International Journal of Modern Physics B

Magnetic cluster systems can be considered as nanomagnets consisting of a small number of interacting spins that are magnetically isolated from the neighboring clusters of the compound by nonmagnetic ligands. Inelastic neutron scattering is a powerful experimental tool for the study of magnetic clusters, since it provides direct access to energy splittings. The present work provides an overview on this subject. The underlying concepts are presented and illustrated for some representative examples such as single-molecule magnets, diluted magnets, magnetic polarons, and dimer based compounds associated with quantum phase transitions and Bose–Einstein condensation as well as spin-Peierls dimerization. It is shown that — besides the dominant Heisenberg interaction — anisotropic and higher-order exchange terms are often needed to rationalize the experimental data.

Single phase M₂Si (M = Mg, Ca, Sr) silicides were grown using Si substrates, by thermal treatment of the substrates in the vapors of the metallic sources, M, and the electronic structures and optical property of the silicides were investigated. The electronic band structures of the silicides were calculated using the first-principles total-energy calculation program in pseudopotential schemes with plane-wave basis functions. The calculated optical reflectance spectra were also deduced from the theoretical band structures, and roughly agreed with the experimental results except for the low reflectance intensity around 2 eV. This suggests that the energy band gap of the silicides roughly agree with the calculated values of 0.15, 0.31 and 0.35 eV for Mg₂Si, Ca₂Si and Sr₂Si, respectively, within the underestimation of the band gap by the density functional calculation. The optical property of the silicides is also discussed in relation to the morphological structures of the silicides.

Based on the concepts of a superpropagator, multiple Debye temperatures, and equivalence of the binding energy of a Cooper pair and the BCS energy gap, the set of generalized BCS equations obtained recently via a temperature-generalized Bethe–Salpeter equation is employed for a unified study of the following composite superconductors: MgB₂, Nb₃Sn, and YBCO. In addition, we study the Nb–Al system in which Cooper pairs as resonances have recently been reported to have been observed. Our approach seems to suggest that a simple extension of the BCS theory that accommodates the concept of Cooper pairs bound via a more than one phonon exchange mechanism may be an interesting candidate for dealing with high-temperature superconductors.

The transport of a spatially periodic system with time delayed feedback driven by coupled noise terms is investigated. A general approximate equation of the current is derived. For the superconduction Josephson junction, it is found that suitable time delay can enhance the current in the system. In the presence of the coupling between noise terms, the current direction is determined by the sign of the coupling. The negative coupling can induce positive current, while the positive coupling can induce negative current. The absolute value of the current is a peaked function of the additive noise but a monotonically increasing function of the multiplicative noise. Numerical simulations are in good agreement with the approximate theoretical results.

Electronic processes in a semiconductor system consisting of some resonant tunneling structures, built in the depletion region of a Schottky barrier, are investigated. It is shown that the Schottky barrier can block or unblock the resonant tunneling current effectively. Tunneling processes do reveal the coherent character. Sharply nonlinear current–voltage characteristics are observed for both the forward and the reverse branches.

Double permutation (DP) method is developed here for designing Feynman diagrams for mass operator (MO) of interacting electrons in high orders of perturbation theory (PT). The derived expression allows finding the Young diagrams for the class of permutations corresponding to disconnect Feynman diagrams. The classification of DPs, carried out before, allows to identify the permutations corresponding to disconnected, singly connected (improper) diagrams and to derive expressions for intolerant cycles of permutations. Ordering the nonprimed digits in natural order in the cycles of DP, we avoid the permutations, corresponding to the Feynman diagrams of the same topology because of other numbering of nodes. Thus, the numbers of considered permutations is sufficiently reduced: (from 24 to 6 and from 720 to 42) in the second and the third orders of PT. All 414 expressions (diagrams) for MO in the fourth order of PT were designed using this method. The use of group theory allows us to conclude that no more Feynman diagrams can be designed. The developed method can be used as algorithm for Feynman diagrams designing for MO of interacting electrons (one sort fermions) in higher orders of PT.

We calculate in this study the volume of ice I as functions of temperature and pressure close to the melting point by analyzing the experimental data for the thermal expansivity. Using an approximate relation, the temperature dependence of the volume is calculated at 202.4 MPa from the thermal expansivity of ice I. The pressure dependence of the volume is also calculated at 252.3 K from the isothermal compressibility of ice I close to the melting point.

The volume calculated here as functions of temperature and pressure shows critical behavior close to the melting point in ice I, which can be tested by the experimental measurements.

The amplitude of nonlinear excitations in BECs with inhomogeneities is governed by a generalized variable-coefficient Korteweg–de Vries model. With symbolic computation, the Exp-function method is modified to obtain analytical nontraveling solitary-wave and periodic-wave solutions. Through the qualitative analysis and graphical illustration, the inhomogeneous propagation features of solitary waves are discussed, and some observable effects for BEC dynamic in the presence of external potentials are provided. The modified Exp-function method is also applicable to other variable-coefficient nonlinear evolution equations.

In this paper, periodic wave solutions for Pochhammer–Chree equation (PC-equation) with fifth order nonlinear term and their relationship with solitary wave solutions are studied. By designing innovative structure of solution, sixteen bounded periodic wave solutions in fractional form of Jacobi elliptic function (JEF) for PC-equation are given. Furthermore, global phase figure in the plane of the traveling solution for the PC-equation are obtained through dynamic systematic method, we indicate the region in the phase where the given sixteen solutions for PC-equation belong to. We find that two couples of these solutions change into two bell profile solitary wave solutions as k → 1 and four solutions change into four periodic wave solutions in fractional form of cosine function as k → 0. Finally, four figures are shown to describe the evolvement from periodic wave solutions to bell profile solitary wave solutions as k → 1.