It is shown that the Weierstrass function, which gives a fractal curve, can be derived from a nonlinear map with an exact chaos solution.

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A method for constructing Bäcklund transformations (BT's) for sech-squared soliton systems is presented as an alternative to the usual procedure based on the bilinear exchange formalism. It is shown to work without the need of a bilinear representation in the case of a nonlocal Boussinesq equation. The obtained bilinear BT produces a modified nonlocal Boussinesq equation.

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A new particle beam cooling scheme “cyclotron maser cooling” (CMC) was examined. Under a stimulating rf field below the critical value prescribed by an action time of the field, a beam of gyrating electrons obeyed the Liouville's theorem. However, when the field reached the critical value, the beam abruptly jumped to a critical point of the radiative system undergoing CMC, where all electrons accumulated at one discrete energy within about 30, ns. On the other hand, when the field exceeded the critical value by less than 1, dB, a coherent energy modulation took place in gyrations. As a possible mechanism of this remarkable phenomena, a phase transition or a macroscopic quantum jump induced by the “quantum field action effect” on radiation cooling was presented. Under a stimulating ratiation field below the quantum field action any oscillator system remains non-radiative. However, under the stimulating quantum field action, a macroscopic quantum jump to the radiative system takes place leading to its cooling to a stable state irrespective of photon emission mode.

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The closed-form solution to the memory function in the generalized Langevin equation (Mori formula), obtained as a series expansion in terms of the projection operator, is rederived without use of the expansion method. The procedure for approximation of the closed-form solution is briefly mentioned.

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The density matrix renormalization group (DMRG) method is applied to the anisotropic Heisenberg chain at finite temperatures. The free energy of the system is obtained using the quantum transfer matrix which is iteratively enlarged in the imaginary time direction. The magnetic susceptibility and the specific heat are calculated down to T=0.01J and compared with the Bethe ansatz results. The agreement including the logarithmic correction in the magnetic susceptibility at the isotropic point is fairly good.

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In open systems, velocity distribution functions of end-loss ions provide information not only about ion axial confinement but also about the noticeable structure which appears on the ion distribution in loss regions. An end-loss energy component analyzer (ELECA) has been developed to measure the velocity distribution functions of the end-loss ions in the tandem mirror GAMMA 10. The distribution functions and the physical quantities related to the end-loss ions are derived as functions of the output currents of the ELECA. The ion temperature in the loss region is estimated on the assumption that the distribution function is Maxwellian in consideration of the loss region characterized by the magnetic field strength and the electrostatic potentials in the tandem mirror.

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Four resonances have been observed in the current-voltage characteristics of a GaAs/AlAs single-barrier diode incorporating a δ -layer of silicon donors in the barrier. High magnetic fields applied perpendicular to the plane of the barrier are used to examine the nature of the resonant features in the current-voltage characteristics of the diode. The diode has been modelled, showing that the voltage positions and magnetic field dependence of the lower bias resonances are consistent with tunnelling through strain-field split ground states of silicon impurities below the X-conduction band minima of AlAs.

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Magnetic susceptibility in a heavy fermion system is composed of the Pauli term (χ_P) and the Van-Vleck term (χ_V). The latter comes from the interband excitation, where f-orbital degeneracy is essential. In this work, we study χ_P and χ_V in the orbitally degenerate (J=5/2) periodic Anderson model for both the metallic and insulating cases. The effect of the correlation between f-electrons is investigated using the self-consistent second-order perturbation theory. The main results are as follows. (i) Sixfold degenerate model: both χ_P and χ_V are enhanced by a factor of 1/z (z is the renormalization constant). (ii) Nondegenerate model: only χ_P is enhanced by 1/z. Thus, orbital degeneracy is indispensable for the enhancement of χ_V. Moreover, orbital degeneracy reduces the Wilson ratio and stabilizes the nonmagnetic Fermi liquid state.

