International Journal of Modern Physics B

Using the Lagrangian formalism we attempt to calculate the interaction energy between the two bodies, nonconnected and connected, in a linear lattice. The obtained results show that the interaction is dependent on the dispersion relation ω (q). On this basis we calculate the binding energy of an ionic lattice and we have found a good agreement with experimental data.

According to the characteristics of the magnetic structures of the CE phase and the A phase for half-doped manganites, a two-dimensional model based on double exchange via degenerate e_g orbitals as well as the Coulomb interaction and the superexchange interaction has been proposed to discuss the two phases on an equal footing. It is explained why the CE phase is usually easier to be realized for many half-doped manganites, while the A phase occasionally occurs. Moreover, our numerical calculations show that the two phases at x = 0.5 are not spin-canted, which is in good agreement with experimental observations.

A large d (space dimension) expansion together with the ∊-expansion is implemented to calculate the Kolmogorov constant from the energy equation of Kraichnan's direct-interaction approximation using the Heisenberg's eddy-viscosity approximation and Kraichnan's distant-interaction algorithm. The Kolmogorov constant C is found to be C = C₀ d^1/3 in the leading order of a 1/d expansion. This is consistent with Fournier, Frisch, and Rose. The constant C₀ evaluated in the above scheme, is found to be C₀ = (16/27)^1/3.

We have investigated the structural phase stability of crystalline alkali metals under external pressure in terms of their pair potentials, structural free energies, thermomechanical properties viz. the elastic constants and the density-of-sates [DOS] at the Fermi level. The pair potentials are calculated using amenable model potentials, the structural energies and the elastic constants are calculated in terms of the effective pair potentials and the DOS for the systems are calculated by employing the augmented-spherical-waves [ASW] method. The matching between the minima of the pair potentials and the relative positions of the first few lattice vectors of the relevant structures gives a qualitative impression on the relative stability of a crystal phase. Similarly the appearance of a minimum in the energy difference curves between relevant crystal structures manifests a relatively stable structure. On the contrary, a maximum in the bulk modulus indicates a stable structure; these maximum-minimum criteria are controlled by the profile of the effective pair interactions of the constituent atoms. If the relevant lattice vectors are populated in and around the minimum of the respective pair potential the corresponding bulk modulus shows a maximum trend. The same situation gives rise to a minimum in the free energy. Both of these tendencies favor a particular crystalline phase against other relevant structures. Similarly a maximum in the DOS curves gives rise to a minimum in the energy curve manifesting a stable structure. The population of electronic states plays the responsible role here. To treat the two entirely different methods, namely, the perturbative pseudopotential theory and the non-perturbative ASW method on the same footing, we have used the same metallic density in both the methods for the respective element. The calculated results show a qualitative trend in support of the observed structures for these elemental systems.

The paper deals with influence of two-scale variations of parameters on the behavior of different dynamical systems. By two-scale we mean parameter oscillations occur in an alternating manner with large and small temporal gradient, on a typical period intervals. The shape of such parameter dependence resembles relaxation oscillations. Parametric instability is revealed under these conditions. We call it two-scale geometric resonance (TGR). TGR can be described with the help of certain geometric structures on the extended phase space. TGR possesses similar properties and can be described in similar ways in seemingly different systems. The article presents general models for the TGR description and considers a few specific examples: classical oscillator, Van-der-Pol oscillator and thermodynamic system with ideal gas.

Mechanism of ion transport in periodic interacting systems is investigated by employing the Fokker–Planck approach. This is done through an investigation of the quasielastic peak in the dynamic structure factor S(q, ω). Its half width at half maximum (hwhm) exhibits an oscillatory behavior as a function of the scattering wave-vectors q, reflecting the role of correlations among diffusing particles. All calculations are performed at low temperature and at high friction limit.

The electric conductance of the graphite ribbon with locally applied gate voltage has been studied in terms of the Landauer approach. In the low-energy region, nano-graphite ribbon with zigzag boundaries exhibits the single electronic transport channel due to the edge states. The chemical potential dependence of the electric conductance shows qualitatively different behavior, depending on whether the magnitude of the potential barrier (gate voltage bias) V_g is larger than the energy gap Δ of the single channel region of the zigzag ribbon. For positive V_g with V_g < Δ, the zero-conductance resonances appear for 0 ≤ E ≤ V_g, and average transmission probability is quite small in this region. However the transmission probability is almost one, i.e. perfect transmission, for E > V_g. This step-function-like behavior of the conductance shows that it is possible to fabricate a nano-graphite-based switching device by the application of weak gate voltage bias.

We have calculated the low-temperature series expansions of the spontaneous magnetization and the zero-field susceptibility of the square-lattice ferromagnetic Ising model with first-neighbour interaction J₁ and second-neighbour interaction J₂ to the 30th and 26th order respectively by computer. Our results extend the previous calculations by Lee and Lin to six more orders. We use the Padé approximants to estimate the critical exponents and the critical temperature for different ratios of R = J₂/J₁. The estimated critical temperature as a function of R agrees with the estimation by Oitmaa from high-temperature series expansions.

We have calculated the high-temperature series expansion of the zero-field susceptibility of the square-lattice Ising model with first and second neighbour interactions to the 20th order by computer. Our results extend the previous calculation by Hsiao and Lin to two more orders. We use the Padé approximants to estimate the critical exponent γ and the critical temperature. Our result 1.747 < γ < 1.753 supports the universality conjecture that all two-dimensional Ising models have the same critical exponent γ = 1.75.

Ultrasonic properties of bulk TlSr₂ (M_{1 - x}Y_x)Cu₂O₇(M = Ca, Sr) high temperature superconductors have been measured between 80 and 280 K. Sound velocity measurements show that all samples exhibit an overall stiffening trend with decreasing temperature. The longitudinal sound velocity shows a pronounced slope change and attenuation peak around 200 K. The results were explained in terms of phase transition and distortion of Tl and O atoms associated with local oxygen ordering. The calculated acoustic Debye temperature does not show strong correlation with the transition temperature. The electron-phonon coupling constant was calculated using the weak and strong limit of the BCS theory as well as the van Hove scenario.

A big discrepancy was found between the calculated transition dipole length and the experimental one for the anthracene crystal. The cause of the discrepancy is ascribed to the screening of the light electric field by the internal field within the molecule due to the induced dipole charges. It is indicated that this screening effect is important in big molecules like aromatic molecules and that this effect is not important in atoms having small sizes.