A new integrable equation is found by a new inverse scattering method. The inverse method gives a hierarchy and an infinite number of conserved densities.

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We study correlations of observables in energy eigenstates of chaotic systems of a large size N. We show that the bipartite entanglement of two subsystems is quite strong, whereas macroscopic entanglement of the total system is absent. It is also found that correlations, either quantum or classical, among fewer than N⁄2 points are quite small. These results imply that chaotic states are stable. Invariance of these properties under local operations is also shown.

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To elucidate the mechanism leading to the breakdown of a particle picture for multicomponent Bose–Einstein condensates (BECs) with a harmonic trap in high dimensions, we investigate the corresponding two-dimensional nonlinear Schrödinger equation (Gross–Pitaevskii equation) using a modified variational principle. A molecule of two identical Gaussian wave packets has two degrees of freedom (DFs): the separation of center of masses and the wave-packet width. Without intercomponent interaction (ICI), these DFs show independent regular oscillations with degenerate eigenfrequencies. The inclusion of ICI strongly mixes these DFs, generating a fat mode that breaks the particle picture, which, however, can be recovered by introducing a time-periodic ICI with zero average. In the case of a molecule of three wave packets for a three-component BEC, the increase of the ICI amplitude yields a transition from regular to chaotic oscillations in wave-packet breathing.

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We formulate a conserving gapless mean-field theory for Bose–Einstein condensates on the basis of a Luttinger–Ward thermodynamic functional. It is applied to a weakly interacting uniform gas with density n and s-wave scattering length a to clarify its fundamental thermodynamic properties. It is found that the condensation here occurs as a first-order transition. The shift of the transition temperature ΔT_c from the ideal-gas result T₀ is positive and given to the leading order by ΔT_c=2.33an^1⁄3T₀, in agreement with a couple of previous estimates. The theory is expected to form a new theoretical basis for trapped Bose–Einstein condensates at finite temperatures.

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We propose a realistic model for electric conduction, and study transport phenomena by molecular dynamics simulation. We observe that the system reaches a nonequilibrium steady state in the presence of an external electric field. The electrical conductivity is almost independent of the impurity distribution and the system size, and there is no long-time tail. The fluctuation–dissipation theorem and the Kramers–Kronig relation hold at all frequencies. These results show that this model has normal transport properties.

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A new method of analyzing nonequilibrium phenomena in a rarefied gas is explored through studying one-dimensional stationary heat conduction in a gas at rest by the third-order theory of consistent-order extended thermodynamics. We propose a consistent series solution for the moment equations and an order expansion for the uncontrollable value. The temperature solutions and the optimum uncontrollable data agree quantitatively with the numerical calculations. Temperature jumps and entropy production at the boundaries are also explicitly calculated as illustrations.

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The pressure dependences of the antiferromagnetic and superconducting transition temperatures have been investigated by ac heat capacity measurement under high pressures for the heavy-fermion superconductor CePt₃Si without inversion symmetry in the tetragonal structure. The Néel temperature T_N=2.2 K decreases with increasing pressure and becomes zero at the critical pressure P_AF\\simeq0.6 GPa. On the other hand, the superconducting phase exists in a wider pressure region from ambient pressure to about 1.5 GPa. The pressure phase diagram of CePt₃Si is thus very unique and has never been reported before for other heavy fermion superconductors.

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The steady sliding state of periodic structures such as charge density waves and flux line lattices is numerically studied based on the three dimensional driven random-field XY model. We focus on the dynamical phase transition between plastic flow and moving solid phases controlled by the magnitude of the driving force. By analyzing the connectivity of comoving clusters, we find that they percolate the system under driving forces larger than a certain critical force within a finite observation time. The critical force, however, logarithmically diverges with the observation time, i.e., the moving solid phase exists only within a certain finite time, which exponentially grows with driving force.

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The possibility of a quartet superfluidity in fermionic systems is studied as a new aspect of atomic gas at ultralow temperatures. The fourfold degeneracy of a hyperfine state and moderate coupling is indispensable for the quartet superfluidity to occur. Possible superconductivity with quartet condensation in electron systems is discussed.