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The occupation number densities N(k)s of Li and Na are obtained from a first-principle calculation of the spectral function within the GW approximation. The dielectric matrix needed to form the screened potential W is computed within the random-phase approximation. The Compton profiles (CPs) of Li and Na are computed using the N(k)s. The computed CPs are in very close agreement with the results of recent high-resolution CP experiments. The renormalization factors on the Fermi surface Z_Fs are estimated for Li along the three principal symmetry directions. Although the Z_Fs are significantly smaller compared to those obtained so far using jellium models, they compare well with those evaluated from recent experimental CPs.

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The thermoelectric power S and magneto-thermoelectric power δ S=S(H)-S(0) were measured for Fe--Cu and Fe--Ag granular alloys. The sign of both S and δ S of the measured samples was confirmed to be negative, similar to that of all the other granular alloys, contrary to the theories proposed hitherto. We point out the importance of the Kondo effect of the magnetic impurities between the magnetic and non-magnetic clusters, and we show we can understand successfully the sign of both S and δ S from this standpoint.

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Peak heights of the Coulomb oscillation are examined based on the exact-diagonal calculations of many-body states in a quantum dot, where the Coulomb interaction energy is comparable with the one-electron level spacings. At nearly degenerate levels, high-spin states appear, in accordance with recent experimental results [Tarucha et al.: Phys. Rev. Lett. 77 (1996) 3613], and some peaks of the conductance can increase with temperature. Two mechanisms are proposed for this anomalous temperature dependence. This phenomenon reflects a level spacing as small as one Kelvin and the total spin of the electronic states.

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The magnetoresistance of a quasi-one-dimensional (Q1D) organic superconductor, (DMET)₂I₃, where DMET is dimethyl(ethylenedithio)diselenadithiafulvalene, was measured up to 30, T at 1.5, K. An electrical current was applied perpendicular to the conducting ab plane and a magnetic field is rotated in the ab plane. An anomalous hump of the magnetoresistance reported previously was observed at 7, T between -15° and 15° from the most conducting b-axis. It was found that the hump has a fine structure at higher magnetic fields with two additional sharp local minima at about ± 3°. Partial disappearance of the Q1D Fermi surface at a critical angle, where a kind of quantum limit is realized, is proposed to interpret the fine structure.

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In a heavy fermion system, there exists the anomalous Hall effect caused by localized f-orbital freedom, in addition to the normal Hall effect due to the Lorentz force. In 1994, we found that the Hall coefficient caused by the anomalous Hall effect (R_H^AHE) is predominant and the relation R_H^AHE ∝ ρ² (ρ is the electrical resistivity) holds at low temperatures in many compounds. In this work, we study the system where the magnetic susceptibility is highly anisotropic due to the strong crystalline electric field on f-orbitals. Interestingly, we find that R_H^AHE is nearly isotropic in general. This tendency is frequently observed experimentally, which has casted suspicion that the anomalous Hall effect may be irrelevant in real materials. Our theory corresponds to corrections and generalizations of the pioneering work on ferromagnetic metals by Karplus and Luttinger.

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We have studied the behavior of second-order nonlinear susceptibility χ⁽²⁾ of an infinite-layer superconductor (Sr_0.7Ca_0.3)_0.95CuO_2-x to search for the chiral-glass state predicted by Kawamura for a d-wave ceramic. The linear and nonlinear susceptibilities are composed of the measured harmonic susceptibilities up to the seventh-order harmonics. The second-order nonlinear susceptibility χ⁽²⁾ shows a negative peak but oscillates as a function of temperature near T_c. This is not consistent with the prediction based on a chiral-glass transition. The Bean critical-state model explains the observed χ⁽²⁾ behavior well. It is necessary to avoid the effect of vortex pinning to find a chiral-glass transition.

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We have grown single crystals of CeRh₂Si₂ and LaRh₂Si₂ by the Czochralski pulling method in a tetra-arc furnace. The electrical resistivity and magnetic susceptibility are highly anisotropic, reflecting the tetragonal crystal structure. A metamagnetic transition is found for the magnetic field along the [001] direction at 26 T.

