In this letter let us first show a fractal structure of the chaos region, with positive Lyapunov exponents, appearing in the two-dimensional parameter space spanned by the temperature parameter and the effective stimulus. From the dynamical results for the modified Nagumo-Sato model of a neural element, it is found that such a chaos region showing chaos behaviour has a global self-similar structure in it. The fractal dimensions evaluated from the capacity and the entropy are found to increase with the increase in the decay parameter of the refractory memory.

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When a point mass (radiator) is moving with speed v on a circular orbit around another massive point mass (accelerator) at a distance r, the metric seen by an observer far from the accelerator but close by and moving with the radiator, shows space anisotropy, g_xx−g_yy=g_xx−g_zz=4(v⁄c)⁴, where the x-axis gives the direction of the velocity v of the radiator. The value of this anisotropy is 10⁻¹² for the sun, accelerated by the center of our galaxy Milky Way, and is 4×10⁻¹⁶ for Earth, accelerated by the sun. Brillet and Hall’s experiment, which claims accuracy to 0.5×10⁻¹⁴ for the anisotropy of space, can detect the predicted anisotropy near the sun if the detector is modified properly.

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The limiting irreducible cluster sums for infinite volume, and hence the virial coefficients, are investigated for the one-dimensional, the two-dimensional square, the three-dimensional simple cubic and the two-dimensional triangular lattice gas with nearest-neighbour (attractive) interactions. It is concluded that all the virial coefficients for the two-dimensional triangular lattice gas are negative for sufficiently low temperatures, while this does not hold for the other lattice gases dealt with in this paper.

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Transport coefficients and velocity distributions of ions in gas under an electric field of a wide range are analysed using the flight time integral (FTI) method. A thermal region where the ion transport almost solely depends on the thermal motion of gas is clearly found in a range of low reduced field E⁄N, while characteristics dependent only on E⁄N are observed in the high E⁄N range. Understanding of the ion transport property in the thermal region and the temperature dependence will be important for the derivation of interaction potentials between ion and neutrals.

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Numerical analysis for radiation level in a high-power backward wave oscillator with a finite-length slow-wave structure with end reflections has been made using an algorithm called the higher-order implicit difference method (HIDM). Spatial and temporal evolutions of a small localized disturbance in an RF field are followed by relativistic fluid equations and Maxwell equations. The radiation intensity of the oscillation decreases substantially with increasing energy spread beyond 10% of the beam.

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A new quasi-periodic dragon lattice was grown by means of molecular beam epitaxy and examined carefully by high resolution X-ray diffraction. The diffraction pattern shows many satellite peaks, which are symmetric around 1/2, 1/4, 1/8, …, 1/2^p with p integer and are assigned by (2k+1)⁄2^p with k and p integers. The characteristics of the dragon lattice are discussed in terms of the correlation function and compared to other one-dimensional quasi-periodic lattices.

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In electron-focusing geometry in the presence of a magnetic field, numerical calculations have been made for the wave functions of stationary states and for transmission probability of the electron wave from the injector to the collector. The pattern behaviour of transmission probability is demonstrated as a function of the external magnetic field. The results obtained here reproduce the experimental focusing spectra qualitatively.

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Electrical resistivity, thermoelectric power and thermal conductivity due to random exchange potentials at the interfaces of the magnetic superlattices are theoretically studied. Material dependence of these properties is derived for TM/Cu superlattices, where TM’s denote 3d-transition metal elements. It is shown that the magnitude of the magnetic moments and the number of d-electrons of the magnetic atoms are key parameters for these transport properties. Possible candidates for superlattices showing large magnetoresistance are proposed.

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We propose a simple method for tuning interference by appliying gate voltage in 2-dimensional electron systems. Experimental evidence is presented.

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In anisotropic superconductors, the coherence peaks appear differently in the nuclear magnetic relaxation rate, 1⁄T₁, and the homogeneous dynamic conductivity, σ(ω). The peak appears in σ(ω). However, 1⁄T₁ shows no peak but rapid reduction just below critical temperature, if it is mainly due to antiferromagnetic spin fluctuations. The feature is consistent with recent measurements of YBa₂Cu₃O₇.