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Anomalous enhancement of light emission from a Si(001) vicinal surface induced by Au adsorption was observed using a light detecting system combined with a transmission electron microscope. The Si(001) vicinal surface was separated into Si(001)5×3.2–Au terraces and Si(119)“8×2”–Au facets by Au adsorption. It was found that the electron-beam-induced light emission is highly polarized due to anisotropy of the surface structure. The emission intensity from the Si(001)–Au terrace is enhanced for the s-polarized direction parallel to the surface steps in the wavelength range of 270–450 nm, and reduced for the p-polarized direction. This result indicates that the Au adsorption on the Si(001) vicinal surface modifies the optical properties of the materials (in the present case Si), suggesting the formation of a new material phase on the surface.

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We introduce a systematic method for constructing a class of lattice structures that we call “partial line graphs”. In tight-binding models on partial line graphs, energy bands with flat energy dispersions emerge. This method can be applied to two- and three-dimensional systems. We show examples of partial line graphs of square and cubic lattices. The method is useful in providing a guideline for synthesizing materials with flat energy bands, since the tight-binding models on the partial line graphs provide us a large room for modification, maintaining the flat energy dispersions.

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The possibility of metal–insulator transition in molecular conductors has been studied for systems composed of donor molecules and fully ionized anions with an incommensurate ratio close to 2:1 based on the one-dimensional extended Hubbard model, where donor carriers are slightly deviated from quarter filling and under an incommensurate periodic potential from anions. By the renormalization group method, the interplay between commensurability energy on the donor lattice and that from the anion potential has been studied and it has been found that an “incommensurate Mott insulator” can be generated. This theoretical finding will qualitatively explain the appearance of the insulating state in a two-dimensional material with an incommensurate filling, (MDT-TS)(AuI₂)_0.441.

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The thermoelectric power, S, of metals is known to be linear with respect to temperature, T, in the low-temperature limit. The proportionality between the initial slope of the S(T) curve and the electronic specific-heat constant, γ, both at the T=0 limit, has been attracting attention for Ce compounds and other substances showing the heavy-Fermion state. However, there has been no study on solid solutions in relation to the present interest. We collected existing data of both S(T) and γ on solid solutions based on Ce and Eu compounds, and we confirmed again the proportionality between the two quantities for their composition ranges covering the emergence of the heavy-Fermion state but having no magnetic order. The heavy-Fermion state in the Eu-based compounds has never been investigated in relation to the present interest. The similarity between the valence-transition temperature, T_V, for Eu compounds and the Kondo temperature, T_K, for Ce compounds is discussed. Observations of the sign change in the S(T) curves and the existence of a peak in the ρ(T) curves, ρ being the resistivity, at around T_V for Eu compounds are noteworthy.

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Electronic state evolution in the metal–nonmetal transition of PrRu₄P₁₂ has been studied by X-ray and polarized neutron diffraction experiments. It has been revealed that, in the low-temperature nonmetallic phase, two inequivalent crystal-field (CF) schemes of Pr³⁺ 4f² electrons with Γ₁ and Γ₄⁽²⁾ ground states are located at Pr1 and Pr2 sites forming the bcc unit cell surrounded by the smaller and larger cubic Ru-ion sublattices, respectively. This modulated electronic state can be explained by the p–f hybridization mechanism taking two intermediate states of 4f¹ and 4f³. The p–f hybridization effect plays an important role in the electronic energy gain in the metal–nonmetal transition originated from the Fermi surface nesting.

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Semiconductor point contacts can be a useful tool for producing spin-polarized currents in the presence of spin–orbit (SO) interaction. Neither magnetic fields nor magnetic materials are required. By numerical studies, we show that (i) the conductance is quantized in units of 2e²⁄h unless the SO interaction is too strong, (ii) the current is spin-polarized in the transverse direction, and (iii) a spin polarization of more than 50% can be realized with experimentally accessible values of the SO interaction strength. The spin-polarization ratio is determined by the adiabaticity of the transition between subbands of different spins during the transport through the point contacts.

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We have carried out nuclear quadrupole resonance (NQR) measurements in the filled skutterudite compounds Pr(Os_1−xRu_x)₄Sb₁₂ (x=0.1, 0.2), in order to gain insights into the symmetry of the superconducting gap function. Upon replacing Os with Ru, the spin–lattice relaxation rate 1⁄T₁ becomes proportional to temperature (T) at low T far below T_c, and the magnitude of (1⁄T₁T)_low-T increases with increasing Ru content. These results indicate that a finite density of states is induced at the Fermi level by the impurity, and thus suggest that there exist nodes in the gap function of PrOs₄Sb₁₂.

