Modern Physics Letters B

The concept of resonance has been instrumental to the study of Hamiltonian systems with divided phase space. One can also define such systems over discrete spaces, which have a finite or countable number of points, but in this new setting the notion of resonance must be re-considered from scratch. I review some recent developments in the area of arithmetic dynamics which outline some salient features of linear and nonlinear stable (elliptic) orbits over a discrete space, and also underline the difficulties that emerge in their analysis.

We give an exact quantitative solution for the motion of three vortices of any strength, which Poincaré showed to be integrable. The absolute motion of one vortex is generally biperiodic: in uniformly rotating axes, the motion is periodic. There are two kinds of relative equilibrium configuration: two equilateral triangles and one or three colinear configurations, their stability conditions split the strengths space into three domains in which the sets of trajectories are topologically distinct.

According to the values of the strengths and the initial positions, all the possible motions are classified. Two sets of strengths lead to generic motions other than biperiodic. First, when the angular momentum vanishes, besides the biperiodic regime there exists an expansion spiral motion and even a triple collision in a finite time, but the latter motion is nongeneric. Second, when two strengths are opposite, the system also exhibits the elastic diffusion of a vortex doublet by the third vortex.

For given values of the invariants, the volume of the phase space of this Hamiltonian system is proportional to the period of the reduced motion, a well known result of the theory of adiabatic invariants. We then formally examine the behaviour of the quantities that Onsager defined only for a large number of interacting vortices.

We study the organization of stability phases in the control parameter space of a periodically driven Brusselator. Specifically, we report high-resolution stability diagrams classifying periodic phases in terms of the number of spikes per period of their regular oscillations. Such diagrams contain accumulations of periodic oscillations with an apparently unbounded growth in the number of their spikes. In addition to the entrainment horns, we investigate the organization of oscillations in the limit of small frequencies and amplitudes of the drive. We find this limit to be free from chaotic oscillations and to display an extended and regular tiling of periodic phases. The Brusselator contains also several features discovered recently in more complex scenarios like, e.g. in lasers and in biochemical reactions, and exhibits properties which are helpful in the generic classification of entrainment in driven systems. Our stability diagrams reveal snippets of how the full classification of oscillations might look like for a wide class of flows.

Tunable phase control of the slow and fast light propagation through a defect slab medium doped by four-level InGaN/GaN quantum dot structure is demonstrated. By solving the Schrödinger and Poisson’s equations self-consistently, a spherical InGaN quantum dot with GaN barrier shell which can interact by terahertz (THz) signal field is designed numerically. It is found that the phase variation of THz signal field imparts the tunability in the group velocity of the transmitted and reflected pulses through a dielectric slab.

The transverse electrical resistance of HoBa₂Cu₃O${}_{7-\delta }$ single crystals is investigated in the temperature range $T_c-300\mathrm{\text{K}}$ for optimally-doped $(T_c\approx 91\mathrm{\text{K}})$ and oxygen-poor $(T_c\approx 51\mathrm{\text{K}})$ samples. With decreasing temperature, the resistivity of the optimally-doped samples has been found to transit from the regime of scattering on phonons and defects to the regime of “semiconductor” character and, near $T_c$, of the fluctuation conductivity. The oxygen-poor samples have been revealed to exhibit only a variable range hopping conductivity of “semiconductor” character, which near $T_c$ transits into the fluctuation conductivity. A significant anisotropy of the residual resistivity and characteristics of the fluctuation conductivity is observed for samples of both types.

