Table of contents

The solar system started to form about 4.56 Gyr ago and despite the long intervening time span, there still exist several clues about its formation. The three major sources for this information are meteorites, the present solar system structure and the planet-forming systems around young stars. In this introduction we give an overview of the current understanding of the solar system formation from all these different research fields. This includes the question of the lifetime of the solar protoplanetary disc, the different stages of planet formation, their duration, and their relative importance. We consider whether meteorite evidence and observations of protoplanetary discs point in the same direction. This will tell us whether our solar system had a typical formation history or an exceptional one. There are also many indications that the solar system formed as part of a star cluster. Here we examine the types of cluster the Sun could have formed in, especially whether its stellar density was at any stage high enough to influence the properties of today's solar system. The likelihood of identifying siblings of the Sun is discussed. Finally, the possible dynamical evolution of the solar system since its formation and its future are considered.

The properties of parallel propagating large amplitude electromagnetic solitons are investigated in a thermal, magnetized pair plasma. These solitons are proven to be charge neutral and to have a linearly polarized magnetic but no electric field. From a Sagdeev pseudopotential analysis it transpires that such solitons are compressive in the species densities and destroyed when the species' sound velocity exceeds a fraction of their Alfvén speed. The existence domain in compositional parameter space shows maxima for the soliton Mach numbers, densities and perpendicular magnetic field components. These maxima depend on the ratio between thermal and Alfvén velocities and do not themselves correspond to physically valid solutions. A short discussion is given about possible generalizations, and the assumptions required for that.

A hydrodynamic model for dust devil dynamics in the internal vortex region is analyzed. It is shown that the results concerning the growing plumes investigated by Onishchenko et al (2014) for the short time domain can be applied to the study of vortex motion in the internal region for longer times. It is demonstrated that these convective plumes in an atmosphere with weak, large-scale toroidal motion inhomogeneity in the vertical direction can be a subject for further exponential growth over time.

The existence of soliton-like electromagnetic (EM) distributions in a fully degenerate electron–positron plasma is studied applying relativistic hydrodynamic and Maxwell equations. For a circularly polarized wave it is found that the soliton solutions exist both in relativistic as well as nonrelativistic degenerate plasmas. Plasma density in the region of soliton pulse localization is reduced considerably. The possibility of plasma cavitation is also shown.

Starting from the Wigner–Moyal equation coupled to Poisson's equation, a simplified set of equations describing nonlinear Landau damping of Langmuir waves is derived. This system is studied numerically, with a particular focus on the transition from the classical to the quantum regime. In the quantum regime several new features are found. This includes a quantum modified bounce frequency, and the discovery that bounce-like amplitude oscillations can take place even in the absence of trapped particles. The implications of our results are discussed.

Dynamics of Langmuir solitons is considered in plasmas with spatially inhomogeneous electron temperature. An underlying Zakharov-type system of two unidirectional equations for the Langmuir and ion-sound fields is reduced to an inhomogeneous nonlinear Schrödinger equation with spatial variation of the second-order dispersion and self-phase modulation coefficients, induced by a spatially inhomogeneous profile of the electron temperature. Analytical trajectories of motion of a soliton in the plasma with an electron-temperature hole, barrier, or cavity between two barriers are found, using the method of integral moments. The possibility of the soliton to pass a high-temperature barrier is shown too. Analytical results are well corroborated by numerical simulations.

More than 30 years ago, Arnowitt–Chamseddine–Nath and others established the compelling framework of supergravity gauge theories (SUGRA) as a picture for the next step in beyond the standard model physics. We review the current SUGRA scenario in light of recent data from LHC8 collider searches and the Higgs boson discovery. While many SUSY and non-SUSY scenarios are highly disfavored or even excluded by LHC, the essential SUGRA scenario remains intact and as compelling as ever. For naturalness, some non-universality between matter and Higgs sector soft terms is required along with substantial trilinear soft terms. SUSY models with radiatively-driven naturalness are found with high scale fine-tuning at a modest $\sim 10\%$. In this case, natural SUSY might be discovered at LHC13 but could also easily elude sparticle search endeavors. A linear ${{e}^{+}}{{e}^{-}}$ collider with $\sqrt{s}\gt 2m(higgsino)$ is needed to provide the definitive search for the required light higgsino states which are the hallmark of natural SUSY. In the most conservative scenario, we advocate inclusion of a Peccei–Quinn sector so that dark matter is composed of a WIMP/axion admixture i.e. two dark matter particles.