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The phase diagram for spin 1/2 fermions with attractive interband interactions (−V) is obtained for the two-band Hubbard model in the space of −V, intraband repulsion (U), and the band filling from the quantum Monte Carlo calculation along with the mean-field theory in one dimension. The competition of an off-diagonal long-range order with diagonal orders (CDW and SDW) is shown to result in a superconducting ground state arising from interband pairing (i) in the presence of U of right magnitude (∼V) and (ii) in non-half-filled bands.

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The occurrence of high-spin ground states in the strongly correlated electron system is clarified in one and two dimensions. Even for infinitesimal Hubbard U, the ground state with a spin-polarized Fermi surface periodically arises as the number of electrons is varied due to a ‘k-space Hund’s coupling’. A non-perturbative crossover to strong U regime, which is accompanied by a series of level crossings and involves the stability of the Nagaoka state, is also demonstrated.

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We have investigated the relationship between the magnetoresistance and the paracrystalline disorder of lattice plane spacings at the interface in Fe/Cr multilayer films prepared by rf sputtering. The X-ray linewidths for the (110) and (220) peaks were analysed using a modified paracrystalline theory to obtain the grain size and the lattice uncertainty, which represents the degree of paracrystalline disorder. We have found that the magnetoresistance increases with decreasing lattice uncertainty.

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The relationship between quantum fluctuations and Néel-type ordering for the ground state in s=1⁄2 Heisenberg antiferromagnet on a square lattice is discussed in connection with the role of the off-diagonal part of the exchange interaction (flip-flop terms). In particular, the smallest number of flip-flops f(\ ildef) necessary to change the Néel state (the alternative Néel state) into each α−β base are introduced. The probability distribution of α−β bases to (f, \ ildef) for the ground state is obtained in the numerical calculation. The behavior of the staggered magnetisation and the averaged RVB length as to (f, \ ildef) is also investigated.

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Thallic oxide, Tl₂O_3−δ, an oxide with high conductivity, has been investigated using the pulsed NMR method. The shift and spin-lattice relaxation time (T₁) measured for ²⁰⁵Tl nuclei showed Korringa-like behavior, but their values were found to be strongly sample dependent. This suggests that the carriers belong to the thallium 6s band, and that the materials which we regard as Tl₂O₃ are not stoichiometric and deficient in oxygen.

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We have measured ¹³⁹La nuclear magnetic resonance and nuclear quadrupole resonance in La_2−xSr_xNiO_4+δ at low temperatures (1.4–4.2 K) in order to investigate the change in the magnetic and electronic structures when Sr is doped into La₂NiO_4+δ. The Sr-substituted compound shows an antiferromagnetic order up to x∼1 with a monotonous decrease in the internal magnetic field H_int at the La sites. In the high Sr-content region at x∼1, we find a phase transition to a nonmagnetic state where H_int disappears. In the nonmagnetic state, the Knight shift of ¹³⁹La is about −1.5% for x=1.0 and −1.0% for x=1.3, and the ¹³⁹La spin-lattice relaxation time T₁ follows the Korringa relation of T₁T∼7.6 sK for x=1.0 and \simeq48 sK for x=1.3, which indicates that the system is in a normal metallic state.

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A new hamiltonian amplitude equation,
iψ_x+ψ_tt+2σ|ψ|²ψ−εψ_xt=0 σ=±1, ε<<1,
is introduced. The equation governs certain instabilities of modulated wave-trains, and the addition of the term −εψ_xt overcomes the ill-posedness of the unstable nonlinear Schrödinger equation. This new equation is apparently not integrable, but it is a Hamiltonian analogue of the Kuramoto-Sivashinsky equation, which arises in dissipative systems.

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Starting from a quantum mechanical approach the transition probability between charged particles is transformed to inelastic cross-section. From this a simple and useful approximation is obtained for the multiphoton energy transfer processes which accompany the scattering of a charged particle. Due to the plasma potential in the presence of a strong laser field, an effective collision frequency is found. The amplitude of the electron oscillatory velocity v₀ in the radiation field is assumed to exceed the electron thermal velocity v_te. Under these conditions, the absorption rate is independent of the initial distribution function and depends only on the photon flux intensity. The calculated effective collision frequency can be scaled as I^p, where the p-parameter is in the range of −0.5<p≤0.5. Our results are compared with those of other formalisms and experimental results.