The sintering behavior and dielectric properties of Bi${}^{3+}$-substituted Nd(Zn${}_{0.5}$Ti${}_{0.5})$O₃ (abbreviated as NZT) microwave ceramics (Nd${}_{1-x}$Bi${}_x$)(Zn${}_{0.5}$Ti${}_{0.5}$)O₃ $(0\le x\le 0.15)$ (abbreviated as NBZT) are investigated. XRD results reveal the formation of single perovskite solid solutions for $x\le 0.05$ samples. For $x>0.05$ samples, pyrochlore phase begins to segregate from the perovskite phase and its volume fraction increases with $x$. B-site Zn${}^{2+}$/Ti${}^{4+}$ 1:1 long range order (LRO) is detected by Raman Spectroscopy. The degree of LRO varies as a function of sintering conditions and chemical composition. The microwave dielectric properties of the composition are measured. By substituting Bi${}^{3+}$ for Nd${}^{3+}$, the temperature coefficient of resonant frequency $({\tau }_f)$ tunes toward zero, however, the microwave quality factor, $(Qf)$ deteriorates. For $x=0.03$, ${\tau }_f$ reaches a minimum value of $-18.9\mathrm{\text{ppm}}{/}^{\circ }\mathrm{\text{C}}$ with relative permittivity of ${\epsilon }_r=48.2$ and $Qf=1430\mathrm{\text{GHz}}$, respectively. The effect of Bi-doping on the $Qf$ value is discussed.

Point defect structure of B2 TrSc (Tr$=$Cd, Ru) alloys was investigated using supercell and special quasi-random structure (SQS) approaches. According to our results, Tr and Sc anti-sites are the constitutional point defects in Tr-rich and Sc-rich B2 TrSc, respectively. To investigate the thermal defect concentrations at finite temperatures, we adopted the Wagner–Schottky model using point defect formation enthalpies obtained from supercell and SQS approaches. The present results suggest that the predominant thermal defects in B2 CdSc are of exchange type, and in B2 RuSc are of interbranch Sc type. The calculated results show an agreement with the available theoretical and experimental data.

The inclined incidence of the femto laser on the phase mask in fiber Bragg grating (FBG) carving has a significant effect on the quality of FBG fabrication. Based on that the infrared femto laser has highly spatial coherence and the order walk-off will happen behind the phase mask, the interferogram generated at the fiber core by the inclined femto laser beam has been analyzed using the multi-beam interference principle. The influence of beam inclination on the coherence of the 0th and $\pm 1\mathrm{\text{st}}$ orders diffraction with different exposure distance, the visibility of interferogram and the frequency component of the transverse interferogram intensity has also been analyzed. It is meaningful for the FBG fabricating with the femto laser.

The dynamic magnetic behaviors of the spin-1 Blume–Capel Ising bilayer system (BCIS) are studied in an oscillating external magnetic field on a two-layer square lattice by utilizing the mean field theory (MFT) based on Glauber-type stochastic dynamics [dynamic mean field theory (DMFT)]. The dynamic equations describing the time-dependencies of the average magnetizations are obtained with the Master equation. The dynamic phases in this system are found by solving these dynamic equations. The temperature dependence of the dynamic order parameters is examined to characterize the nature (continuous or discontinuous) of the phase transitions and to obtain the dynamic phase transition (DPT) points. The dynamic phase diagrams (DPDs) are shown for ferromagnetic/ferromagnetic, antiferromagnetic/ferromagnetic, antiferromagnetic/antiferromagnetic interactions in the plane of the reduced temperature versus magnetic field amplitude and they display dynamic tricritical and re-entrant behavior as well as the dynamic triple point (tp).

When a droplet of a higher-density solution (HDS) is placed on the top of a lower-density solution (LDS), the HDS on the surface of the LDS sinks due to gravitational instability. In the sinking process, the HDS draws a fractal pattern or a hole/cell pattern on the surface of the LDS. It is observed that the surface pattern is determined by an aspect ratio of the container and viscosity of the LDS. In the formation of the surface pattern, a time series of the HDS density is analyzed. It is found that the profile of the series for the fractal pattern is different from that for the hole/cell pattern. In order to clarify the difference, we propose a phenomenological model for the time series to obtain fitting functions for both patterns.

In this paper, firstly we have synthesized ZnO nanowires using zinc acetate, ethanol and ammonium hydroxide by a thermo-chemical method and then ZnO nanorods (NRs) have been prepared by microwave irradiation (MI) of an initial solution containing ZnO nanowires. X-ray diffraction (XRD) analysis showed the rare zinc-blende phase which grows on the surface of NRs and its crystallite size increases with the increase of microwave power. The average length and width of rods were observed several hundreds of nanometer and 80nm, respectively, from scanning electron microscope (SEM) analysis. Ultraviolet-visible (UV-vis) absorption spectroscopy indicates that a band tail forms due to MI, which has roughly 2eV energy gap. Photoluminescence (PL) spectroscopy indicated a blue emission and a white emission for ZnO nanowires and NRs, respectively. MI quenches the UV emission from ZnO NRs and enhances the surface defects’ emission. The resultant visible PL of the samples increases with the increase of microwave power that shows the growth of zinc-blende phase which has crucial effect on the defect density of NRs.