This tribute to the memory of my old friend and collaborator, Richard Arnowitt, focuses on the history, results and physical significance of the Arnowitt–Deser–Misner (ADM) formulation of general relativity, starting from its birth in 1958–9 through its completion, in a series of over a dozen papers, in 1962–3. A few of its later applications are also mentioned.

This article contains reminiscences of the collaborative work that Richard Arnowitt and I did together which stretched over many years and encompasses several areas of particle theory. The article is an extended version of my talk at the Memorial Symposium in honor of Richard Arnowitt at Texas A&M, College Station, Texas, 19–20 September 2014.

We obtain a partial differential equation for a pulse travelling inside a Bose–Einstein condensate under conditions of electromagnetically induced transparency. The equation is valid for a weak probe pulse. We solve the equation for the case of a three-level BEC in Λ configuration with one of its ground state spatial profiles initially constant. The solution characterizes, in detail, the effect that the evolution of the condensate wave function has on pulse propagation, including the process of stopping and releasing it.

We address the study of quantum Bose fluids confined in optical lattices subject to the influence of a time varying disordered external potential. The aim is to elucidate the interplay among lattice structure, interparticle interactions and the influence of structural disorder on dynamical and stationary ground state properties. The analysis in quasi one-dimension systems is done combining both mean field and Bose–Hubbard schemes to capture the essence of the quantum many body problem. Our predictions include the manifestation of superfluid, Mott and Anderson-like phases. We also present a natural extension of our technique to investigate two-dimensions systems. A general panorama of the current studies in bosonic systems is also given.

We study the mirror-field interaction in several frameworks: when it is driven, when it is affected by an environment, and when a two-level atom is introduced in the cavity. By using operator techniques, we show either how these problems may be solved or how the Hamiltonians involved, via sets of unitary transformations, may be taken to known Hamiltonians for which there exist approximate solutions.

We consider a system composed of a mobile slab and the electromagnetic field. We assume that the slab is made of a material that has the following properties when it is at rest: it is linear, isotropic, non-magnetizable, and ohmic with zero free charge density. Using instantaneous Lorentz transformations, we deduce the set of self-consistent equations governing the dynamics of the system and we obtain approximate equations to first order in the velocity and the acceleration of the slab. As a consequence of the motion of the slab, the field must satisfy a wave equation with damping and slowly varying coefficients plus terms that are small when the time-scale of the evolution of the mirror is much larger than that of the field. Also, the motion of the slab and its interaction with the field introduce two effects in the slab's equation of motion. The first one is a position- and time-dependent mass related to the effective mass taken in phenomenological treatments of this type of systems. The second one is a velocity-dependent force that can give rise to friction and that is related to the much sought cooling of mechanical objects.

We study the process of spontaneous parametric down conversion of a coherent structured electromagnetic (EM) field into a pair of photons that are also described by structured EM modes. We explore the relevance of a full vectorial description when the pump beam is outside the paraxial regime. A particularly interesting new phenomenon in such a regime corresponds to the conversion of angular momentum of the EM field associated with its polarization (usually referred to as spin angular momentum or SAM) into angular momentum related to optical vortices (usually referred to as orbital angular momentum or OAM). We show that such a conversion can take place using Bessel pump beams and standard nonlinear crystals with their birefringent axis parallel to the vector normal to its surface. Phase matching conditions are studied in detail for this configuration. Signatures of the conversion of SAM into OAM on the angular spectrum of the down converted photons are described.

In this work we study, for the spontaneous parametric downconversion process, how the transverse amplitude of the pump may be transferred to one of the emitted photons in a given pair when heralded by the detection of the remaining photon. We present a theoretical description of this process along with a discussion of the short-crystal regime within which faithful transfer of the transverse amplitude occurs. We show experimental results for Gaussian and Bessel–Gauss pump beams. In both cases, we verify that the transverse amplitude mechanism occurs and for the former also shows the effects of a departure from the short crystal regime. For the latter we show that our heralded single photons exhibit a non-diffractive behavior, and for orders l = 1 and l = 2 we show that these heralded single photons are in fact vortices with orbital angular momentum transferred from the pump.