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The dynamic process of the coupling of tearing modes in the normal RFP discharge, is studied with the help of 3-D MHD simulations. Almost of studies on the mechanism of the dynamo and the mode coupling have been carried out in the special operation mode “the deep reversal discharge” where the toroidal field at the wall is negatively increased. In this paper the dynamic process in the normal (ordinary) RFP discharge is reported. The process is as follows: The m=1 modes resonant near the plasma axis start growing in the initial stage. After growing enough, they interact with each other and the subsequent reconnection of magnetic field lines takes place. Consequently, m=0 modes are excited. In the normal RFP discharge, these couplings of tearing modes are frequently and periodically generated.

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A modified Hubbard-Beeby theory is used to calculate the dynamical structure factors of the superionic conductor α-AgI. It is found that the partial dynamical structure factors of cations and anions are almost the same at long wavelengths but very different at short wavelengths. From analysis of the partial dynamical structure factors it is found that the vibrational motion of cations is strongly correlated with the low-frequency longitudinal acoustic mode of the anion sublattice at long wavelengths. It is also found that this cation motion has no correlation with the high-frequency longitudinal optical mode of the anion sublattice at short wavelengths. These results closely resemble those of the molecular dynamics performed by Kaneko and Ueda except for the lack of a quasielastic peak. However, the cation motion has a strong correlation with the longitudinal acoustic mode even at short wavelengths.

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The structural properties of liquid lithium-sodium alloys near the phase separation curve are investigated in the modified hypernetted-chain approximation, by employing the new bridge-function scheme proposed recently by us and the effective interatomic potentials obtained by the pseudopotential theory. The concentration dependence of our results is consistent with the asymmetrical phase separation curve with respect to the concentration. We could also reproduce qualitatively the characteristic features of the concentration-concentration structure factor S_cc(q) of the ‘zero alloy’ Li_0.61Na_0.39 obtained by the neutron diffraction experiment, that is, the divergence of S_cc(q) in the long-wavelength limit and the ripple around q=2.2 A⁻¹, and the origin of the latter is clarified.

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The ferroelectric-to-ferroelectric phase transition of K₂ZnCl₄ at 144.5 K has been studied by dielectric, calorimetric, and neutron diffraction measurements. In addition to the first order transition at 144.5 K, there is a break on the dielectric constant along the a-direction at 148.0 K, where a slight anomaly in the specific heat is found by the a.c. calorimetry. Below 144.5 K superlattice reflections are found at (h+0.5, k+0.5, l). Weak satellite reflections are found between 145.5 K and 148.0 K at the incommensurate positions of (2.5±δ, 1.5±δ, 0). The misfit parameter δ is about 0.04 and it is almost temperature independent.

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The role of the fluctuation around the mean field of the antiferromagnetic state has been examined by applying the path integral method to the calculation of the ground state energy of the one-dimensional half-filled Hubbard model with the repulsion, U. In the case of the weak interaction, our result is compared with that of the exactly solvable one the dominant part of which consists of the power series of U. It is found that the present method with the lowest order contribution due to the fluctuation gives the sufficient energy for small U while the higher order of the fluctuation is needed for large U.

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To study the relation between the interchain and intrachain interactions as well as to compare the chain-like features with the bulk characteristics in chalcogenide alloys, the Te concentration (x) dependence of the optical gap E_g is theoretically analyzed for Se_1−xTe_x of an isolated chain and a trigonal crystal. In the first place, band structures are calculated for an isolated chain and for a trigonal crystal by the tight-binding approximation. The behaviour of the interaction parameters obtained from our calculations indicates that the chain-like nature of a trigonal crystal becomes less distinguished as the increase of x. Secondly, the electronic density of states of Se_1−xTe_x is calculated by the coherent potential approximation. The results show that the optical gap E_g for a bulk mixture decreases as x increases while E_g for a chain does not change very much for x≥0.2. These results are in good agreement with the experimental data.