In this paper, we examine the influence of photon excitation on the monogamy property of quantum discord in tripartite coherent states of Greenberger–Horne–Zeilinger (GHZ) type. The Hilbert–Schmidt norm is used as quantifier of pairwise quantum correlations. The geometric quantum discord in all bipartite subsystems are explicitly given. We show that the geometric discord is monogamous for any photon excitation order.

The analytical expressions have been obtained to describe the dependence of spinodal curve at which isotropic state of polydisperse melt of semiflexible diblock copolymer becomes unstable with respect to formation of nematic state on the polydispersity indices of the blocks, parameters of anisotropic interactions, and flexibility of blocks. The flexibility of blocks is taken into account within discrete worm-like chain model, lengths of blocks are assumed to be distributed by the Schulz–Zimm distribution. It is shown that increase of degree of polydispersity of blocks yields the increase of nematic spinodal temperature.

In this paper, we calculate the time evolution of the quantum mechanical state of a bound magnetopolaron in a modified cylindrical quantum dot. In the condition of strong coupling, we investigate the eigen energies and the eigenfunctions of the ground state and the first excited state, respectively. This system may be employed as a two-level quantum system qubit and therefore be helpful for storage of information. The Shannon entropy is used to investigate the decoherence of the qubit when the latter is in the superposition state of the ground and the first excited states. We also study the influence of the electric field, the magnetic field and the Coulomb potential on the decoherence time, eigen energies of the ground state, and the first excited state. It is shown that, the phonon spontaneous emission causes the decoherence of the qubit. We plot the decay of the density matrix of the qubit and the coherent term of the density matrix element $p_{01}$ (or $p_{10}$) in a function of time for different coupling strengths, confinement lengths and dispersion coefficient.

The plane wave expansion (PWE) method is used to calculate the band gaps of two-dimensional (2D) phononic crystals (PCs) with a hybrid square-like (HSL) lattice. Band structures of both XY-mode and Z-mode are calculated. Numerical results show that the band gaps between any two bands could be maximized by altering the radius ratio of the inclusions at different positions. By comparing with square lattice and bathroom lattice, the HSL lattice is more efficient in creating larger gaps.

A new model, based on an asymptotic procedure for solving the spinor kinetic equations of electrons and phonons is proposed, which gives naturally the displaced Fermi–Dirac distribution function at the leading order. The balance equations for the electron number, energy density and momentum, plus the Poisson’s equation, constitute now a system of six equations. Moreover, two equations for the evolution of the spin densities are added, which account for a general dispersion relation.

In this paper, a low-cost Ti/TiO₂/HfO₂/TiO₂/Ti stack structure is proposed as a selector for bipolar resistive random access memory (RRAM) cross-bar array applications. We demonstrate reproducible resistive switching characteristics with significant nonlinearity and good uniformity in the one selector and one resistor (1S1R) structure device that integrate the bidirectional selector with a bipolar Pt/Ti/HfO₂/Pt RRAM device. These results provide a good point of reference for evaluating the potential low-cost applications in bipolar RRAM cross-bar array.

Under investigation in this paper is the $(3+1)$-dimensional coupled nonlinear Schrödinger system for an optical fiber with birefringence. With the Hirota method, bilinear forms of the system are derived via an auxiliary function, and the bright one- and two-soliton solutions are constructed. Based on those soliton solutions, soliton propagation and interaction are investigated analytically and graphically. Non-singular cases of the bright one-soliton solutions are presented, from which the single-peak and two-peak solitons can arise, respectively. Through the analysis on the bright two-soliton solutions, the elastic and inelastic interactions are investigated. Three kinds of the elastic interactions are presented, between the two one-peak solitons, a one-peak soliton and a two-peak soliton, and the two two-peak solitons.