We present the theoretical basis needed to work in the field of photonic lattices. We start by studying the field modes inside and outside a single waveguide. Then we use perturbation theory to deal with an array of coupled waveguides and construct a mode-coupling theory. Finally, we show how quantum optics models can be used as a toolbox to design photonic integrated circuits that behave as multiplexors, optical couplers, and optical oscillators.

The emergence of chaos in an atom-field system is studied employing both semiclassical and numerical quantum techniques, taking advantage of the algebraic character of the Hamiltonian. A semiclassical Hamiltonian is obtained by considering the expectation value of the quantum Hamiltonian in Glauber (for the field) and Bloch (for the atoms) coherent states. Regular and chaotic regions are identified by looking at the Poincaré sections for different energies and parameter values. An analytical expression for the semiclassical energy density of states is obtained by integrating the available phase space, which provides an exact unfolding to extract the fluctuations in the level statistics. Quantum chaos is recognized in these fluctuations, as a function of the coupling strength, for different regions in the energy spectrum, evaluating the Anderson–Darling (A–D) parameter, which distinguishes the Wigner- or Poisson-like distributions. Peres lattices play a role similar to the Poincaré section for quantum states. They are calculated employing efficient numerical solutions and are a powerful visual tool to identify individual states belonging to a regular or chaotic region, classified by utilizing the Poincaré sections and the A–D parameter. Finally, the quantum Husimi function for selected excited states is shown to have a noticeable similitude with the Poincaré sections at the same energy.

We introduce a combination of coherent states as variational test functions for the atomic and radiation sectors to describe a system of N_a three-level atoms interacting with a one-mode quantised electromagnetic field, with and without the rotating wave approximation, which preserves the symmetry presented by the Hamiltonian. These provide us with the possibility of finding analytical solutions for the ground and first excited states. We study the properties of these solutions for the V-configuration in the double resonance condition, and calculate the expectation values of the number of photons, the atomic populations, the total number of excitations, and their corresponding fluctuations. We also calculate the photon number distribution and the linear entropy of the reduced density matrix to estimate the entanglement between matter and radiation. For the first time, we exhibit analytical expressions for all of these quantities, as well as an analytical description for the phase diagram in parameter space, which distinguishes the normal and collective regions, and which gives us all the quantum phase transitions of the ground state from one region to the other as we vary the interaction parameters (the matter-field coupling constants) of the model, in functional form.

Polarized velocity selective spectra for rubidium atoms in a room temperature cell are presented. The experiments were performed in the lambda configuration (D2 manifold) and in the $5{\rm s}\to 5{{{\rm p}}_{3/2}}\to 5{{{\rm d}}_{j}}$ ladder configuration. For the lambda configuration the effect of the probe beam intensity in the absorption and polarization spectra are compared with results of a rate equation approximation. Good overall agreement between experiment and theory is found. The results indicate different saturation rates for each of the atomic transitions. Distinctive polarization signals with hyperfine-resolved components are found for the ladder $5{{{\rm d}}_{3/2}}$ and $5{{{\rm d}}_{5/2}}$ upper states. Fluorescence detection of the 420 nm that results from the second step in the cascade decay $5{{{\rm d}}_{j}}\to 6{{{\rm p}}_{{{j}^{\prime }}}}\to 5{\rm s}$ was used in the ladder experiments. This fluorescence was also used for the detection of the $5{{{\rm p}}_{3/2}}\to 6{{{\rm p}}_{3/2}}$ electric dipole forbidden transition in atomic rubidium that occurs at 911 nm. The $6{{{\rm p}}_{3/2}}$ hyperfine structure was resolved in this continuous wave, non-dipole excitation.

Lorentz boosts applied to particles with spin and momentum degrees of freedom induce momentum-dependent rotations. As, in general, different particles have different momenta, the transformation of the whole state is not a representation of the rotation group. Here we identify the group that acts on a two-particle system and, for the case where the momenta of the particles are correlated, find invariant subspaces that have interesting properties for quantum information processes in relativistic scenarios. A basis of states for the study of transformations of spin states under Lorentz boosts is proposed, which is a good candidate for use in building quantum communication protocols in relativistic scenarios.