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Applying a variational Monte Carlo method to a two-dimensional t–J model, we study the nonmonotonic d_x²−y²-wave superconductivity observed by Raman scattering and angle-resolved photoelectron spectroscopy experiments in electron-doped cuprates. As a gap function in the trial state, we extend the d-wave form (ext.d) so as to have its maxima located near hot spots of the system. It is found that the ext.d wave is always more stable than the simple d wave in the electron-doped case, and the magnetic correlation of the wave vector (π,π) as well as the pair correlation is enhanced. These results corroborate spin-correlation-mediated superconductivity in cuprates, which was recently argued from a FLEX calculation. In addition, we confirm that s- and p-wave symmetries are never stabilized even in an overdoped regime.

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We observed an unusual magnetic phase transition in the magnetic phase of ε-Fe₂O₃ nanorods (Néel temperature = 495 K). In the cooling process at 1 kOe, the magnetization value (M) of the ε-Fe₂O₃ phase decreased at 154 K and then sharply decreased between T=115 and 70 K. During the heating process, the M value returned to the original value at T=125 K with a thermal hysteresis of 10 K. This phase transition is accompanied by a decrease in coercive field from 21 kOe (200 K) to 0.6 kOe (100 K). This unusual magnetic phase transition is interpreted as a spin reorientation phenomenon due to the compensation between the magnetic dipole–dipole interaction and the single-ion anisotropy.

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We report on a novel phase transition at T=0.9 K in the Ce-based filled-skutterudite compound CeOs₄Sb₁₂ via measurements of the nuclear-spin lattice relaxation rate 1⁄T₁ and nuclear quadrupole resonance (NQR) spectrum of Sb nuclei. The temperature (T) dependence of 1⁄T₁ behaves as if approaching closely an antiferromagnetic (AFM) quantum critical point (QCP), following the relation 1⁄T₁∝T⁄(T−T_N)^1⁄2 with T_N=0.06 K in the range of T=1.3–25 K. The onset of either the spin-density-wave (SDW) or charge-density-wave (CDW) order at T₀=0.9 K, that is, of the first order, is evidenced by a broadening of the NQR spectrum and a marked reduction in 1⁄T₁ just below T₀. The f-electron-derived correlated band realized in CeOs₄Sb₁₂ is demonstrated to give rise to the novel phase transition on the verge of AFM QCP.

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The optical conductivity [σ(ω)] of the Kondo semiconductor YbB₁₂ has been measured over wide ranges of temperature (T=8–690 K) and photon energy (hω≥1.3 meV). The σ(ω) data reveal the entire crossover of YbB₁₂ from a metallic electronic structure at high T’s to a semiconducting one at low T’s. Associated with the gap development in σ(ω), a clear onset is newly found at hω=15 meV for T≤20 K. The onset energy is identified as the gap magnitude of YbB₁₂ appearing in σ(ω). This gap in σ(ω) is interpreted as the indirect gap, which has been predicted by the renormalized-band model of the Kondo semiconductor. On the other hand, the strong mid-infrared (mIR) peak observed in σ(ω) is interpreted as arising from the direct gap. The absorption coefficient around the onset and the mIR peak indeed show the characteristic energy dependences expected for indirect and direct optical transitions in conventional semiconductors.

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During the last decade, the laser trapping technique has been actively applied to elucidate the property of macromolecules such as deoxyribonucleic acid (DNA), ribonucleic acid (RNA) and cytoskeleton fibres. Due to the inherent difficulty in the direct trapping of single molecules at approximately 300 K, most of the current studies on laser trapping utilize the experimental technique to grasp microbeads that are attached to a single macromolecule, instead of using direct trapping. A few studies have demonstrated the applicability of laser trapping for highly packed compact DNA under a ‘poor’ solvent condition without any beads. In the present study, we achieve laser trapping on a single DNA molecule under a ‘good’ solvent condition without any microbeads. The time-dependent change of the conformation accompanied by ON/OFF laser irradiation was measured and analysed in terms of the entrapment and release of a coiled polymer around a micrometer-sized potential.

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We have shown that the scheme of the ladder operation method can be formulated on the basis of the dressed special functions. By this technique we can construct both the Gram-type and the Casorati-type general N-soliton solutions with given special functions. As the concrete examples, we show that the present scheme can be applied to obtain the various solutions of the 2+1d Toda equations corresponding to the cylindrical solitons of both the infinite and finite chain, and the line shape propagating solitons of the finite chain (expressed by the multi-dimensional hyper-geometric functions.)

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N soliton solution is obtained for integrable differential-difference equations with a new inverse scheme. Interaction between solitons are considered and conserved densities and recursion formula are presented.

