International Journal of Modern Physics B

The alternating transverse Ising model with A and B sublattices is solved exactly in one and two dimensions, when a transverse field applied only to the A sublattice. The critical point of the honeycomb lattice is given as a function of the alternating transverse field. Moreover, the zero-temperature phase transition in the one-dimensional model with another alternating transverse field is discussed rigorously.

In this study, we have investigated the ground state energy level of electrons in modulation doped GaAs/Al_xGa_{1 - x}As heterojunctions. For this purpose, Schrödinger and Poisson equations are solved self consistently using quantum genetic algorithm (QGA). In this way, we have found the potential profile, the ground state subband energy and their corresponding envelope functions, Fermi level, and the amount of tunneling charge from barrier to channel region. Their dependence on various device parameters are also examined.

The d–p band model, a periodic array of strongly correlated d states with hopping to a p band, and in the presence of a uniform applied magnetic field is studied as a function of temperature using Roth's variational method. Expanding the σ spin electron occupation numbers of d and p states to first order in the magnetic field h, we calculate the linear term of the field induced magnetization and thus the susceptibility. This is given in terms of the number of holes for La_{2 - x}Sr_xCuO₄, in the limit of strongd–d correlations and we study the role of doping x and temperature "T" on the susceptibility.

We introduce a new class of quantum models with time-dependent Hamiltonians of a special scaling form. By using a couple of time-dependent unitary transformations, the time evolution of these models is expressed in terms of related systems with time-independent Hamiltonians. The mapping of dynamics can be performed in any dimension, for an arbitrary number of interacting particles and for any type of the scaling interaction potential. The exact solvability of a "dual" time-independent Hamiltonian automatically means the exact solvability of the original problem with model time-dependence.

This article is an illustration of the construction of coherent and generalized intelligent states which has been recently proposed by us for an arbitrary quantum system.¹ We treat the quantum system submitted to the infinite square well potential and the nonlinear oscillators. By means of the analytical representation of the coherent states à la Gazeau–Klauder and those à la Klauder–Perelomov, we derive the generalized intelligent states in analytical ways.

In the present paper exact formulae for the calculation of zeros of R_nl(r) and ₁F₁(-a; c; z), where z = 2λr, a = n - l - 1 ≥ 0 and c = 2l + 2 ≥ 2 are presented. For a ≤ 4 the method due to Tartallia and Cardono, and that due to L. Ferrai, L. Euler and J. L. Lagrange are used. In other cases (a > 4)numerical methods are employed to obtain the results (to within 10^-15). For greater geometrical obviousness of the irregulary distribution (as a > 3) of zeros x_k = z_k - (c + a - 1) on the axis y = 0, the circular diagrams with the radius are presented for the first time. It is possible to notice some singularities of distribution of these zeros and their images — the points T_k — on the circle. For a = 3 and 4 their exact "angle" asymptotics (as c → ∞) are obtained. It is shown that in the basis of the L. Ferrari, L. Euler and J.-L. Lagrange methods, using for solving the equation ₁F₁(-4; c; z) = 0, one equation is obtained viz., the cubic resolvent equation of FEL-type. Calculating of zeros x_k of the R_nl(r) and ₁F₁(z) functions enable us to show the "singular" cases (a, c) = (4, 6), (6, 4), (8, 14), …

The ultraviolet/visible photon transmission technique was applied to study the phase diagram of a mixture of 4-ethoxy-4′-(6-vinyloxyhexyloxyl) azobenzene (VE), a smectogen, and 4-hexoxy-3′-methyl-4′-(6-acryloyloxyhexyloxy) azobenzene (AH), which by itself exhibits no liquid crystalline behavior. It has been found that the N-Sm-A phase line terminates at either a tricritical point at about X_VE = 0.9, where X_VE is the weight percentage of VE in the binary mixture, or at least at a tricritical region 0.9 < X_VE < 1 within the experimental resolution. For X_VE = 1 the nematic phase region is not large enough to drive the transition second-order. It is found that the value of the critical exponent β for X_VE = 0.9 is consistent with the tricritical value.

