressed by E_n-E_c=-1.6/n² (n: integer) in eV, and show quite a good consistency with the result by Esaki et al. Esaki From the investigation using the hydrogen-like ionization model, these donor-like deep centers seem to be realized only in such a highly degenerated p-type semiconductor with the minor n-type centers in the vicinity of surface region.

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Based on a theoretical model for quasi-one-dimensional polymer, the kink distortion in a π -conjugated carbon chain with a single side radical, which contains an unpaired electron, is investigated. When the hopping integral between the main chain and the side radical is larger than a critical value, there exists a transition from the Peierls dimerization to a solitonlike structure along the main chain. In addition, it is found that the up spin density at the dangling site has been transferred to the main chain, while the down spin density of the main chain is transferred to the side radical due to the hopping mediated interaction between the main chain and side radical.

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(1) The wave number dependence of the static spin susceptibility χ(q) and (2) the effective interaction between quasiparticlesmediated by spin fluctuations in the dilute two dimensional Hubbard modelare investigated.The quantum Monte Carlo method (QMC) and the fluctuation exchange approximation (FLEX)are applied to this model.It is found that a maximum at wave number q=0 emerges and develops in χ(q) as the interaction U gets strong.It is also found that the most attractive component of the effective interaction mediated by spin fluctuationsis the p-wave component in the strong coupling region where a maximum at q=0 devolops in χ(q).

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The t^′ and t^{′ ′}-dependences of the dynamical spin correlation function S(q, , ω) of the 2D t-t^′-t^{′ ′}-J model are studied numerically based on the Lanczos algorithmfor two holes on 4 × 4 sites.In particular the spin excitations at q=( π, , π) ≡ q₀ are examined in detailand compared with results of the mean-field theory.The spin excitations turned out to be drastically different between YBCO(t^′=-0.17, t^{′ ′}=0.2) and YBCO(II)(t^′=-0.5, t^{′ ′}=0)-type, although both types reproduce the similar Fermisurfaces of YBCO and have the similar S(q₀, , ω) in themean-field theory.Further understanding of the properties of spin excitationfor these two choices of t^′ and t^{′ ′} are pursued by calculatingthe momentum distribution in the excited states.The spin excitations S(q₀, , ω) for YBCO(II)-typeare shown to be of collective type, while those for YBCO appear to be mainly individual.

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Transition temperature T_c of superconducting-normal (S-N) periodic multi-layer system is studied in the clean limit. The finite reflection coefficient R at the interface is explicitlytaken into account. The obtained gap equation of S-N multi-layer israther compact and is similar to that of S-N double-layer. The behaviorof T_c of a periodic multi-layer qualitatively agrees with that ofthe corresponding double-layer except when the thickness of layer isshorter than the coherence length and R ~= 0.5 . Thicknessdependence of T_c of a periodic multi-layer is in good agreement withthe experimental data of Banerjee et al. on the Nb/Cu superlattice.

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A huge peak of irreversible magnetization in CeRu₂ single crystal, together with the equilibrium magnetization, was investigated by means of a static magnetization measurement using a Faraday force magnetometer. The residual resistance ratio of the used crystal exceeds 250, indicating that it is a clean superconductor. Contrary to the previous reports, there is no pinning-free region in the magnetization curves below the upper critical field H_c2. The detailed minor-hysteresis-loop measurement has revealed that the peak structure in the increasing-field magnetization curve around the onset field of the peak strongly depends on previous field-history, resulting in an apparent asymmetry of the peak structure. No trace of paramagnetic suppression of superconductivity in the vortex-penetrated state is observed from the superconducting equilibrium magnetization curves. The peak position, although highly anisotropic, can be interrelated to the peak strength, regardless of the applied field direction. It is likely that the irreversibility peak is due to a synchronization pinning of the defective flux line lattice, rather than due to a first-order transition from the mixed state to the Fulde-Ferrell-Larkin-Ovchinnikov state.

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We have measured both the specific heat and the susceptibility of thesingle crystal PrCu₆ in magnetic fields systematically for the firsttime. Our measurements performed in fields up to 4.2, T has revealed theanisotopy; the specific heat decreases with the field when the field isparallel to the b-axis. From the result of the susceptibility measurementperformed in fields up to 5, T, we show that the electronic specific heatcoefficient γ decreases from 16.1, mJ/K²·mol at zero fielddown to 15.5, mJ/K²·mol at 4.2, T when the field is applied alongthe b-axis. The increase of Δ up to 20.8, K at 4.2, T from 19.3, K atzero field has been obtained as well from our analysis, where Δ isthe energy separation between the ground state and the first excited state.On the other hand, γ and Δ remain unchanged for the fieldaligned along other orientation. We have concluded that the decrease of thespecific heat is attributed to the increase of Δ and to thereduction of γ.

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Inelastic neutron measurements have been performed on a quasi-one-dimensional spin-gap system CuNb₂O₆. From the dispersion curve of the triplet excitation, the compound has been found to have a ferromagnetic-antiferromagnetic alternating bond chain. The temperature (T) dependence of the magnetic excitation spectra indicates that both the singlet correlation and the antiferromagnetic correlation begin to grow with decreasing T at around T₀, where the spin susceptibility becomes maximum.