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In this paper, multi-soliton solutions of two (2+1)-dimensional systems \\left[D_tsinh\\left(\\frac12D_n\\ ight)+D^3_xsinh\\left(\\frac12D_n\\ ight)\\ ight] f_n·f_n & =0
\\intertextand\\left[D_xD_tcosh\\left(\\frac12D_n\\ ight)+D_tsinh\\left(\\frac12D_n\\ ight)\\ ight] f_n·f_n & =0 are derived and expressed by pfaffians.

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The parametric representation is given to the multisoliton solution of the Camassa–Holm equation. It has a simple structure expressed in terms of determinants. The proof of the solution is carried out by an elementary theory of determinants. The large time asymptotic of the solution is derived with the formula for the phase shift. The latter reveals a new feature when compared with the one for the typical soliton solutions. The peakon limit of the phase shift is also considered, showing that it reproduces the known result.

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A novel method is developed for estimating the diffusion constant D_c and the non-Gaussian parameter A(t) on the basis of measurement in the frequency region. This method is shown to have merits over the conventional one in which a limited time window is used. To confirm the validity of this method, it is applied to a binary soft-sphere fluid which was studied by molecular dynamics (MD) simulation. The diffusion constant D_c is determined in the region closer to the glass transition than in the conventional MD simulation. The temperature dependence of the exponent of A(t) is consistent with that predicted by the trapping diffusion model.

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Level statistics is discussed for XXZ spin chains with discrete symmetries for some values of the next-nearest-neighbor (NNN) coupling parameter. We show how the level statistics of the finite-size systems depends on the NNN coupling and the XXZ anisotropy, which should reflect competition among quantum chaos, integrability and finite-size effects. Here discrete symmetries play a central role in our analysis. Evaluating the level-spacing distribution, the spectral rigidity and the number variance, we confirm the correspondence between non-integrability and Wigner behavior in the spectrum. We also show that non-Wigner behavior appears due to mixed symmetries and finite-size effects in some nonintegrable cases.

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The influence of the turbulence spreading is studied on the self-sustained turbulence which is induced by the subcritical instability. It is found that there is a minimum system size that can sustain the self-sustained turbulence, and an analytic formula is derived. The generalization of the Maxwell’s construction rule is also derived.

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In the equilibrium immiscible Fe–Ag systems, unique fcc-structured solid solutions were obtained in their nanosized multilayered films upon ion beam manipulation, indicating that the solid solubility of Fe in Ag can be extended from nearly zero up to 60 at. %. In contrast, an unusual hexagonal (4H) Ag phase was observed in the Fe–Ag multilayered films upon steady-state thermal annealing. We report, in this paper, the detailed structural phase transitions observed in the Fe–Ag multilayered films upon ion irradiation and thermal annealing, together with a brief discussion concerning the significantly different mechanisms involved in the two processes.

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The crystal structure of θ-(BEDT-TTF)₂RbCo(SCN)₄ in its insulating state below T_MI (approximately 200 K) was investigated by X-ray diffraction experiments. The transfer integrals between the BEDT-TTF molecules were also calculated from the structural data, and the ionicities of BEDT-TTF molecules were estimated from the intramolecular bond length distribution. A large modulation of transfer integrals and charge disproportionation between BEDT-TTF molecules were found. The ratio of ionicities was 0 to +0.2:+0.8 to +1.0. These results were compared with thoes of the analogous salt θ-(BEDT-TTF)₂RbZn(SCN)₄.

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We have studied the structural and the electronic properties of liquid carbon as a function of the pressure using ab initio molecular-dynamics simulation. We are particularly concerned with the pressure-induced structural change. When the density (pressure) is increased from 2.9 g/cm³ (16 GPa) to 11.6 g/cm³ (2000 GPa) at the constant temperature of 9000 K, the structure of liquid carbon changes drastically as follows: The peaks of the radial distribution functions g(r) shift to shorter distances and become higher and sharper, and the average coordination number increases from three to eight. The structure factor S(k) changes its shape qualitatively at extremely high pressure and becomes similar to those of liquid Si and Ge at ambient pressure, which is characterized by a shoulder on the high-wavenumber side of the first peak of S(k). We have shown that, with increasing density, the bonding character changes from covalent bonding to metallic bonding based on the bond-angle distribution, the electron density distribution and the overlap population. We have also investigated the dynamical properties of liquid carbon such as the velocity autocorrelation function and the self-diffusion coefficient in relation to the pressure-induced structural change.