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An anisotropic Hubbard model in quasi-two dimension under perpendicular fields is treated theoretically to explain cascade of first phase transitions in field-induced spin density wave states (FISDW) observed in the Bechgaard salts; (TMTSF)₂X (X=ClO₄, PF₆, ReO₄). We show that under a fixed field (H) and temperature (T) there exist abundant local minima of the free energy, each of which corresponds to the FISDW subphase characterized by a distribution of many order parameters. As T varies, the free energy curves for these subphases cross each other, giving rise to a first order transition between the integer subphases. In addition to this sub-subphase transition, the sub-subphases themselves split further via a first order, followed by sub-sub-subphase transition. This process proceeds iteratively to infinity. We discuss the observed recursive phase diagram in the T vs H in terms of this theory.

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A theory of the hot electron transport in strong magnetic fields is presented and is applied to the magnetophonon resonance (MPR) in semiconductors in high electric fields. The balance equations for energy and momentum are derived based on Zubarev’s theory of nonequilibirium density matrices without employing a conventional warm electron approximation. Explicit numerical results are presented for GaAs and splitting of the MPR peak and the reduction of MPR amplitude with the increase of the electric field are demonstrated. The drift velocity due to scattering from acoustic phonons is much smaller than that due to LO phonon scattering, showing that the quasi-elastic-inter-Landau-level scattering does not take place in this material.

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Experimental results on the variation of various physical properties in Bi_1.6Pb_0.5Sr_1.9−yLa_yCu_1.05O_z with varying y through the superconducting and nonsuperconducting metallic phase boundary are presented. The magnetic susceptibility at fixed temperatures is monotonous functions of y. The Hall coefficient does not indicate even a weak tendency of the sign change at the boundary. The thermoelectric power has a systematic change with y and exhibits quite unusual behavior even in the nonsuperconducting metallic phase.

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In order to explain phase diagrams independent of field-orientation, which is now evident in UPt₃, we present a scenario based on a superconducting (SC) class belonging to the one-dimensional representation (1D-REP) with odd-parity. The preexisting antiferromagnetic order (AF) lifts the spin space degeneracy of the pairing function to split T_c, which is contrasted with the orbital degeneracy lifting mechanism in the previous 2D-REP scenario. A non-trivial coupling of the two orderings, SC and AF is derived and a GL theory is developed to examine the successive phase transitions. We calculate several quantities, including the upper and lower critical fields, specific heat jumps and derive the phase diagrams under applied fields. It is demonstrated that the present 1D-REP scenario is more consistent with various experiments on UPt₃ than the previous 2D-REP one. We emphasize that the 1D-REP scenario is the only choice remained within the symmetry breaking framework, which is able to consistently explain the experiments.

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We have measured the temperature dependence of the transverse relaxation time of ⁶³Cu(2) nuclear spin in YBa₂Cu₃O_6.98, YBa₂(⁶³Cu)₃O₇, and YBa₂Cu₄O₈. After subtraction of the T₁ process, the decay curve of the spin-echo envelope for YBa₂Cu₄O₈ in a strong H₁ followed a single Gaussian form from 280 K to 4.2 K, while for YBa₂Cu₃O_6.98 it follows only above T_c. The absolute value and the temperature dependence of the decay rate 1⁄⁶³T_G could be understood by the combined contributions of the direct dipole-dipole and the temperature-dependent indirect nuclear spin-spin coupling via χ(q). From the temperature dependence of 1⁄⁶³T_G for YBa₂Cu₄O₈ below T_c, we considered that χ(Q) even below T_c remains enhanced. In a viewpoint of the ⁶³Cu(2) nuclear spin-spin relaxation experiments, so far as YBa₂Cu₄O₈ is concerned, the high-T_c superconductivity seems to exhibit the d-wave pairing.

