International Journal of Modern Physics B

Random constraint satisfaction problems are interesting model systems for spin-glasses and glassy dynamics studies. As the constraint density of such a system reaches certain threshold value, its solution space may split into extremely many clusters. In this work we argue that this ergodicity-breaking transition is preceded by a homogeneity-breaking transition. For random K-SAT and K-XORSAT, we show that many solution communities start to form in the solution space as the constraint density reaches a critical value α_cm, with each community containing a set of solutions that are more similar with each other than with the outsider solutions. At α_cm the solution space is in a critical state. The connection of these results to the onset of dynamical heterogeneity in lattice glass models is discussed.

We consider a two-dimensional strongly correlated electronic system in a strong perpendicular magnetic field at half-filling of the lowest Landau level (LLL). We seek to build a wave function that, by construction, lies entirely in the Hilbert space of the LLL. Quite generally, a wave function of this nature can be built as a linear combination of all possible Slater determinants formed by using the complete set of single-electron states that belong to the LLL. However, due to the vast number of Slater determinant states required to form such basis functions, the expansion is impractical for any but the smallest systems. Thus, in practice, the expansion must be truncated to a small number of Slater determinants. Among many possible LLL Slater determinant states, we note a particular special class of such wave functions in which electrons occupy either only even, or only odd angular momentum states. We focus on such a class of wave functions and obtain analytic expressions for various quantities of interest. Results seem to suggest that these special wave functions, while interesting and physically appealing, are unlikely to be a very good approximation for the exact ground state at half-filling factor. The overall quality of the description can be improved by including other additional LLL Slater determinant states. It is during this process that we identify another special family of suitable LLL Slater determinant states to be used in an enlarged expansion.

The characteristics of the localized Wannier exciton in defect layer (GaAs) embedded between two semi-infinite superlattices (GaAs/Al_xGa_1-xAs) are investigated theoretically using a variational approach. It can be clearly seen the exciton changes in character between three- and quasi-two-dimensional states from the variation of exciton binding energy, in-plane radius, and probability in the superlattices (SLs) growth direction. We find that the extensions of exciton in directions both parallel and perpendicular to the interface of SLs almost approach their minimums as the exciton binding energy reaches peak value at a certain defect width. Our results show that the binding energy of the ground exciton state is sensitive to Al concentration x in Al_xGa_1-xAs and thicknesses of the constituent layers. The comparison between excitonic behavior in structural defect SLs and single quantum well is made.

Titanium dioxide has been in close examination for application development due to its high index of refraction and transparency across the visible range. One of the most active researches is hydrophilicity and photocatalysis in TiO₂ films. In this study, a close investigation to TiO₂ films' microstructural transformation was examined. A number of thin film samples were prepared by ion-assisted electron-beam evaporation at 200-nm nominal thickness, 2.0 Å/s deposition rate and 250°C deposition temperature. The varying parameter was the oxygen flow rate at 2, 4, 6 and 8 sccm. The films were eventually annealed for three hours in air atmosphere. The crystalline structures of as-deposited (ASD) and annealed films were deduced by variable-angle spectroscopic ellipsometry (VASE), and supported by X-ray diffractometry (XRD) and atomic force microscopy (AFM). Film characterization based on VASE is desirable in order to understand physical and optical characteristics of the films. Transmittance spectra were derived from UV/Vis spectrophotometer. It was found that all as-deposited films were all amorphous with low luminous transmittance. Higher oxygen flow rate during the deposition, however, resulted in sub-oxide TiO₂ film. With this film, annealing at 300 and 500°C were presumed as transition temperatures for amorphous-to-anatase and anatase-to-rutile phases, respectively. The luminous transmittance also increased and was found to be the highest at 75.75% at 400°C annealing. The optical energy band gap for this film also increased up to 3.26 eV at 600°C annealing.

For describing some nonlinear localized excitations, the (2+1)-dimensional dispersive long wave (DLW) system is investigated with symbolic computation in this paper. Based on two different dependent variable transformations obtained through the truncated Painlevé expansion, the (2+1)-dimensional DLW system can be bilinearized or linearized. Through the Hirota bilinear method, the analytic one-, two-, three-, and N-soliton solutions are derived. On the other hand, by means of the variable separation approach, localized excitations, such as the resonant dromion, resonant solitoff, lump and compacton excitations, are obtained. Figures are plotted to illustrate the structures of those solutions.

We have predicted the phase transition pressures and corresponding relative volume changes of CeSb, LaSb, and LuSb having NaCl-type structure under high pressure using three-body interaction potential approach (TBIPA) incorporated with short-range van der Walls (vdW) interaction and zero point energy effects. We have obtained phase transition pressures and relative volume changes which are in close agreement with measured values. Thus TBIPA with vdW interaction and zero point energy effects are found to be promising potential models for the prediction of transition pressure and stability of rare-earth compounds.

Phase synchronization of parametric excited Rössler system has been investigated in this paper. By introducing the conception of phase for a chaotic motion, it has been demonstrated that the mean frequency of chaotic attractor and the frequency of the parametric excitation may be locked in different ratios for certain parameter conditions, implying phase synchronization can be observed. The evolution from nonsynchronized state to phase synchronization has been discussed in detail, which reveals different phase dynamics may exist during the process. With the variation of parameters, the imaging point on the Poincaré plane may finally settle down onto the attractor, which yields phase synchronization.