In this paper, the initial stage of films assembled by energetic C₃₆ fullerenes on diamond (001)–(2 × 1) surface at low-temperature was investigated by molecular dynamics simulation using the Brenner potential. The incident energy was first uniformly distributed within an energy interval 20–50 eV, which was known to be the optimum energy range for chemisorption of single C₃₆ on diamond (001) surface. More than one hundred C₃₆ cages were impacted one after the other onto the diamond surface by randomly selecting their orientation as well as the impact position relative to the surface. The growth of films was found to be in three-dimensional island mode, where the deposited C₃₆ acted as building blocks. The study of film morphology shows that it retains the structure of a free C₃₆ cage, which is consistent with Low Energy Cluster Beam Deposition (LECBD) experiments. The adlayer is composed of many C₃₆-monomers as well as the covalently bonded C₃₆ dimers and trimers which is quite different from that of C₂₀ fullerene-assembled film, where a big polymerlike chain was observed due to the stronger interaction between C₂₀ cages. In addition, the chemisorption probability of C₃₆ fullerenes is decreased with increasing coverage because the interaction between these clusters is weaker than that between the cluster and the surface. When the incident energy is increased to 40–65 eV, the chemisorption probability is found to increased and more dimers and trimers as well as polymerlike-C₃₆ were observed on the deposited films. Furthermore, C₃₆ film also showed high thermal stability even when the temperature was raised to 1500 K.

A reported experimental evidence for gravitational quantum bound states of neutrons in the Earth's gravitational field¹ is discussed regarding possible employment of these states to prove the existence of gravitational field quanta through their interaction with a beam of ultracold neutrons.

The Dynamics of the excited He atoms formation in He–Ar mixture nanosecond discharge under the gas pressure range of 1–100 Torr with various component's content in the mixture are investigated. The contribution of a number of processes to the formation of excited atoms in the rear front of current pulse is analyzed.

X-ray diffraction patterns of melt-spun Fe-Cu-Nb-Si-B (FINEMET-type) alloys reveal that crystallites of Fe₂Si and Fe₃B phases with average sizes of 15(5) and 20(2) nm are present in the surface layer of thickness ≈ 10 Å and these nanocrystallites occupy 5–10% of the total volume. The results of an elaborate analysis of the high-resolution electrical resistivity data taken in a temperature range from 13 K to 300 K and their discussion in the light of existing theories demonstrates that the enhanced electron–electron interaction (EEI), quantum interference (QI) effects, inelastic electron–phonon scattering, coherent electron–magnon (and/or electron-spin fluctuation) scattering are the main mechanisms that govern the temperature dependence of resistivity. Of all the inelastic scattering processes, inelastic electron–phonon scattering is the most effective mechanism to destroy phase coherence of electron wavefunctions. The physical quantities such as diffusion constant, density of states at the Fermi level and the phase-breaking time, determined for the first time for the alloys in question, exhibit a systematic variation with the copper concentration.

Transparent sols of crystalline gadolinium doped zirconia particles with the general formula Zr_{1 - x}Gd_xO_{2 - x/2} (where x = 0–0.20), were prepared by a hydrothermal sol-gel method using cheap inorganic precursors. The composition, structure, crystallite size and lattice parameters of the crystalline dried sol particles and heated powders were studied. Thin films were deposited on quartz substrates using a simple dipping process and the structure, composition and crystallite size found to be identical to the powders with respect to the variation in temperature. Spectral transmittance studies showed that the films were transparent in the region between 400 and 1100 nm. The refractive index increased with the increase in annealing temperature, varying between 1.56 and 1.74. Optical band gap calculations gave band of 5.52 to 5.55 eV. Refractive indices and optical band gaps were compared with those of films containing other lanthanide dopants previously reported in the literature.