We study the dynamics of two kinds of entanglement and their interplay. On one hand, we consider the intrinsic entanglement within a central system composed of three two-level atoms and measured by multipartite concurrence; on the other, we consider the entanglement between the central system and a cavity, acting as an environment and measured with purity. Using dipole-dipole and Ising interactions between atoms, we propose two Hamiltonians: one homogeneous and one quasi-homogeneous. We find an upper bound for concurrence as a function of purity, associated with the evolution of the W state. A lower bound is also observed for the homogeneous case. In both situations, we show the existence of critical values of the interaction, for which the dynamics of entanglement seem complex.

The geometry of the rotating disk is revisited and the quantum consequences are discussed in view of the appearence of the geometric potential in the quantum problem on the rotating disk. A suggestion to detect the presence of the Gaussian curvature on the rotating disk in a resonance absorption experiment measuring transition frequencies is made. A quantum equivalent of the Newtonian bucket is considered.

We suggest a new deformed Schiöberg-type potential for diatomic molecules. We show that it is equivalent to Tietz–Hua oscillator potential. We discuss how to relate our deformed Schiöberg potential to Morse, to Deng–Fan, to the improved Manning–Rosen, and to the deformed modified Rosen–Morse potential models. We transform our potential into a proper form and use the supersymmetric quantization to find a closed form analytical solution for the ro-vibrational energy levels that are highly accurate over a wide range of vibrational and rotational quantum numbers. We discuss our results using four-diatomic molecules ${\rm NO}\left( {{X}^{2}}{{\Pi }_{r}} \right)$, ${{{\rm O}}_{2}}\left( {{X}^{3}}\Sigma _{g}^{-} \right)$, ${\rm O}_{2}^{+}\left( {{X}^{2}}{{\Pi }_{g}} \right)$, and ${{{\rm N}}_{2}}\left( {{X}^{1}}\Sigma _{g}^{+} \right)$. Our results turn out to compare excellently with those from a generalized pseudospectral numerical method.

We elaborate on the notion of generalized tomograms, both in the classical and quantum domains. We construct a scheme of star-products of thick tomographic symbols and obtain in explicit form the kernels of classical and quantum generalized tomograms. Some of the new tomograms may have interesting applications in quantum optical tomography.

In this paper, we investigate periodic behaviors of the Lorenz–Stenflo equations in wide ranges of parameters. Regimes of periodic solutions and chaotic solutions are computed and distinguished by local maximum values of a dynamic variable Z. Complex behaviors of the periodic solutions are observed inside a regime of the chaotic solutions which is closed and surrounded by a regime of the periodic solutions where a feature of disconnected bifurcations is observed. It is found that not only a regime of fixed solutions but also regimes of solutions with period 1 and 2 remain for sufficiently large parameters.

We study the unstable harmonic oscillator and the unstable linear potential in the presence of the point potential, which is the superposition of the Dirac $\delta (x)$ and its derivative ${{\delta }^{\prime }}(x)$. Using the physical boundary conditions for the Green's function we derive for both systems the resonance poles and the resonance wave functions. The matching conditions for the resonance wave functions coincide with those obtained by the self-adjoint extensions of the point potentials and also by the modelling of the ${{\delta }^{\prime }}(x)$ function. We find that, with our definitions, the pure $b{{\delta }^{\prime }}(x)$ barrier is semi-transparent independent of the value of b.

A generalized variable-coefficient Korteweg–de Vries (KdV) equation with variable-coefficients of x and t from fluids and plasmas is investigated in this paper. The explicit Painlevé-integrable conditions are given out by Painlevé test, and an auto-Bäcklund transformation is presented via the truncated Painlevé expansion. Under the integrable condition and auto-Bäcklund transformation, the analytic solutions are provided, including the soliton-like, periodic and rational solutions. Lax pair, Riccati-type auto-Bäcklund transformation (R-BT) and Wahlquist–Estabrook-type auto-Bäcklund transformation (WE-BT) are constructed in extended AKNS system. One-soliton-like and two-soliton-like solutions are obtained by R-BT and nonlinear superposition formula is obtained by WE-BT. The bilinear form and N-soliton-like solutions are presented by Bell-polynomial approach. Based on the obtained analytic solutions, the propagation characteristics of waves effected by the variable coefficients are discussed.