By using the high-temperature series expansion technique, we have analyzed the phase transition and the critical phenomena of a ferromagnetic thin film and ferromagnetic semi-infinite film, through three models: Ising, XY and Heisenberg. The critical reduced temperature τ_C(v) is studied as a function of the thickness of the film. In the case of the magnetic film and semi-infinite film, on the simple cubic lattice and the face-centered cubic lattice, τ_C(v) is studied as a function of the exchange interactions in the bulk, and on the surface. A critical value of the surface exchange interaction in the film above which the surface and the interface magnetism appears is obtained. The dependence of the reduced critical temperature on the thickness of the film has been investigated. These shifts of the critical temperatures T_C(L) from the bulk value can be described by a power law. The obtained values for the simple cubic lattice and face centered cubic ferromagnetic thin film are in qualitative accordance with the universality class hypothesis. The critical exponent associated with the magnetic susceptibility is studied as a function of interactions. In a defined range of the exchange interactions, the obtained values for Heisenberg, XY and Ising models, for simple cubic thin film are comparable to the universal ones and are independent of the film thickness. The asymmetry of the structure and the competition of the effects of the exchange coupling, are important for the magnetic properties of the system. A critical value of the surface exchange interaction above which the surface magnetism appears is obtained. For the dependence of the critical parameter of surface reduced coupling as a function of the dilution x and the ratio of the exchange interaction between the surface and nearest neighbour layer to the bulk one R₁ for the three studied models has been investigated. The magnetic phase diagrams are obtained for two structures. The percolation threshold is defined as the concentration x_p at which τ_C=0. In the case of the thin film, the obtained values are x_p≈0.2 in the bulk and x_p≈0.4 at the surface. For the case of the semi-infinite film, the value obtained in the surface and the nearest layer at the surface is x_p≈0.2.

This study introduces a new method of measuring the stiffness (spring constant) of cantilevers that is designed to improve the measurement accuracy of (atomic force microscopy) (AFM). AFM cantilever spring constants are determined by the relation between the slope of the step height ascertained from the surface profile measurement results, and the size of the cantilever. The surface profile measurements of the standard specimens with three different step heights (height: 100, 500, and 1000 nm) were conducted using a standard cantilever with different stiffness. As a result of this exercise, the profile slope was found to be proportional to cantilever stiffness, and the necessity was uncovered to conduct a similar experiment in order to clarify the quantitative relation between stiffness and the profile slope when the same kind of cantilever is utilized.

The independent particle model (IPM) coupled with empirical pseudopotential method (EPM) was used to compute the thermalized positron charge densities in specific family of binary tetrahedrally coordinated crystals of formula A^NB^8-N. Initial results show a clear asymmetrical positron charge distribution relative to the bond center. It is observed that the positron density is maximum in the open interstices and is excluded not only from the ion cores but also to a considerable degree from the valence bonds. Electron-positron momentum densities are calculated for the (001, 110) planes. The results are used to analyze the positron effects in GeC and SnC. Our computational technique provides the theoretical means of interpreting the k-space densities obtained experimentally using the two-dimensional angular correlation of annihilation radiation (2D-ACAR).

In this paper, based on a two-mechanism model, we derive the complete high-order perturbation formulas of the spin-Hamiltonian (SH) parameters (g factors g_‖, g_⊥ and hyperfine structure constants A_‖, A_⊥) for 3d⁹ ions in tetragonally elongated octahedral clusters. In the model, the contributions to SH parameters due to the crystal-field (CF) mechanism related to CF excited states and the charge-transfer (CT) mechanism related to CT exacted states (the CT mechanism is neglected in CF theory, which is widely used to study the SH parameters) are taken into account. From these formulas, the SH parameters of Cu²⁺ ions in AgCl and NaCl crystals are calculated. It is found that for the exact explanation of SH parameters of (CuCl₆)^4- clusters in crystals, the contribution due to CT mechanism should be considered. The relative importance of CT mechanism (characterized by Q^CT/Q^CF, where Q = Δg_i or , i = ‖ or ⊥) increases with the decreasing metal-ligand distance in ( CuCl₆)^4- clusters. The causes are discussed. The signs of A_i and the defect structures of Cu²⁺ centers in AgCl and NaCl crystals are suggested from the calculations.

In paper III of this series we proposed a scenario of superconductivity driven by hole "undressing" that involved a complete redistribution of the occupation of single particle energy levels: the holes near the top of the band were proposed to all condense to the bottom of the band. Here we consider a less drastic redistribution involving electrons with a definite spin chirality and show that it is in fact energetically favored by the Coulomb exchange matrix element J over the scenario proposed earlier. It is shown that spin splitting with chiral states reduces the Coulomb repulsion and hence that the Coulomb repulsion promotes spin splitting. Superconductors are proposed to possess a spin-split hole "core" at the bottom of the electronic conduction band in addition to a spin-split Fermi surface. The Dirac sea is proposed to play a key role. The new scenario leads naturally to the existence of a spin current in the superconducting state and is consistent with the Spin Meissner effect and negative charge expulsion discussed earlier within the theory of hole superconductivity.