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The spin dynamics of La_1-xSr_xMnO₃ for Sr concentrations of x ≤ 0.3 were studied by inelastic neutron scattering. For the entire concentration range studied, we found that the spin-wave stiffness constant D and the paramagnetic spin-diffusion constant A^* are ruled by the nearest neighbor interaction, i.e., the strength of double exchange interactions. The Sr concentration dependence of both the constants, D and A^*, scale that of the Curie temperature T_C very well, and the ratios T_CMF/T_C (T_CMF: Mean field T_C determined from D) and A^*/T_C fit in the universal table for typical transition metal ferromagnets.

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DC magnetization of single crystals of Ce_xLa_1-xB₆, 0.5≤ x≤ 1, have been measured at low temperatures (T) down to 40 mK in magnetic field H//[100], and the H-T-x phase diagrams were obtained. At zero field, the antiferro-quadrupolar (AFQ) transition temperature T_Q rapidly decreases with decreasing x and vanishes abruptly between x=0.75 and 0.7. The Néel temperature T_N, which is lower than T_Q in CeB₆, varies more slowly with x and exceeds T_Q for x >~ 0.8. A clear peak observed in the susceptibility strongly suggests that a new antiferromagnetic (AF) state having no AFQ moment (phase IV) exists for 0.8>~ x>~ 0.5, in addition to the two ordered phases II (AFQ) and III (AF+AFQ). As H increases, a first-order phase IV-III transition is observed with a metamagnetic jump in the magnetization. Successive I (paramagnetic)-IV-III phase transitions are observable in a very narrow region of the H-T-x space.

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The 90°domains in tetragonal barium titanate BaTiO₃ have been observed with atomic force microscopy (AFM) under application of an electric field. The nucleation and growth of a wedge-shaped c-domain and the movement of the 90°domain boundary were observed.

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The separation of variables for x- and t_n-constrained flows of some kind of soliton hierarchy is shown. Since each equation in soliton hierarchy can be factorized into two commuting x- and t_n-constrained flow, the separability of x- and t_n-constrained flow provides the Jacobi inversion problem for soliton equations which is solvable in terms of Riemann theta function by standard Jacobi inversion technique. We use Kaup-Newell hierarchy to illustrate the method.

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Random scatterings among N neutral modes of the chiral Luttinger liquid can be absorbed into the random SU(N) rotations of local fields. Perturbation to the so-called random fixed point must be treated as the random perturbation. This random perturbation is characterized by random matrices with fixed eigenvalues. In this article the ensemble average of the random fixed point is obtained exactly. In the sequel, it is shown that simplifications which assume the two-sided SU(N) invariance of the random rotation lead to incorrect consequences.

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We discuss the integrable boundary conditions for the one-dimensional (1D) Hubbard Model in the framework of the Quantum Inverse Scattering Method (QISM). We use the fermionic R-matrix proposed by Olmedilla et al. to treat the twisted periodic boundary condition and the open boundary condition. We determine the most general form of the integrable twisted periodic boundary condition by considering the symmetry matrix of the fermionic R-matrix. To find the integrable open boundary condition, we shall solve the graded reflection equation, and find there are two diagonal solutions, which correspond to a) the boundary chemical potential and b) the boundary magnetic field. Non-diagonal solutions are obtained using the symmetry matrix of the fermionic R-matrix and the covariance property of the graded reflection equation. They can be interpreted as the SO(4) rotations of the diagonal solutions.

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In this paper it is shown by numerical calculations that chaos exists in a quantum-classical coupled system and behavior of the system depends on the initial condition of the system. It is also found that relatively regular or irregular behavior of one subsystem corresponds to similar behavior of the other. So one way arise naturally in which quantum information about such a coupled system can be obtained only by observing the different kinds of motions of the classical subsystem.

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Optical solitons in fiber grating in which the dielectric constant varies periodically along it, are investigated. It is proved that the envelope of the Bloch wave obeys the nonlinear Schrödinger equation. As an application, gap solitons in a super-lattice are discussed. The concept and method presented in this paper are useful not only for explaining recently observed Bragg grating soliton but for analyzing a large class of nonlinear periodic systems.