We investigate solitons in optical waveguides and Bose–Einstein condensates (BECs) governed by a (3+1)-dimensional Gross–Pitaevskii system, which describes the propagation of electromagnetic waves in the optical waveguides and ground-state wave functions of the BECs. We use the symbolic computation and Hirota method to derive analytic bright one- and two-soliton solutions under certain conditions. Soliton amplitude/width amplification and the influence of time-modulated dispersion on the bright-soliton shape are studied via graphic analysis. Through the analysis of bright solitons in optical waveguides and BECs, we find that both the amplitude and the width of bright solitons can become larger during propagation with certain choices of time-modulated dispersion, and that the shape of the bright soliton can also be affected by the time-modulated dispersion; when the time-modulated dispersion is different, we can obtain bright parabolic-like and periodic-type solitons.

This paper investigates the real (2+1)-dimensional Nizhnik–Novikov–Veselov equation. Using the Hirota trilinear form and the Taylor expansion method, the rational rogue wave is constructed. The complicated structures of rogue wave—including bright rogue wave, four-lump type rogue wave, and dark rogue wave—are presented. The existence conditions of bright and dark rogue waves are given. The dynamic behaviors of rogue waves are discussed mathematically and graphically. These results demonstrate the diversity of the structures of the rational rogue wave to the real system. It is hoped that these results may be useful for explaining some related nonlinear phenomena.

The nonlocal symmetries for the modified Kadomtsev–Petviashvili (mKP) equation are obtained with the truncated Painlevé method. The nonlocal symmetries can be localized to the Lie point symmetries by introducing auxiliary dependent variables. The finite symmetry transformations and similarity reductions related with the nonlocal symmetries are computed. The multi-solitary wave solution and interaction solutions among a soliton and cnoidal waves of the mKP equation are presented. In the meantime, the consistent tanh expansion method is applied to the mKP equation. The explicit interaction solutions among a soliton and other types of nonlinear waves such as cnoidal periodic waves and multiple resonant soliton solutions are given.

In this paper we study quantum–classical correspondence of a periodically driven two-dimensional (2D) anisotropic-oscillator. In terms of the time-dependent canonical transformation the stationary Lissajous orbits are found along with the Hannay's angle. On the other hand, the stationary wave functions are derived analytically with the help of the generalized gauge transformation. The Berry phase in the original gauge is found to be $(n+1/2)$ times the nonadiabatic Hannay's angle with the integer number n being the eigenstate index. By using the SU(2) coherent superposition of degenerate 2D-eigenstates for a fixed energy we construct the stationary wave function, the probability cloud of which is shown to coincide perfectly with the classical orbits.

The family of displacement operators $D(x,p)$, a central concept in the theory of coherent states of a quantum mechanical harmonic oscillator, has been successfully generalized to systems of quantized, cyclic or finite position coordinates. However, out of the plethora of mutually equivalent expressions for the displacement operators valid in the continuous case, only few are directly applicable in the other systems of interest. The aim of this paper is to strengthen the analogy between the different cases by identifying the root cause of the issues accompanying the straightforward generalization of certain important expressions and, more importantly, offering alternative ones of general validity. Ultimately we arrive at an algorithm allowing one to express any displacement operator as an exponential of a pure imaginary multiple of a generalized 'quadrature' observable that is not obtained by a linear combination of position and momentum observables but rather by a shear transform of one of them in the system's phase space.

The spin density matrix (SDM) used in atomic and molecular physics is revisited for nuclear physics, in the context of the radial density functional theory. The vector part of the SDM defines a 'hedgehog' situation, which exists only if nuclear states contain some amount of parity violation. A toy model is given as an illustrative example.

We calculated the half-lives of two-neutrino double beta decay $(2\nu \beta \beta )$ of ⁷⁶Ge, ⁸²Se, ⁹⁶Zr and ¹⁰⁰Mo nuclei for the 0⁺ ↦ 0⁺ transition. Quasiparticle random phase approximation (QRPA) was used by considering the charge-exchange spin–spin interactions among the nucleons by considering both particle–hole (p–h) and particle–particle (p–p) channels in the separable form. Calculations were performed for the spherical form of the nuclei.

