International Journal of Modern Physics B

We consider the possibilities of the formation of quasistationary distributions of particles over energy with power asymptotics in nonequilibrium systems and dynamical systems with couplings. It is shown that the Tsallis distribution is related to the exact solutions of a kinetic equation of the Boltzmann type and those of covariant kinetic equations of the Vlasov nonlocal statistical mechanics.

We have studied the connection of the power-like solutions of kinetic equations with the eigenfunctions of fractional integro-differential operators and Jackson operators within quantum analysis, and that of nonextensiveness parameters in the framework of the Tsallis thermostatics, with flows in the phase space. It is shown that the processes running in a nonequilibrium nonconservative medium can be described by the solutions of the equation with fractional derivatives or Jackson derivatives for oscillations.

The shape of the solid lipid monolayer domain surrounded by a fluid phase is of considerable interest from both physical and mathematical points of view. Here, we report two new results about this topic. First, we find an exact analytical solution to an approximated shape equation that we derived recently. This solution can well-describe the kidney- and boojum-like domains that abound in lipid monolayer. Second, we derive an exact domain shape equation by a direct variation of domain energy without any artificial cutoff. We find no continuous solutions that satisfy this shape equation due to the divergence of its coefficients, which is rooted in the continuous description of electrostatic dipoles.

The bound states in the (CdSe)_Nw–ZnSe(001) single quantum well are investigated versus the well width (N_w monolayers) and the valence-band offset (VBO). The calculation, based on the sp³s* tight-binding method which includes the spin-orbit interactions, is employed to calculate the band-gap energy (E_g), quantum-confinement energy (E_Q), and band structures. It is found that the studied systems possess a vanishing valence-band offset (VBO ≃ 0) in consistency with the common-anion rule, and a large conduction band offset of about (CBO ≃ 1 eV); both of which made the electronic confinement become predominant. The bi-axial strain, on the other hand, remains to control the hole states. Namely, the two highest (spin-degenerate) hole states are found to localize at the two interfaces due to the formation of two similar strain-induced potential dips at these interfaces, each of depth equal to the strain energy ~35 meV. More importantly, the ultrathin CdSe wells (with N_w ≤ 4 monolayers) are found to contain only a single (spin-degenerate) bound state; but by increasing the well width further, a new (spin-degenerate) bound state falls into the well every time N_w hits a multiple of 4 monolayers (more specifically, for 4n+1 ≤ N_w ≤ 4 (n+1), the number of bound states is (n+1), where n is an integer). The rule governing the variation of the quantum-confinement energy E_Q versus the well width N_w has been derived. Our theoretical results are in excellent agreement with the available experimental photoluminescence data.

Pr-doped Pb(Zr_0.65Ti_0.35)O₃ (Pb_1-xPr_x(Zr_0.65Ti_0.35)_1-x/4O₃, PPZT) ceramic samples are prepared using conventional solid-state sintering method, and their structural, dielectric, ferroelectric, and piezoelectric properties are investigated, focusing on the effects of Pr-doping. Upon increasing Pr doping level x, a transition of the crystallographic structure from rhombohedral symmetry to tetrahedral and finally to pseudocubic symmetry is observed at x ~ 0.08. The detailed dielectric measurements present a clear indication of relaxor-like behaviors at x = 0.08, while the samples at x < 0.08 offer slightly improved ferroelectric properties compared with pure Pb( Zr_0.65Ti_0.35)O₃. In spite of the dielectric relaxor behaviors induced by Pr-doping, both the ferroelectric and piezoelectric properties of PPZT are degraded at x = 0.08. The physics underlying the Pr-doping induced relaxor behaviors is then discussed.

A systematic investigation of the ac susceptibility of polycrystalline RuSr₂GdCu₂O₈ was carried out with different field amplitudes and various frequencies. The study covered a wide range of frequencies between 0.020 to 12.5 kHz and temperatures from 7 to 50 K. The first derivative of susceptibility curves indicated the presence of a superconducting intragranular transition coupled by weak links distribution of intergranular transitions. The intragranular-, χ_g, and intergranular-, χ_i contribution to susceptibility were estimated and found to be consistent with the prediction of the critical state model. Variation of the peak temperature of the imaginary part with frequency was employed to determine the vortex activation energy. The derived low activation energy values provide clear evidence of the thermally activated flux creep process in the superconducting state. Qualitative analysis of the χ′′ - χ′ parametric relation was carried out.

Manganese-doped calcium aluminate powder was prepared at furnace temperatures as low as 500°C using the combustion route without further calcining treatment. Powder X-ray diffraction, thermogravimetric analysis and scanning electron microscopy measurements were used to characterize the as-prepared combustion products, while the optical properties were studied using photoluminescence. Photoluminescence studies of Mn doped CaAl₂O₄ showed green emission from Mn²⁺ ions. EPR investigations also indicated the presence of Mn²⁺ ions in the prepared material.