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Neutron scattering measurements of an antiferromagnet spinel LiMn₂O₄ were performed using a polycrystalline sample. A bump signal peaked at 1.4, Å^-1 appears below 100, K, though the line width of the magnetic diffraction pattern remains broad even at 8, K. Additionally, Mn spins freeze below 60, K. In LiMn₂O₄, magnetic ions, i.e., Mn³⁺ and Mn⁴⁺, form a network of corner-shared-tetrahedra. The observed magnetic pattern is explained by the following charge and the magnetic ordering. Two Mn³⁺ ions and two Mn⁴⁺ ions randomly distribute on four corners of each tetrahedron. The antiferromagnetic correlation exists only in the arrangements of Mn³⁺--Mn³⁺ and Mn⁴⁺--Mn⁴⁺ and no correlation in Mn³⁺--Mn⁴⁺; this is due to the frustration of spins between the arrangements of Mn³⁺--Mn³⁺ and Mn⁴⁺--Mn⁴⁺.

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Bond-operator mean field equations for the square-lattice, S=1/2 bilayer Heisenberg model are developed and solvednumerically. In the vicinity of both the zero-fieldcritical point and the field-induced transitions, comparisons are made with T=0 and finite-temperaturestrong coupling expansions.The mean-field theory suggests that the quantum criticalregion for the field-induced transitions is restricted tosignificantly lower temperatures than one might have concluded based on strong-coupling expansions or othernumerical studies.

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Antiferromagnetic spin arrangement of Mn formate di-urea is studied by proton NMR measurements below T_N (3.78, K). Observed spectra are compared with possible spin arrangements. The antiferromagnetic moments within the layer point to the direction rotating 15 degrees around the c-axis from the middle direction between the [001]- and [100]-directions. The layer including antiferromagnetic moments rotates following to the stacking of four-fold screw axis along the c-axis. The origin of this spin arrangement is discussed.

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Effective spin Hamiltonians with t_2g orbital degeneracy have been investigated theoretically. We assume that a d electron occupies one of doubly degenerate d_zx and d_yz orbitals which have the lowest energy in atomic level. The orbital degrees of freedom are represented as Ising iso-spin operators because of the symmetry of the orbital characters. We apply the Hamiltonians to a ladder and a chain lattices and investigate the models using the exact diagonalization. For the ladder model, a spin gap opens above a finite value of the spin exchange coupling on rung, which is qualitatively different from the ladder model with single orbital. For the chain model, the spin gap behavior is observed in the uniform spin correlation at low temperature. Origin of the spin gap is a spin-dimer triggered by the occurrence of the ferromagnetic orbital ordering, which suggests a new mechanism of the spin gap formation.

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A neutron powder diffraction study revealed thatCa₂Y₂Cu₅O₁₀, which consists of edge-sharingCuO₂ chains, shows an antiferromagnetic long-range orderingbelow --29, K. The arrangement of the Cu²⁺ spins isferromagnetic along the chain (a axis) with a spin directionalong the b axis. The magnetic structure has the propagation vectork = [001]. The ordered moment ofthe Cu²⁺ spins is --0.9, μ_B at 10, K, suggesting thatthe interchain interactions are fairly large. The observed intensitiescan be better described by assuming an ordering of oxygen momentswhich are induced due to the strong hybridization between thecopper and oxygen ions.

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NMR Knight shifts K and nuclear relaxation rates 1/T₁ have been studied on the V⁴⁺ sites of two compounds [N(CH₃)₄]V₃O₇ and (en)₂ZnV₆O₁₄ which are known to exhibit spin-gap behavior from their susceptibility data. The activation-type behavior has been observed in K and 1/T₁, confirming the existence of the spin-gap in these systems. The frequency (ω _N) dependence of 1/T₁ of [N(CH₃)₄]V₃O₇ has been found to be 1/√ ω _N-type one and 1/T₁ of (en)₂ZnV₆O₁₄ is linear in -ln (ω _N), indicating the diffusive and ballistic characters of the triplet excitations, respectively. The results are discussed in relation to the theory recently developed by Sachdev and Damle [Phys. Rev. B 57 (1998) 8307].

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The dielectric dispersions in the mixed crystals KBr_1-x(NO₂)_x (x=0.06, 0.11, 0.26 and 0.36) were measured in the frequency range from 100, Hz to 10, MHz. In order to clarify the orientational dynamics of the NO₂^- ions with a dipole moment and the glassy phase transition, the dielectric dispersions were discussed on the basis of the Clausius-Mossotti and the Arrhenius relations. The value of the permanent dipole moment of the NO₂^- ion in the host crystal was estimated to be about 0.5 D. It turns out that the origin of the glass transition, if any, is not freezing of dipole moments.

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Fluorescence spectra of pure biphenyl crystals were measured over a wide temperature range. In contrast to the sharp peaks near 530, nm observed in crystals grown from methyl alcohol solution, a new broad band around 500, nm was found in zone-refined crystals at 5.0, K when the intense exciting laser was employed. From the temperature dependent behavior and the fluorescence decay characters, it is suggested that the new excimer-like band is related to photo-induced structural deformation in biphenyl crystals.

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