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A quantum statistical model for the relaxation of two strongly coupled spin 1/2 particles toward thermal equilibrium is formulated microscopically using a master equation. Raman-type dissipation mechanisms are introduced in addition to the usual bilinear coupling between the coupled system and the reservoir. The effects of two different rotating wave approximations to derive the master equation are investigated. Decoherence is considered as a process toward thermal equilibrium for the dissipative system and is studied by observing the phase and energy relaxation.

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Relaxation phenomena such as the dielectric, magnetic and mechanical relaxation of many disordered physical systems exhibit universal features in particular for long time one often observes an exponential behavior known as long time tail relaxation. We show that if individual clusters in these materials have a relaxation time proportional to the cluster size, the existence of a stable probability size distribution with a long tail power law changes dramatically the relaxation rate, from an initial exponential relaxation to a long time tail t^-α. In this case it is the morphology of the system which determines its kinetics.

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Relativistic effects on covalent bonding, in particular the role of individual valence atomic orbitals, have been investigated for diatomic (AuH and Pb₂) and hexafluoride (XF₆: X=S, Se, Mo, Ru, Rh, Te, W, Re, Os, Ir, Pt, Po, Np, U and Pu) molecules, by analysis of bond overlap population using both nonrelativistic and relativistic DV-Xα molecular orbital methods. The contributions of valence atomic orbitals to the relativistic effects on covalent bonding for the molecules are clarified. The present approach is applied to interpret the physical picture of the relativistic effects on bond length of the AuH molecule. The origin of the relativistic bond-length contraction is discussed in comparison with previously reported results obtained by bonding energy calculations.

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Stability of fluid in a cubic cavity heated from below is investigated by linear stability theory. All the boundaries are assumed to be rigid and perfectly thermal conducting. The critical Rayleigh number for the onset of the thermal convection is evaluated numerically as Ra_c=6798. The velocity and temperature fields at the critical state are obtained and discussed.

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Mesh bias experiments, in which secondary electron emission from an endplate is suppressed, suggest that simple balance between an end loss electron current and an end loss ion current does not hold at the endplate. An ion current flowing into the endplate from its back side is observed, and a theoretical model is constructed which takes account of this current and secondary electrons emitted from the mesh wires. Mirror reflection of secondary electrons off an outer mirror throat is also considered in this model. The model includes the current balance and the endplate potential self-consistently. The current balance at the endplate is well accounted for by this model.

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Anomalous structures were recently found at the liquid-vapor interfaces in n-alkanes, n-alcohols, etc. In this paper, detailed surface structure of the liquid n-alkane is investigated by molecular dynamics simulation. The computation is considerably accelerated by use of a simplified molecular model, in which detailed molecular structures of hydrocarbons are neglected; the systematic investigation of the melting and freezing of relatively large system is thereby enabled. Around the bulk melting point, an appreciable ordered monolayer is observed at the liquid-vapor interface. The momolayer is characterized by the preferred bond orientation perpendicular to the surface normal and the accumulation of the chain ends at the surface.

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Elastic constants of CeRu₂ have been measured as functions of temperature and magnetic field. The tilt elastic strain couples strongly with the vortices. The elastic anomaly Δ c due to the vortices is well described by the formula Δ c=(B²/4π)cos²θ/(1+λ²k²), where θ is the angle between the propagation of the transverse sound with the wave number k and the magnetic flux density B. By using this formula, we got the number of the pinned vortices and the coefficient λ as functions of temperature and magnetic field. The vortex state can be classified into three regions with respect of the fraction of the pinned vortices; flux-flow, strong pinning and weak pinning. The strong vortex pinning is associated with the tetragonal deformation of the lattice in the magnetic field caused by the soft (c₁₁-c₁₂)/2 of CeRu₂, which is due to high density of states in the Brillouin zone.