With the help of the scattering-matrix method, the quantum states of ballistic electrons and conductance, as well as resistance are studied in a four-terminal junction of narrow wire with various widths. We find that these observable quantities are highly sensitive to the geometries of junctions and differ from the conventional structure with the same width. In particular, the predicted quantization conductance phenomena are striking and are also in self-consistency with calculated scattering probabilities, relating to electronic subbands and transmission states.

Interaction of the previously described [V. D. Khavryuchenko, Y. A. Tarasenko, V. V. Strelko, O. V. Khavryuchenko and V. V. Lisnyak, Quantum chemical study of polyaromatic hydrocarbons in high multiplicity states, Int. J. Modern. Phys. B21, 4507 (2007), in press] polyaromatic hydrocarbon (PAH) C₉₆H₂₄ with dioxygen molecule and KO₂ have been quantum chemically examined. The probability of existence of the oxygen superoxide ion-radical O₂ adsorbed on the surface of the PAH is critically discussed.

We present two schemes for probabilistically teleporting a two-atom entangled state using a three-atom partially entangled state as the quantum channel in cavity QED with the help of separate atomic measurements. The first scheme is only based on the interaction between two driven atoms and a quantized cavity mode in the large detuning limit, so the effects of both cavity decay and the thermal field are eliminated. In the second scheme, it is necessary to introduce an additional resonant cavity besides the thermal cavity to realize the teleportation, and the corresponding success probability is improved.

The Barabási–Albert (BA) model is extended here to include the concept of modifying the preferential attachment and combining the global preferential attachment with local preferential attachment. Our preferential attachment makes the nodes with higher degree increase less rapidly than the BA model after a long time. The maximum degree is introduced. We compare the time-evolution of the degree of the BA model and our model to illustrate that our model can control the degree of some nodes increasing dramatically with increasing time. Using the continuum theory and the rate equation method, we obtain the analytical expressions of the time-evolution of the degree and the power-law degree distribution.

In a recent paper, Giri and Gupta [Int. J. Mod. Phys. B19, 1943 (2005)] discussed the possibility of obtaining nth-order squeezing of the field amplitude of the fundamental mode in spontaneous Raman processes. These investigations are based on the earlier works of Kumar and Gupta [Quantum & Semiclassical Opt.7, 835 (1995)] and Giri and Gupta [J. Mod. Opt.51, 1705 (2004)]. As a consequence of our re-investigation on the same model, we found that the calculations and hence the conclusion of Giri and Gupta [Int. J. Mod. Phys. B19, 1943 (2005) and J. Mod. Opt.51, 1705 (2004)] and Kumar and Gupta are entirely baseless and misleading. There will be no squeezing of the fundamental mode in stimulated and/or in spontaneous Raman processes.

The electronic structure, and optical and mechanical properties of gamma-Si₃N₄ are calculated by means of the plane-wave pseudo-potential method (PWP) with generalized gradient approximation (GGA) and local density approximation (LDA). The calculated values are in good agreement with experimental results. A comparative investigation reveals that the band gap calculated by GGA agrees better with the experimental value than by the other methods, while the calculated bulk modulus by LDA is comparable with that by the method of orthogonalized linear combinations of atomic orbitals (OLCAO). Our results indicate that a satisfactory calculation of the structures and properties of gamma-Si₃N₄ could be achieved by combining GGA and LDA methods.

Potassium niobate KNbO₃ and some compounds of (K_1-xNa_x)NbO₃ (x = 0.3, 0.4, 0.6, 0.7) ceramics powders were successfully prepared by the solid-state reaction method using a non-stoichiometric mixture of starting materials. A possible formation of these phases was proposed based on the experimental results. All of the prepared compounds were characterized using the X-ray diffraction method, and grain size has been calculated using SEM images, and their stoichiometry was obtained from the EDAX results.

A growth mechanism of ramified aggregates on nonlattice substrates with fixed impurities is studied systematically. Based on the experimental observations of Au atomic aggregates on molten glass surfaces, an Improved Restricted Cluster-Cluster Aggregation (IRCCA) model is established. In this model, fixed impurities are distributed randomly on a nonlattice substrate, and all the aggregates with different sizes are allowed to diffuse and rotate. The influence of the liquid substrate and impurity on the structure of the ramified aggregates is studied systematically. The simulation results are in good agreement with the experimental findings.

This paper designs the controller for uncertain Lorenz system with multiple inputs containing sector nonlinearities and dead zone, and theoretically demonstrates the effectiveness of this controller. By this controller, the controlled Lorenz system can asymptotically drive the system orbits to arbitrarily objective trajectories even with uncertainties and sector nonlinearities and dead zone in the inputs, and thus has strong robustness. Finally, through the emulation studies of controlled Lorenz systems, it demonstrates the effectiveness of this controller.