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The results of extensive Monte Carlo simulations are reported on XY and Heisenberg antiferromagnets on a d=3-dimensional stacked-triangular lattice, which are expected to belong to the recently identified n=2 and 3 chiral universality classes, respectively. The lattices studied consist of L³ spins with 18≤L≤60. The study is an extension of earlier Monte Carlo simulations for the same system with smaller lattices. A continuous transition characterized by the novel critical exponents is found with α=0.34±0.06, β=0.253±0.01, γ=1.13±0.05 and ν=0.54±0.02 for the XY (n=2) case, and with α=0.24±0.08, β=0.30±0.02, γ=1.17±0.07 and ν=0.59±0.02 for the Heisenberg (n=3) case. The specific-heat amplitude ratio is estimated to be A⁺⁄A⁻=0.36±0.2 and A⁺⁄A⁻=0.54±0.2 in the n=2 and n=3 cases, respectively. The nature of the chiral ordering is also studied, and various chirality exponents are determined. The results are discussed in conjunction with the recent renormalization-group calculations and experiments.

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The electron spin resonance of the optically induced paramagnetic valence anomalies has been studied in the linear chain complex [Pt(en)₂][Pt(en)₂Cl₂](ClO₄)₄, en=ethylenediamine. The unpaired spins of S=1⁄2 are found to be confined in the molecular orbitals of dimerized Pt ions and the tightly ligating N atoms and Cl⁻ ions. The states have biaxial symmetries with the principal axes of spins nearly parallel to the crystal axes of the orthorhombic phase. These results support the previous assignment that the induced paramagnetic valence anomalies are neutral solitons. At low temperatures, the resonance spectrum exhibits an evidence that the solitons are fluctuating around their equilibrium positions.

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Basing on a unified picture changing from ferro- to antiferro-electric phase through a glass state, ⁸⁷Rb NMR–NQR spectra are derived theoretically for each phase of hydrogen-bonded mixed crystals Rb_1−x(NH₄)_xH₂PO₄ and their deuterated systems. The spectra have been compared with the observed NMR signals in rather good agreement. Proton (deuteron) glass structure is discussed from the viewpoint of local resonance techniques.

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The ESR Modes in CsCuCl₃ are calculated using a model of spins forming a helix with a long period along the c-axis due to the Dzyaloshinsky-Moriya interaction and a 120° structure in the c-plane due to the antiferromagnetic interaction on the triangular lattice. For the case of the external field H parallel to the c-axis the resonance condition for the two observable modes is approximately
ω_±⁄γ={3H_E1(H²_DM⁄H_E0+H_A)+(H⁄2)²}^1⁄2±H⁄2,
whereas the third mode is a zero mode. H_E0 and H_E1 are the intrachain and interchain exchange fields, H_DM and H_A are the effective fields due to the Dzyaloshinsky-Moriya interaction and the anisotropy in the exchange interaction. The frequency versus field diagram is in good agreement with the experimental findings of Palme et al., however our analysis is different from theirs in order to be compatible with the neutron scattering results of Adachi et al.

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Real and imaginary part of the dielectric constant, ε_c′ and ε_c″, along the c-axis in Sr₂Ta₂O₇ have been measured over a wide frequency range of 10² Hz∼10⁶ Hz. A cusp-like anomaly and a broad maximum of ε_c′ are found at T₁=440 K and at T₂=155 K, respectively. At around T₃=60 K∼110 K in the ferroelectric phase, a large dielectric dispersion of the Debye type is observed; ε_c′ changes abruptly by about 600 and ε_c″ shows a peak. The temperature T_AN, at which the ε_c″ shows a maximum, shifts to the high temperature side as the frequency increases. Arrhenius relation holds well; the attempt frequency and the activation energy are estimated respectively as 3.1×10¹¹ Hz and 0.11 eV. Some discussions are presented for the causes of the low frequency dielectric dispersion in the crystal.

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Elastic and dielectric properties of ferroelectric LiTlC₄H₄O₆·H₂O (LTT) were studied in the paraelectric phase. The Curie-Weiss type anomalies were observed in the elastic stiffness constant at constant electric field, the free dielectric constant and the clamped dielectric constant, while no definite anomaly was found in the elastic stiffness constant at constant electric displacement. The phase transition of LTT is proper ferroelectric, in contrast to the case of isomorphic LiNH₄C₄H₄O₆·H₂O (LAT) known as proper ferroelastic. The dielectric instability in LTT is consistently explained by the low-lying soft TO mode reported previously.