The new derivation of the equation of the spin precession is given for a particle possessing electric and magnetic dipole moments. Contributions from classical electrodynamics and from the Thomas effect are explicitly separated. A fully covariant approach is used. The final equation is expressed in a very simple form in terms of the fields in the instantaneously accompanying frame. The Lorentz transformations of the electric and magnetic dipole moments and of the spin are derived from basic equations of classical electrodynamics. For this purpose, the Maxwell equations in matter are used and the result is confirmed by other methods. An antisymmetric four-tensor is correctly constructed from the electric and magnetic dipole moments.

Two-point functions, the mean field squared and the vacuum expectation value (VEV) of the energy–momentum tensor are investigated for the electromagnetic field in the geometry of parallel plates on background of $(D+1)$-dimensional dS spacetime. We assume that the field is prepared in the Bunch–Davies vacuum state and on the plates a boundary condition is imposed that is a generalization of the perfectly conducting boundary condition for an arbitrary number of spatial dimensions. It is shown that for $D\geqslant 4$ the background gravitational field essentially changes the behavior of the VEVs at separations between the plates larger than the curvature radius of dS spacetime. At large separations, the Casimir forces are proportional to the inverse fourth power of the distance for all values of spatial dimension $D\geqslant 3$. For $D\geqslant 4$ this behavior is in sharp contrast with the case of plates in Minkowski bulk where the force decays as the inverse $(D+1){\rm th}$ power of the distance.

Single-/dual-/triple band metamaterial absorbers based on cut wire and square ring are discussed at microwave frequencies. The single-/dual-/triple band characteristics are realized by loading the cut wires in the square ring. The results indicate that the proposed metamaterial absorbers exhibit near-perfect impedance matching with free space and high absorbance of 99.50% at 4.70 GHz for single-band condition, and absorbance of 98.75% and 97.64% at 4.44 and 8.55 GHz, respectively, for dual-band condition. The triple band MMA can achieve the absorbance of 96.94%, 97.91% and 94.83% at 4.48 GHz, 7.81 GHz and 14.05 GHz, respectively. It also exhibits a wide range of angles of incidence for both TE and TM radiation. The physical mechanism of the absorptions is interpreted by the simulated surface current distributions and power-loss of the structures. Microwave experiments are performed to successfully realize these ideas, and measured results are in good agreement with the numerical results.

Based on holographic interferometry technique, we develop a quantitative method for on-site characterization of surface topology and 3D reconstruction. The optical set-up with 2D spatial light modulator for surface characterization of 3D micro-structures is presented. It is shown that this non-destructive and non-contact method made possible the rapid investigation of 3D polymer structures employing diffractive masks and phase modulation based on two beams interference. The experimental results obtained with this method demonstrated the quantitative high-resolution measurement of samples topology with faster processing details comparing to the actual screening methods which cannot be used on-site conditions.

For the development of novel devices, the correlation of oxygen vacancies and room temperature ferromagnetism in cobalt doped zinc oxide nanostructures synthesized by Co precipitation route reported earlier Zia et al (2014 Phys. Scr.89 105802) has been further explored on the basis of structural, optical, magnetic and photoelectrical measurements. In the current study, x-ray diffraction data is further exploited for the measurement of d-spacing, c-direction growth for the plane (002) and cell volume. Increased volume of the unit cell is observed with the increase in cobalt content. UV–visible absorption spectroscopy analysis reveals the reduction in optical energy band gap with the increase in cobalt concentration. The saturated and remanence magnetization were found to be increasing with cobalt addition during the magnetic analysis. The photoelectrical conductivity has maximum value for the sample Co (3% mol) and least recovery time as compared to Co (0% mol). The sensing response was found to be decreasing with the addition of cobalt. The anomalies in the photoelectric parameters clearly reflect the presence of photoconductive nature, which may have ramifications for device engineers.

