International Journal of Modern Physics B

In this work, we prove a weak law and a strong law of large numbers through the concept of $q$-product for dependent random variables, in the context of nonextensive statistical mechanics. Applications for the consistency of estimators are presented and connections with stochastic processes are discussed.

A chemical two-step approach based on solvothermal technique has been adopted to synthesize the reduced graphene oxide (rGO)/Fe₂O₃ hybrid materials. The rGO was prepurified by acidic treatment, followed by sensitization to attach the desired functional groups. The structural, compositional, morphological and magnetic analyzes of the prepared samples were carried out using various characterization techniques. The fabricated rGO/Fe₂O₃ heterostructures were confirmed by X-ray diffraction analysis and Fourier transform infrared spectroscopy. Raman spectroscopy evidenced the fabrication of multilayer graphene and scanning electron microscopy was carried out to study the morphology of the prepared samples. The average particle size of Fe₂O₃ nanoparticles (NPs) loaded on rGO was found to be $\sim$20 nm, as was observed during transmission electron microscopy. Thermogravimetric analysis of rGO/Fe₂O₃ hybrid structures was performed to investigate their thermal behaviors. It was evidenced that the incorporation of Fe₂O₃ NPs into rGO enhanced its thermal stability. Vibrating sample magnetometry showed that ferromagnetic character was induced in rGO due to involvement of Fe₂O₃ NPs. The rGO/Fe₂O₃ hybrid structures can be considered as a competent material for fabrication of various magnetic devices.

The electronic states of a core/shell quantum well (QW) system confined in a modified Pöschl–Teller (PT) plus Woods–Saxon (WS) potential in the presence of electric field are studied with the III-Nitride group owing to their wide bandgap for device applications. The bandgap energy in this regard is obtained by solving analytically the Schrödinger wave equation with the Pekeris-type approximation to the centrifugal term.

The spin–curvature interaction (SCI) and its effects are investigated based on curved Dirac equation. Through the low-energy approximation of curved Dirac equation, the Hamiltonian of SCI is obtained and depends on the geometry and spinor structure of manifold. We find that the curvature can be considered as field strength and couples with spin through Zeeman-like term. Then, we use dimension reduction to derive the local Hamiltonian of SCI for cylinder surface, which implies that the effective Hamiltonian of single-wall carbon nanotubes results from the geometry and spinor structure of lattice and includes two types of interactions: one does not break any symmetries of the lattice and only shifts the Dirac points for all nanotubes, while the other one does and opens the gaps except for armchair nanotubes. At last, analytical expressions of the band gaps and the shifts of their positions induced by curvature are given for metallic nanotubes. These results agree well with experiments and can be verified experimentally.

In this paper, based on Walktrap algorithm with the idea of random walk, and by selecting the neighbor communities, introducing improved signed probabilistic mixture (SPM) model and considering the edges within the community as positive links and the edges between the communities as negative links, a novel algorithm Walktrap-SPM for detecting overlapping community is proposed. This algorithm not only can identify the overlapping communities, but also can greatly increase the objectivity and accuracy of the results. In order to verify the accuracy, the performance of this algorithm is tested on several representative real-world networks and a set of computer-generated networks based on LFR benchmark. The experimental results indicate that this algorithm can identify the communities accurately, and it is more suitable for overlapping community detection. Compared with Walktrap, SPM and LMF algorithms, the presented algorithm can acquire higher values of modularity and NMI. Moreover, this new algorithm has faster running time than SPM and LMF algorithms.

To remedy the failure of minimal coupling method in describing the quantum dynamics of two localized Brownian oscillators interacting with a common medium, a scheme is introduced to model the medium by a continuum of complex scalar fields or equivalently two independent real scalar fields. The starting point is a Lagrangian of the total system and quantization is achieved in the framework of canonical quantization. The equations of motion, memory or response functions and fluctuation–dissipation relations are obtained. An induced force between oscillators is obtained originating from the fluctuations of the medium. Ohmic and non-Ohmic regimes are discussed and the positions of oscillators are obtained approximately in large time limit and weak coupling regime. Quantum entanglement between localized oscillators is obtained in zero temperature and strong coupling regime.

By employing the characteristics matrix method, we have investigated the transmission properties of one-dimensional dielectric–semiconductor metamaterial photonic crystals (PC) at Terahertz (THz) range theoretically. The numerical results show the appearance of cutoff frequency within THz range. Furthermore, the thicknesses of the constituents materials and the filling factor have a significant effect on the cutoff frequency. The proposed structure may be useful in many applications, particularly in THz frequency regions.