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The rare earth compound PrNi₅ has a nonmagnetic singlet ground state. The ground state of PrNi₅ crosses the first excited state when a magnetic field is applicated along the a-axis. This level crossing occurs at 20 T and causes anomalies in some substances. In particular, the elastic constant C₆₆ exhibits a large elastic softening at this level crossing point. The purpose of this paper is to analyze the behavior of C₆₆ when a magnetic field is applied to a system. The behavior of the temperature dependence of C₆₆ has been explained already. However the method of calculating the temperature dependence of C₆₆ cannot explain the field dependence of C₆₆. Hence the elastic softening and behavior above the level crossing point in C₆₆ are analyzed applying the higher order effect of strain to elastic constants. The higher order effect of strain is much smaller than the first-order effect of strains and is usually neglected. Not only a first-order strain but a second-order one is taken into account in our works.

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In this study of fabricated one-dimensional (1D) nanostructures of Fe adatoms on vicinal Au(111) surfaces, the growth mechanism and electronic structures are investigated by scanning tunneling microscopy (STM) and by angle-resolved photoemission spectroscopy (ARPES). STM observations reveal that dosed Fe atoms are trapped at the lower corners of the steps. They create nucleation centers near the intersections between steps and discommensuration lines, and grow into evenly spaced Fe fragments located at face-centered-cubic (fcc) stacking regions of the substrate. The connection of these fragments aligned along the steps results in the formation of Fe monatomic rows. As the Fe coverage increases, the Fe growth proceeds predominantly at the fcc stacking regions, and forms quasi-1D nanostructures with undulating edges. At an Fe coverage of ∼0.6 ML, the fast-growing parts connect with the adjacent Fe structures and a two-dimensional network structure is built up. ARPES measurements reveal that the decoration of the step edges with Fe has a significant influence on the periodic potential of the surface state electrons confined between the regularly arranged steps. On the surface with Fe monatomic rows, photoemission spectra measured in the direction perpendicular to the steps show a parabolic dispersion of the Au(111) surface state with downward energy shift of the band bottom; the clean surface, in contrast, shows two 1D quantum-well levels. A simple analysis using a 1D Kronig–Penny model reveals that the Fe decoration reduces the potential barrier height at the steps from 20 to 4.6 eV Å, suggesting that the Fe adatoms work as attractive scatterers and increase the probability of transmission through the barriers. Furthermore, for the higher Fe coverage, the spectra reflecting the electronic nature of the 1D nanostructures show little dispersion, suggesting that the Fe 3d states are localized in the 1D structures.

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Bulk-sensitive photoemission spectroscopy using hard x-ray up to hν=5450 eV has been performed for heavy-fermion Pr compounds. A significant spectral intensity of the |3d⁹4f³⟩ final state was observed in Pr 3d core-level spectra of PrFe₄P₁₂ at both hν=2450 and 5450 eV. The spectra obtained by the configuration-interaction cluster model calculation reproduce the experimental spectra for well-hybridized PrFe₄P₁₂ and localized Pr metal. Results of the calculations suggest that the Kondo behavior observed in PrFe₄P₁₂ arise from the mixing of the |4f²⟩ and |4f³⟩ configurations due to the c–f hybridization. Whereas a contribution possibly from a disordered surface to the spectrum can be negligible for the fractured PrFe₄P₁₂, they cannot be disregarded for the scraped PrSn₃ and Pr metal even in the high-energy x-ray region.

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We analyze Ni 2p→3d→2p resonant X-ray emission spectroscopy (RXES) of NiO with the impurity Anderson model. We pay attention to the inelastic X-ray scattering structures arising from the interatomic charge transfer (CT) from ligand state to 3d state. We take into account a finite width of the O 2p valence band in order to reproduce the experimental CT excitations in RXES, where two different CT structures are observed depending on the incident photon energy set in the CT satellite region of X-ray absorption spectra. The origin of these two CT excitation peaks is ascribed to the lower and upper edges of the 3d⁹L nonbonding band in the final state of RXES. The value of CT energy Δ is estimated from our calculation. By analyzing XAS and RXES simultaneously with changing Δ from 2.0 eV to 6.5 eV by the step of 0.5 eV, we conclude that the most appropriate value of Δ is 3.5 eV. Also, in our calculation two different geometrical configurations are considered, which are called polarized and depolarized configurations (the polarization vector of incident photon is perpendicular and parallel to the scattering plane, respectively), although only the depolarized configuration is taken in the RXES experiments so far made. Our result predicts larger intensity of RXES near the elastic scattering in the polarized configuration.