We present a novel design for a high quality (Q)-factor, nonlinear planar photonic crystal (PhC) nanocavity incorporating a silicon/polymer material that is well suited to ultrafast all-optical switching. The hybrid nanocavity is created in the centre of a triangular lattice planar PhC made from silicon using the three-missing-holes point defect (L3). It is formed by infiltrating the air hole array of the PhC with polymer and by depositing a polymer layer on top of a PhC membrane. To determine the hybrid nonlinear cavity performance, we analyze the dependence of the refractive index (RI) of the top cladding on the Q-factor and resonant wavelength. The results show that, when the top cladding RI is increased from 1.5 to 1.6, corresponding to that of polymer materials, the Q-factor decreases markedly (Q < 10³). Optimization of the hybrid nonlinear silicon/polymer cavity design by modulating the structure parameters yields a high Q-factor of 54 000 with a small modal volume across the telecommunications band. In addition, the field distribution of the resonant mode indicates that the radiation loss is sufficiently small. Due to the overwhelmingly large Kerr nonlinearity of polymer over silicon, this structure configuration design shows considerable promise as regards the realization of ultrafast response speed in small-sized all-optical switching integrated devices.

Anomalous absorption of a lower hybrid wave via mode coupling to short parallel wavelength density fluctuations in a magnetized plasma is investigated. The mode coupling produces a beat mode with the frequency of the lower hybrid wave but an enhanced parallel wave number. This mode is Landau damped on electrons. The oscillatory velocity associated with the beat mode couples with the density ripple to modify the density perturbation of the lower hybrid wave introducing anomalous resistivity. The anomalous resistivity increases with the normalized wave number of the density ripple.

Radiofrequency discharges can generate non-equilibrium and stable micro-plasmas without a streamer in micro-hollow cathode reactors. In this work, we present the results of a fluid model describing the mechanisms occurring in a micro-reactor in argon plasma, generated by an excitation of 13.56 MHz at high pressures (100 Torr) with and without a secondary emission of electrons. The results of the simulation improve the understanding of the effect of micro-hollow cathodes and of the influence of excited atoms in ionization and sustainment of argon discharge at low voltage (150 V). Simulation results showed that the maximum of penning ionization and stepwise ionization rates are respectively about 25% and 11% of the maximum of direct ionization rate. The metastable atom density reaches a maximum value of 10²⁰/m³ inside the hole and have also two humps near to oppsite cathodes. Accordingly the excitation rate is significant in all the space.

We introduce an approach for numerically solving the Poisson equation by using a physical model, which is a way to solve a partial differential equation without the finite difference method. This method is especially useful for obtaining the solutions in very many free-charge neutral systems with open boundary conditions. It can be used for arbitrary geometry and mesh style and is more efficient comparing with the widely-used iterative algorithm with multigrid methods. It is especially suitable for parallel computing. This method can also be applied to numerically solving other partial differential equations whose Green functions exist in analytic expression.

The Dimits nonlinear upshift has for the first time been explained with good quantitative agreement. This was done with the reactive toroidal advanced fluid model. This is also the first time that the Dimits shift has been simulated in a transport code. The upshift of the critical gradient for transport is due to the fluid resonance, enhancing the zonal flow and the finite width is due to detuning of the resonance by the linear growth rate.

The paper is devoted to developing the theory of parametric excitation of electromagnetic waves propagating across the axis of symmetry in cylindrical waveguides partially filled with isotropic plasma. The problem is studied theoretically in the fluid approximation and expressions for the wave fields are derived from Maxwell's equations. The azimuthally non-symmetric electromagnetic waves propagate in the form of wave packets which are approximately described by the main azimuthal harmonic and two nearest satellite temporal harmonics. The boundary condition, which is cast in a nonlinear form, describes the flowing of a surface current on the plasma interface. This condition allows one to derive an infinite set of equations for harmonics of the tangential electric field of azimuthally non-symmetric surface waves. The dependence of the growth rate of the parametric instability of these waves on parameters of the plasma-filled waveguide and alternating electric field is studied both analytically and numerically.

The lattice dynamics, thermodynamic, mechanical properties and thermal conductivity of L1₂ Al₃X (X = Sc, Er, Tm, Yb) intermetallics have been investigated from first-principles calculations by means of using the VASP code. Our results agree well with the previous experiments and calculations. The phonon dispersion curves and the density of phonon states have been calculated by means of using the PHONONPY code and compared with the experimental results. The four compounds stay dynamically stable in the L1₂ structure. We also calculated the thermodynamics properties and give the relationships between thermal parameters and temperature. The elastic constants of the considered compounds are satisfied with mechanical stability criteria. The related mechanical parameters predict that Al₃Sc has higher hardness than the other three compounds, and four compounds all posses a brittle nature. The mechanical anisotropy is predicted by anisotropic constants A^U and A^Z. The results show that the four compounds are all elastically isotropic. We also calculated the thermal conductivity by means of the Clarke's model and Cahill's model and found that the thermal conductivity of the four intermetallics follows the order: Al₃Sc > Al₃Er > Al₃Tm > Al₃Yb.