The influence of periodic edge vacancies and antidot arrays on the thermoelectric properties of zigzag graphene nanoribbons (ZGNRs) are investigated. Using Green’s function method, the tight-binding approximation for the electron Hamiltonian and the 4th nearest neighbor approximation for the phonon dynamical matrix, we calculate the Seebeck coefficient and the thermoelectric figure of merit. It is found that, at a certain periodic arrangement of vacancies on both edges of zigzag nanoribbon, a finite band gap opens and almost twofold degenerate energy levels appear. As a result, a marked increase in the Seebeck coefficient takes place. It is shown that an additional enhancement of the thermoelectric figure of merit can be achieved by a combination of periodic edge defects with an antidot array.

In this paper, a new two-dimensional (2D) phononic crystal structure composed of periodic slit metal tubes, in which the unit cell consists of straight or curved backstraps, is proposed, and the propagation characteristics of acoustic waves in this structure are theoretically investigated. Using the finite-element method, we calculate the dispersion relations and transmission coefficients of this structure. The results show that, in contrast to the only slit metal tubes, the periodic slit metal tubes with straight or curved backstraps are proved to display band gaps (BGs) at much lower frequency range. Meanwhile, the effect of the slit width of the backstraps on the BGs is investigated. The results show that the positions and widths of the BGs can be effectively modulated by the backstraps without changing the mass density or lattice constant of the material. The lowest frequency falls by about 200 Hz. Moreover, we investigated how the BGs are affected by the location parameter of the backstraps, finding that the acoustic BGs are sensitive to the location parameter of the backstraps. Numerical results show that BGs are significantly dependent upon the slit width and location parameters of the backstraps. The BGs are optimized because, the effect of the Helmholtz resonators of the slit tube is strengthened and changed when the location and slit width of the backstraps change. These results provide a good reference for optimizing BGs, generating filters and designing devices.

We demonstrate that the nonrelativistic fermions open the energy gap when the SU($N$) gauge bosons, mediating the interaction between fermions, acquire the mass. Surprisingly, even though there is the SU($N$) gauge symmetry, there is always one fermionic energy gap which is not degenerate to the rest of the $N-1$ fermions for $N\ge 3$ in the fundamental representation.

We have performed a new analysis on the dynamics and structure to investigate the aluminum-silicate melt under pressure. It is shown that the low-pressure configuration of the melt exhibits dynamic heterogeneity. The mobile and immobile atoms tend to reside in regions which have extremely high or low density. We reveal two moving types: the simply hopping or collective moving via supermolecule. The latter type is responsible for the positive pressure dependence on diffusivity. The structure is analyzed via SC-particle and SC-cluster. Our simulation reveals the structural heterogeneity in local environment and chemical composition. The densification of the melt is accompanied with the decreasing of the radius of core of SC-particle and the number of large SC-particles. We found that the liquid comprises two types of SC-particles. The SC-clusters of second type form large space regions which represent the diffusion pathway for aluminum.

A series of single-composition phosphors Sr₃B₂O₆: Tb${}^{3+}$, Eu${}^{3+}$have been prepared via a combustion method. The structural and luminescent properties of phosphor are investigated in detail. Under ultraviolet radiation excitation, Sr₃B₂O₆: Tb${}^{3+}$, Eu${}^{3+}$ phosphors show the characteristic $f$–$f$ transitions of both Eu${}^{3+}$ and Tb${}^{3+}$ and give a bright yellow emission. The investigations on photoluminescence and lifetime of Eu${}^{3+}$ show that there are two sites of luminescence center of Eu${}^{3+}$ in host matrix. The energy transfer from Tb${}^{3+}$ ion to Eu${}^{3+}$ ion are observed and the mechanism of energy transfer is dipole–quadrupole interaction.

The problem of the interaction between a two-level atom and a two-mode field in the parametric amplifier-type is considered. A similar problem appears in an ion trapped in a two-dimensional trap. The problem is transformed into an interaction governed by su(1,1) Lie algebraic operators with phase and coupling parameter depending on time. Under an integrability condition, that relates phase and coupling, a solution to the wavefunction is obtained using the Schrödinger equation. The effects of the functional dependence of the coupling and the initial state of the two-level atom on atomic inversion, the degree of entanglement, the fidelity and the Glauber second-order correlation function are investigated. It is shown that the acceleration term plays an important role in controlling the function behavior of the considered quantities.