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We introduce new avalanche models on the d-dimensional hyper-cubic lattices which show the self-organized criticality (SOC). They are generalization of the two-state exclusive diffusion model introduced in our previous paper and called the n-state exclusive diffusion models (1≤ n≤ 2d). If n=2d, this model is the sandpile model of Bak, Tang and Wiesenfeld. By Monte Carlo simulations, we evaluated the height distributions of particles and the avalanche exponents for d=2,3, and 4. Numerical results imply that the n-state exclusive diffusion models belong to the same universality class for each d, if 2≤ n≤ 2d. We apply the mean-field approximation and evaluate the height distributions of particles in the SOC states. It is shown that the mean-field theory by Tang and Bak is the d→ ∞ limit of our mean-field approximation.

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The coupled phonon-lattice gas model is used to calculate the frequency dependent hopping rate of mobile ions in superionic conductors. It is found that the hopping rate is composed of several Gaussians including both contributions of the ion-phonon and ion-ion interactions. The calculated hopping rate is compared with the far infra-red conductivity for silver halides, AgI, AgCl and AgBr.

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Influence of high magnetic fields and pressure onband structure of FeSi has been studied by thefull-potential LMTO--ASA method. It is found that the semiconducting ground state of FeSi is stable in the wide volume range of ± 15\At the same time, as follows from the LSDA calculations, the applied external magnetic fields induce the metallic magnetic state. At low fields our results agreewith the measured magnetization. There is steep increaseof calculated magnetization at high critical field H_cr= 170 T (itinerant metamagnetic transition).

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We present a microscopic examination for the itinerant-localized duality model which has been proposed to understand anomalous properties of strongly correlated systems like the heavy fermions by Kuramoto and Miyake, and also useful to describe the anomalous properties of the high-T_c cupurates. The action of the duality model consists of two components of dynamical degrees of freedom. One of them is coherent itinerant degree of fermion and the other is incoherent localized one describing mainly the spin which has not been explicitly considered so far. We show that the thermodynamic potential of the strongly interacting Hubbard model can be rearranged in the form of duality model on the basis of renormalized perturbation expansion of the Luttinger-Ward functional if the one-particle spectral weight exhibits triple peak structure. We also examine the incoherent degrees of freedom described as a “localized spin” and show on the basis of the pertubation expansion that there exists commensurate superexchange-type interaction among the “localized spins”.

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The effects of Umklapp scattering on electronic states are studied in one spatial dimension at absolute zero. The model is basically the Hubbard model, where parameters characterizing the normal (U) and Umklapp (V) scattering are treated independently. The density of states is calculated in the t-matrix approximation by taking only the forward and Umklapp scattering into account. It is found that the Umklapp scattering causes the global splitting of the density of states. In the presence of sufficiently strong Umklapp scattering, a pole in the t-matrix appears in the upper half plane, signalling an instability towards the `G/2-pairing' ordered state (G is the reciprocal lattice vector), whose consequences are studied in the mean field approximation. It turns out that this ordered state coexists with spin-density-wave state and also brings about Cooper-pairs. A phase diagram is determined in the plane of V and electron filling n.

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Comparative study is presented for the in-plane angular effect of magnetoresistance of quasi-one-dimensional organic conductors, (DMET)₂AuBr₂ and (TMTSF)₂ClO₄. The magnetoresistance for the magnetic and electrical fields parallel and perpendicular to the most conducting plane, respectively, was measured at 4.2, K and up to 7.0, T. (DMET)₂AuBr₂ shows an anomalous hump in the field-orientation dependence of the magnetoresistance for the magnetic field nearly parallel to the most conducting axis and this is very similar to what previously reported for (DMET)₂I₃. Weak anomaly was detected for the magnetoresistance of (TMTSF)₂ClO₄ in the Relaxed state, while no anomaly was observed in the SDW phase in the Quenched state. By comparing the numerical angular derivatives of the magnetoresistance, it is shown that the anomaly in the in-plane angular effect continuously develops from zero magnetic field and is closely related to the quasi-one-dimensional Fermi surface. A simple method is proposed to estimate the anisotropy of the transfer integral from the width of the hump anomaly.