A simple analytical method for electron energy spectrum calculations of cylindrical quantum dots (QDs) and quantum rods (QRs) is presented. The method is based on a replacement of an actual QD or QR hamiltonian with an approximate one, which allows for a separation of variables. Though this approach is known in the literature, it is essentially expanded in the present paper by taking into account a discontinuity of the effective mass, which is of importance in actual semiconductor heterostructures, e.g., InGaAs QDs or QRs embedded in GaAs matrix. Several examples of InGaAs QDs and QRs are considered—their energy spectrum calculations show that the suggested method yields reliable results both for the ground and excited states. The proposed analytical model is verified by numerical calculations, results of which coincide with an accuracy of ∼1 meV.

The paper reports on the preparation and characterization of Sm³⁺ doped zinc borophosphate (ZBP) glasses. The density was measured and the corresponding molar volume was evaluated. The present glass system was investigated by the XRD, optical absorption, photoluminescence, decay curves and FTIR analysis. The Judd–Ofelt theory has been used to evaluate the JO intensity parameters (Ω_2,4,6) and calculated oscillator strengths (ƒ_cal). Using JO intensity parameters, various radiative parameters such as transition probability (A_R), radiative lifetime (τ_R), measured lifetime (τ_m), calculated branching ratios (β_R), measured branching ratios (β_m) have been calculated for the excited ⁴G_5/2 level. The nature of the decay curves of ⁴G_5/2 level for different Sm³⁺ ion concentration in all ZBP glasses has been analyzed and the lifetimes are noticed to decrease with increase of concentration.

The electronic and magnetic properties of EuAlO₃ are calculated by first-principles full-potential linearized augmented plane wave (FP-LAPW) method based on density functional theory (DFT). The exchange and correlation potential is treated with different approximations: mBJ and GGA + U. Coulomb repulsion (U) has been calculated using super-cell calculations for EuAlO₃. The GGA + U calculations reveal an indirect band gap of 4.6 eV for EuAlO₃ in the spin down channel supporting the half metallic (HM) nature of the system. An effective integral magnetic moment also supported the HM nature of EuAlO₃.

New data about the ground state of the Mn²⁺ impurity ions in a series of single crystals of alumbrados MAl₃(BO₃)₄, where M = Y,Eu,Tm were obtained. The electron paramagnetic resonance (EPR) spectra of the Mn²⁺ spectra were studied, the parameters of the spin Hamiltonian describing the angular dependence of the spectrum were defined. It was shown that Mn²⁺ ions substitute trivalent ions of rare earth metals without changing the symmetry of the substitution site. The charge compensation process was found to be a nonlocal one. The cooling of the crystals leads to the increase of the splitting of the ground state, which is associated with the anisotropy of the thermal expansion coefficient. It was shown that an application of the superposition model to explain the distortions induced by an impurity Mn²⁺ ion has some limitations. The EPR linewidth of the Mn²⁺ ion in the TmAl₃(BO₃)₄ crystal increases with increasing temperature as a result of the dipole–dipole and exchange interactions with the excited states of the host lattice Tm³⁺ ion.

A study on temperature dependent magnetic properties of single-phase orthorhombic perovskites system associated with space group Pbnm compounds Pr_1−x(Gd/Nd)_xMnO₃ (x = 0.3, 0.5, 0.7) was carried out. A magnetization reversal is observed below the Néel temperature (T_N), in dc magnetization measurements (at 50 Oe) in the doped compounds. This may be due to the antiparallel coupling between the two magnetic sublattices (|Pr + Gd/Nd|and Mn). With lowering of temperature, the |Pr + Gd/Nd| ions begin to polarize under the negative internal field due to canted moment of Mn moments. The hysteresis plot taken at 50 K shows a ferrimagnetic characteristic and the presence of spin canting of ions in the magnetic sublattices. Arrott plot indicates field induced second-order paramagnetic to ferrimagnetic (PM–FiM) phase transition in this system.