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The systematic band-filling control has been performed in β′-ET₃(MCl₄²⁻)_2−x(M′Cl₄¹⁻)_x (ET = bis(ethylenedithio)tetrathiafulvalene, M=Co, Zn, M′=Ga, Fe, x=0–1.24). By means of band-filling control to the parent narrow-gap semiconductor, β′-ET₃(ZnCl₄²⁻)₂, the conductivity at room temperature (rt) is increased from 0.2 S cm⁻¹ to 50 S cm⁻¹ (M′=Ga, x=0.44) and the metallic behavior is observed down to 90 K. The increase of resistivity below 90 K caused by the randomness of the anion potential is suppressed by the external pressure and the metallic behavior is maintained down to 3 K. The thermoelectric power measurements and their fitting based upon the band calculation demonstrate that the doping occurs at the two-dimensional donor layer and the one-dimensional array for β′-ET₃(CoCl₄²⁻)_0.76(FeCl₄¹⁻)_1.24. Moreover, the introduction of the magnetic anions for β′-ET₃(CoCl₄²⁻)_1.20(FeCl₄¹⁻)_0.80 affords the ferrimagnetic interaction between Co²⁺ (S=3⁄2) and Fe³⁺ (S=5⁄2) through the doped carriers.

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Spatial distributions of the electron temperature perpendicular to the applied current in quantum Hall systems with slowly-varying confining potentials are calculated in the linear-response regime by employing hydrodynamic equations for number conservation and energy conservation. The electron temperature exhibits spatial pattern, reflecting the confining potential, along the Hall field induced by the current. The local electron temperature shows oscillations as a function of the filling factor. Such spatially dependent electron temperature causes a certain change in distributions of the current density and the current-induced potential even in the linear-response regime.

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We found evidence that two successive antiferromagnetic orderings of a rare earth cuprate NdCu₂O₄ (nonstandard monoclinic structure with magnetic Cu(1) and nonmagnetic Cu(2) sites) are strongly coupled with phonon mode anomalies. The nuclear quadrupole resonance frequency of ^63,65Cu on the Cu(2) site shows a step decrease below each of the ordering temperatures T_N1∼20 K and T_N2∼10 K, that originates from changes in the symmetry of the charge distribution on the surrounding lattice. In the Raman spectrum, the shift of a phonon mode near 300 cm⁻¹ displays an anomalous temperature dependence, which suggests a hardening of the lattice below T_N1 and a softening below T_N2. The Cu²⁺ spins on the Cu(1) site order antiferromagnetically below T_N1, and the complex magnetic behavior is ascribed to the variations in the exchange interactions between the Cu(1) spins and in the paramagnetic spin polarization of Nd³⁺ below T_N2.

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Dynamics of the singlet–triplet crystalline electric field (CEF) system at finite temperatures is discussed by use of the non-crossing approximation. Even though the Kondo temperature is smaller than the excitation energy to the CEF triplet, the Kondo effect appears at temperatures higher than the CEF splitting, and accordingly only quasi-elastic peak is found in the magnetic spectra. On the other hand, at lower temperatures the CEF splitting suppresses the Kondo effect and inelastic peak develops. The broad quasi-elastic neutron scattering spectra observed in PrFe₄P₁₂ at temperatures higher than the quadrupole order correspond to the parameter range where the CEF splittings are unimportant.

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The effect of spatial modulation of the single-site anisotropy D on the ground state of the S=1 Heisenberg chains is investigated. In the case of period 2 modulation, it is found that the phase diagram contains the Haldane phase, large-D phase, Néel phase of udud-type and u0d0-type. It is shown that the hidden antiferromagnetic order in the Haldane phase compatible with the spatial modulation of D-term get frozen resulting in the emergence of various types of Néel orders. The investigation of the model with longer period D-modulation also confirms this picture.

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Signal processing in a simple threshold system is studied with use of a static mutual information between the input and output data, with main emphasis put on stochastic resonance (SR) and a feedback mechanism to enhance information transmission through the system. First we verify that the proposed static mutual information is well correlated with the existing measures for SR, such as the signal to noise ratio and the normalized power norm. Secondly we try to use output information to improve quality of signal processing and show by a self-consistent theory that a feedback mechanism can usefully be applied to improve performance (i.e., to increase the mutual information) of the simple threshold system.

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