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In the framework of the Su-Shrieffer-Heeger (SSH) model, we investigate the effect of Aharonov-Bohm (AB) flux on the dimerization of mesoscopic organic polymer rings. It is shown that an applied AB flux in some flux windows is able to overcome the Peierls instability in mesoscopic organic polymer rings in the reasonably weak electron-phonon coupling regime. The coupling-strength and ring-size dependence of the window size in both half-filled and doped rings are exploited. The nature of the excitations away from half-filling is discussed in the weak coupling regime where there is a de-dimerization window as well as in the strong coupling regime where dimerization prevail at all values of the flux. The plausibility to observe the de-dimerization effect and the persistent current in polymer rings is also addressed.

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Using Co/NM/NiFe/NM (NM=Cu, Ag, Au) multilayers prepared on the substrates with V-groove microstructures, we measured the magnetoresistance both with CIP geometry and with current-at-an-angle-to-the-plane (CAP) geometry for the same sample. It was confirmed that CAP-MR is larger than CIP-MR for all of Cu, Ag and Au based series. We estimated CPP-MR values by extrapolation using observed CIP-MR and CAP-MR values. The deduced CPP data were analyzed by the series resistor model and the obtained parameters for Cu, Ag and Au based series were compared with one another.

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We have studied the superconductor-insulator transitions in the two-dimensional regular arrays of Al/AlO_x/Al small Josephson junctions. We studied the critical tunneling resistance and the temperature dependence of the resistance in detail by varying the interactions of the elementary excitation, i.e., charge solitons and vortices. The charging energy, junction resistance and the system width are the parameters to be changed. The results were compared with the theory of Fazio and Schön. Most of the observed results can be explained by the theory although we found some disagreements.

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We investigate the collective phase oscillations in superconductivity, i.e., the Carlson-Goldman mode in the charged system and the phason in the neutral, focusing on their velocities and how they appear in the structure function of the phase fluctuation of the order parameter. Our microscopic theory can cover from the clean to the dirty system, and furthermore it can treat the Landau damping correctly. Based on our formulation, we obtain following results: (1) The velocity of the phason is proportional to (T_C-T)^1/6 (T<~ T_C) in the clean system, though it has been believed as (T_C-T)^1/4 (T_C: superconducting transition temperature). (2) The structure function has a central peak which grows as T→ T_C. This phenomenon is related to the central peak problem in the field of the structural phase transition. (3) The Carlson-Goldman mode can be observed by a tunneling experiment in case of the dirty system, while not in the clean. It is in contrast to the previous prediction. All of these results are found to be deeply related to the presence of the Landau damping as well as the screening effect, both of which are caused by the quasi-particles excited thermally.

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Spin fluctuation-induced superconductivity is studied on a two-dimensional d-p model by using a strong coupling theory, and is applied to interpret high-T_c cuprates. A self-consistent renormalization scheme is employed within the so-called fluctuation exchange (FLEX) approximation or the renormalized random phase approximation (RRPA). Using the band parameter values which approximately reproduce the observed Fermi surface and the d- and p-hole numbers estimated from NMR experiments, we get reasonable values for T_c in an optimum and overdoped concentration range. The dynamical susceptibility, the nuclear spin-lattice relaxation rate and the one electron spectral density are well compared with the existing experimental results.

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Thermal conductivity κ of La_2-ySr_yCu_1-xZn_xO₄ and Bi_1.6Pb_0.5Sr_1.9-yLa_yCuO₆, in which the electron-number density can be controlled from the underdoped insulating to the nonsuperconducting metallic phase through the superconducting one, has been measured. By considering the systematic difference of the T-dependences of κ among above three phases, the observed κ has been consistently divided into the electron- and phonon-components. In the superconducting phase, the T-dependence of the electron component is found to support the d-symmetry of the order parameter.