The thermodynamics of irreversible processes in continuous media predicts the existence of a magnetic Nernst effect that results from a magnetic analog to the Seebeck effect in a ferromagnet and magnetophoresis occurring in a paramagnetic electrode in contact with the ferromagnet. Thus, a voltage that has DC and AC components is expected across a Pt electrode as a response to the inhomogeneous magnetic induction field generated by magnetostatic waves of an adjacent YIG slab subject to a temperature gradient. The voltage frequency and dependence on the orientation of the applied magnetic induction field are quite distinct from that of spin pumping.

In this paper, based on the time-dependent Ginzburg–Landau theory, we study the dynamics of vortex–antivortex (V–Av) pairs in a mesoscopic superconducting square with a small hole under applied bias currents. For the sample with a centered hole, a V–Av pair can nucleate at the hole edges and moves in opposite directions perpendicular to applied constant DC drive. The influence of the external magnetic field on the (anti)vortex velocity and the lifetime of V–Av pairs is mainly investigated. Different modes in the dynamical process of the V–Av collision and annihilation are identified. Moreover, in the case when the hole is displaced from the center of the square, the V–Av dynamics behaves quite differently from the symmetric case due to the shift of the V–Av creation point.

In this paper, the statistical properties of energy levels are studied numerically for atom in parallel electric and magnetic fields, which is an ideal system to examine the contributions of external fields and ionic core to quantum chaos. The Stark maps of diamagnetic spectra and nearest neighbor spacing (NNS) distributions are obtained by diagonalization method incorporating core effect. We identify obvious level anti-crossing and large value of $q$ for barium, indicating that core effect has predominant contribution to chaotic dynamics in barium. To study the core effect in detail, we sweep the quantum defect artificially and find that larger core effect will undoubtedly induce stronger chaotic dynamics.

The electronic and optical properties of S- and/or Ce-(co)doped anatase titanium dioxide (TiO₂) are investigated using density functional theory plus U (DFT$+$U) calculations. The optimized total energy suggests that TiO₂ codoping by Ce and S favours the configuration of one substitutional Ce atom occupied on a Ti site with one substitutional S atom either on its nearest neighboring O or Ti site. The calculated results show that all doping configurations exhibit remarkable red-shift and excellent photocatalytic properties compared with pure TiO₂. These reinforced features can mainly be ascribed to the appearance of S $3p$ states in the top of valence band (VB) and Ce $4f$ states in the bottom of conduction band (CB) as well as the contribution from the increasing octahedral dipole moments. The synergetic effects of cationic Ce and anionic S can extend optical absorption edge, which results in higher absorption coefficient in the visible light region than that of the anionic S monodoping and cationic Ce monodoping case; in the same time, decreasing the codoping concentration leads to reduced optical absorption. Additionally, Ce and S as cations incorporating into TiO₂ lattices can induce stronger redox potential with a lower defect formation energy under O-rich condition compared with other doping systems.

Nd₂Fe${}_{13.6}$Zr${}_{0.4}$B hard magnetic material were prepared using arc-melting technique on a water-cooled copper hearth kept under argon gas atmosphere. The prepared samples, Nd₂Fe${}_{13.6}$Zr${}_{0.4}$B ingot and ribbon are characterized using X-ray diffraction (XRD), scanning electron microscopy (SEM) for crystal structure determination and morphological studies, respectively. The magnetic properties of the samples have been explored using vibrating sample magnetometer (VSM).

The lattice constants slightly increased due to the difference in the ionic radii of Fe and that of Zr. The bulk density decreased due to smaller molar weight and low density of Zr as compared to that of Fe. Ingot sample shows almost single crystalline phase with larger crystallite sizes whereas ribbon sample shows a mixture of amorphous and crystalline phases with smaller crystallite sizes. The crystallinity of the material was highly affected with high thermal treatments. Magnetic measurements show noticeable variation in magnetic behavior with the change in crystallite size. The sample prepared in ingot type shows soft while ribbon shows hard magnetic behavior.