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Measurement of the complex dielectric constant of Ca₂Pb(C₂H₅CO₂)₆ (DLP) has been made around the ferroelectric phase transition temperature, T_c. The dielectric dispersion of relaxational type of which the relaxation time shows the critical slowing-down has been observed. The results indicate that the ferroelectric phase transition of DLP is essentially of the order-disorder type. No essential differences are found between DLP and isomorphic Ca₂Sr(C₂H₅CO₂)₆ (DSP) in the static and dynamic dielectric properties around T_c.

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Luminescence and optical absorption associated with relaxed excitons in pure RbI have been studied by means of time-resolved spectroscopy. It is found that the emission band near 3.0 eV consists of an intrinsic component and an extrinsic component arising from Br⁻ impurities. The intrinsic component, characterized by the same decay time as that of the π luminescence, exhibits an emission band peaking at 3.07 eV. The results indicate the presence of three intrinsic emission bands in RbI, the 3.07 eV, π and σ bands. The optical absorption originating from the initial states for the 3.07-eV and π luminescence is compared with the corresponding absorption in other alkali halides by means of the Mollwo-Ivey relation. It is shown that the absorption bands from the initial state of the π luminescence in alkali halides, except NaBr and NaI, can be categorized into two groups: one includes that for the 3.07-eV luminescence and the other that for the π luminescence.

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Spectral shapes of optical absorptions in the charge density wave states of halogen-bridged mixed-valent metal complexes are theoretically determined for the first time, using a one-dimensional extended Peierls-Hubbard model. Two important effects beyond the mean field theory are taken into account; the electron-hole (e-h) correlation on the metal atoms, and the classical fluctuation of the halogen sublattice coordinates. It is shown that the exciton strongly affects the spectral shape of the charge transfer (CT) band. When the e-h binding is weak, the CT band is the mixture of the exciton absorption and the interband ones. When it is strong, on the other hand, the exciton dominates over all the CT band and, consequently, its higher energy side becomes very close to a Lorentzian. From the comparison with experimental data, it is concluded that platinum complexes correspond to strong binding cases. The intragap absorptions associated with nonlinear excitations such as solitons and polarons are also studied in a strong binding regime.

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The present paper is concerned with an experimental study of Faraday rotation in a Cd_0.89Mn_0.11Te/Cd_0.61Zn_0.39Te superlattice at 300 K and 4.2 K. As the width of Cd_0.89Mn_0.11Te well decreases, a lying-S shaped dispersion of the Faraday rotation spectrum, which is consistent with a predominant exciton transition of |3⁄2, ±3⁄2⟩ to |1⁄2, ±1⁄2⟩, shifts toward a higher photon energy, and the peak value of the dispersion spectrum becomes larger than that for the Cd_0.89Mn_0.11Te thin film. In the superlattice systems, we also observed a Faraday rotation spectrum consistent with the exciton transition of |3⁄2, ±1⁄2⟩ to |1⁄2, ±1⁄2⟩ at a higher photon energy. The shift of the energy-band gap due to the lattice-mismatch is calculated for this system on the basis of the model of free standing strained superlattice. The positions of calculated energy in the dispersion spectrum are in good agreement with experimental results.

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The breakdown problem in a random system is investigated by numerical simulation for a network of distributed conductance The breakdown voltages are studied in the different conductance configurations. The mean breakdown strength shows anomalous size dependence given by ⟨V_b⟩∝1⁄((ln L))^y for L (the linear dimension of the network). The exponent y depends upon a degree of non-uniformity of the system and gives an information on the critical event of the breakdown. For the case of a comparatively homogeneous network the micro-crack nucleation is the critical event of a breakdown. In such a random resistor network funnel defects act as the appropriate critical defects. On the other hand, in the case of strongly disordered system the critical event in a breakdown is attributed to growth of cracks.

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The immune system is investigated as a complex adaptive network. A nonlinear dynamical model is proposed to study roles of lymphocyte and antibody in the regulation of the immune response. Three kinds of lymphocytes; B cell, T_H cell, and T_S cell, interact and compose a functional unit. Furthermore this unit interacts with other units through antibodies. These two types of interactions cooperatively work and regulate the immune response. The model can explain how the memory state is formed and stabilized in the immune network. Behaviors of the model are verified by the computer simulations.

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