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We report results of neutron-diffraction experiments which have been carried out to study the long range magnetic order developing on the Kondo lattice of the pseudo-binary-alloy system Ce(Ru_1-xRh_x)₂Si₂ with x around 0.15. The ground-state structure of the ordered phase has a sinusoidal modulation of the moment, that is, a modulation with an incommensurable wave number and a uniaxial polarization. We assign this phase to the same category of magnetism as that of the spin-density wave in metals. Several characteristic quantities of this ordering such as the order parameter, the wave number, the amplitude and the anisotropy of the polarization and the anomaly in the lattice-constant are analyzed and discussed in terms of either the s-d model or the hybridized f-band model of Kondo effect.

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YbCu₅ and YbCu₄In forms a solid-solution (YbCu_5-xIn_x) with cubic AuBe₅-type (C15b) structure in the In-concentration range 0.1≤ x≤ 1; and below x=0.1, it coexists with a hexagonal CaCu₅-type YbCu₅ phase under ambient pressure. The magnetic susceptibility and high-field magnetization measurements reveal that the first-order valence transition in YbCu₄In shifts to higher temperature and becomes broadened significantly with decreasing In-content, and simultaneously the delocalized mixed-valent state of Yb ion (x=1) shows a continuous change toward the localized trivalent state (x=0). The electrical resistivities of YbCu_5-xIn_x display various temperature-dependencies: ranging from a pronounced drop at x=1, via a minimum behavior for 0.4≤ x≤ 0.7, to a negative logarithmic increasing behavior (-ln T) for x≤ 0.3. Above results suggest that YbCu_5-xIn_x goes through a crossover from a valence fluctuation system to a dence Kondo one with decreasing x. At x=0, the formation of Kondo lattice is predicted.

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We have studied pressure effects on layered Perovskite-type orbital ordering ferromagnet K₂CuF₂, particularly the pressure-induced transition from ferromagnetic (F) to antiferromagnetic (AF) state. First the magnetic phase diagram of simple one-dimensional multi-band Hubbard Hamiltonian with antiferrodistortive order is constructed with exact diagonalization procedure. It is found that AF and helical (HI) states can be stable in a region of large transfer energy even with keeping antiferrodistortive order. For more realistic two-dimensional models relevant to CuF₂ plane in K₂CuF₄ the magnetic phase diagram is derived by perturbational procedure. Judging from the parameter values estimated by FLAPW band calculations for K₂CuF₄ under high pressure as well as at ambient pressure, it is concluded that the pressure-induced F-AF transition may be realized in K₂CuF₄ without structural transition from antiferrodistortive to ferrodistortive phase. Further the observed pressure dependence of T_C of K₂CuF₄ can be explained qualitatively by our theory.

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The general eigen-mode equation of microscopic nonlocal response theory has been applied to infinite 3-dimensional (3D) crystals. This leads to a simple and general dispersion equation containing several known results as limiting cases. This result unifies various situations, such as the polaritons with Bragg scattering, the X-ray dynamical scattering with resonance, and photonic bands, in a single transparent formalism.

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Auger-free luminescence (AFL) resulting from a radiative transition between the outermost-core bands and the valence bands in BaF₂, RbF, CsF, CsCl and CsBr has been studied in a wide range of temperatures from 10 to 300 K. The AFL spectra are separated from those originating from the valence-band excitation with use of time-resolved luminescence spectroscopy. It is found that the decay profile of AFL in each crystal is essentially the same throughout the spectrum. The remarkable thermal broadening of the linewidth is verified for all systems. This strongly suggests that the core hole generated on a positive ion induces considerable displacement of the surrounding ions within its lifetime. Based on the present results, the spectral shape of AFL is discussed in terms of a cluster model and a two-band model, requiring further development of the investigations in theory and experiment.

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Shapes of a three-dimensional and axially-symmetric vesicle are studied by the Monte Carlo simulation of a joint-segment model. At finite temperatures and pressures, various shapes of a vesicle such as a sphere, a dumbbell, a codocyte-I,II, a torocyte and a rotated triangular-like shape are obtained. The phase diagram at the lowest temperature agrees quantitatively with the one obtained in the ground state by Seifert et al. using the variational calculation of the continuum elastic energy. Dynamical processes of shape transformations are also investigated.

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