Anisotropic harmonic oscillator,non-commutative Landau problem and exotic Newton–Hooke symmetry

We investigate the planar anisotropic harmonic oscillator with explicit rotational symmetry as a particle model with non-commutative coordinates. It includes the exotic Newton–Hooke particle and the non-commutative Landau problem as special, isotropic and maximally anisotropic, cases. The system is described by the same (2+1$2+1$)-dimensional exotic Newton–Hooke symmetry as in the isotropic case, and develops three different phases depending on the values of the two central charges. The special cases of the exotic Newton–Hooke particle and non-commutative Landau problem are shown to be characterized by additional, so(3)$\mathit{so}(3)$ or so(2,1)$\mathit{so}(2,1)$ Lie symmetry, which reflects their peculiar spectral properties.     

Statistical properties of cooperative emission of an ensemble of nonisochronous electrons–oscillators

Effect of shot noise and energy spread of particles on the statistical properties of cooperative emission of an ensemble of nonisochronous electrons–oscillators is analyzed. The dependences of the rootmean-square deviation of the peak radiation power and the autophasing time on the number of particles are determined in the absence of the energy spread. Even a minor energy spread of 4% leads to a decrease in the maximum possible power of cooperative emission.     

Characteristics of in-out intermittency in delay-coupled FitzHugh–Nagumo oscillators

We analyze a pair of delay-coupled FitzHugh–Nagumo oscillators exhibiting in-out intermittency as a part of the generating mechanism of extreme events. We study in detail the characteristics of in-out intermittency and identify the invariant subsets involved – a saddle fixed point and a saddle periodic orbit – neither of which are chaotic as in the previously reported cases of in-out intermittency. Based on the analysis of a periodic attractor possessing in-out dynamics, we can characterize the approach to the invariant synchronization manifold and the spiralling out to the saddle periodic orbit with subsequent ejection from the manifold. Due to the striking similarities, this analysis of in-out dynamics also explains in-out intermittency     

Chimera states in bipartite networks of FitzHugh–Nagumo oscillators

Chimera states consisting of spatially coherent and incoherent domains have been observed in different topologies such as rings, spheres, and complex networks. In this paper, we investigate bipartite networks of nonlocally coupled FitzHugh–Nagumo (FHN) oscillators in which the units are allocated evenly to two layers, and FHN units interact with each other only when they are in different layers. We report the existence of chimera states in bipartite networks. Owing to the interplay between chimera states in the two layers, many types of chimera states such as in-phase chimera states, antiphase chimera states, and out-of-phase chimera states are classified. Stability diagrams of several typical chimera states in the coupling strength–coupling radius plane, which show strong multistability of chimera states, are explored.     

Critical behavior of a stochastic anisotropic Bak–Sneppen model

In this paper we present our study on the critical behavior of a stochastic anisotropic Bak–Sneppen (saBS) model, in which a parameter α is introduced to describe the interaction strength among nearest species. We estimate the threshold fitness f _c and the critical exponent τ _r by numerically integrating a master equation for the distribution of avalanche spatial sizes. Other critical exponents are then evaluated from previously known scaling relations. The numerical results are in good agreement with the counterparts yielded by the Monte Carlo simulations. Our results indicate that all saBS models with nonzero interaction strength exhibit self-organized criticality, and fall into the same universality class, by sharing the universal critical exponents.     

Traveling–stripe forcing of oblique rolls in anisotropic systems

The effects of a traveling, spatially periodic forcing are investigated in a system with axial anisotropy, where oblique stripe patterns occur at threshold in the unforced case and where the forcing wavenumber and the wavenumber of stripes are close to a 2:1 resonance. The forcing induces an interaction between the two degenerate oblique stripe orientations and for larger forcing amplitudes rectangular patterns are induced, which are dragged in phase by the forcing. With increasing forcing velocity a transition from a locked rectangular pattern to an unlocked superposition of a rectangular and oblique stripe pattern takes place. In this transition regime, especially when the ratio between the wavenumber of the forcing and that of the pattern deviates from the 2:1 ratio, surprisingly stable or long living complex patterns, such as zig–zag patterns and patterns including domain walls are found. Even more surprising is the observation, that such coherent structures propagate faster than the stripe forcing.     

Polarization-preserving anisotropic mirror on the basis of metal–dielectric nanocomposite

The model of a polarization-preserving anisotropic mirror is proposed. The mirror is a plane boundary of a metal–dielectric nanocomposite that consists of silver spheroidal nanoparticles dispersed in a transparent matrix. The dependence of reflection spectra on the shape of the nanoparticles is studied. It is shown that in one region of the spectrum, the mirror preserves the sign of polarization in the reflected light.     

Isotropization of solutions of the Einstein–Vlasov system with Bianchi V symmetry

Using the methods developed for different Bianchi class A cosmological models we treat the simplest Bianchi class B model, namely Bianchi type V. The future non-linear stability for solutions of the Einstein–Vlasov system is demonstrated and it is shown that these solutions are asymptotically stable to the Milne solution. Within the isotropic solutions of the Einstein–Vlasov system the spatially flat Friedmann solution is unstable within this class, and expanding models tend also to the Milne solution.     

Staggered anisotropy parameter modification of the anisotropic t–J model

The anisotropic t–J model (U_q(gl(2|1)) Perk–Schultz model) with staggered disposition of the anisotropy parameter along a chain is considered and the corresponding ladder type integrable model is constructed. This is a generalisation to spin-1 case of the staggered XXZ spin-1/2 model considered earlier. The corresponding Hamiltonian is calculated and, since it contains next to nearest neighbour interaction terms, can be written in a zig-zag form. The algebraic Bethe ansatz technique is applied and the eigenstates, along with eigenvalues of the transfer matrix of the model are found.     

The role of conformal symmetry in the Jackiw–Pi model

The Jackiw–Pi model in 2+1$2+1$ dimensions is a non-relativistic conformal field theory of charged particles with point-like self-interaction. For specific values of the interaction strengths the classical theory possesses vortex and multi-vortex solutions, which are all degenerate in energy. We compute the full set of first-order perturbative quantum corrections. Only the coupling constant g²$g^2$ requires renormalization; the fields and electric charge e are not renormalized. It is shown that in general the conformal symmetries are broken by an anomalous contribution to the conservation law, proportional to the β-function. However, the β  -function vanishes upon restricting the coupling constants to values g²=±e²$g^2=\pm e^2$, which includes the case in which vortex solutions exist. Therefore the existence of vortices also guarantees the preservation of the conformal symmetries.     

The symmetry of donor–bound electron wavefunctions in quantum wells

In order to investigate the symmetry (i.e. sphericity) of donor–bound electron wavefunctions in quantum wells, we have invoked a two-parameter trial wavefunction. One parameter is the Bohr radius λ, whilst the other is the eccentricity parameter ζ. The latter incorporates the effect of the quantum well (QW) on the carrier motion in the growth (i.e. the z) direction. Working within the envelope function approximation it is shown that the donor wavefunction has the form of a prolate spheroid. However, calculations of the ratio λ/ζ shows that it is the value of λ which determines the essential symmetry of the wavefunction.     

Decompositions of the Kadomtsev–Petviashvili equation and their symmetry reductions

Starting with a decomposition conjecture, we carefully explain the basic decompositions for the Kadomtsev–Petviashvili(KP) equation as well as the necessary calculation procedures, and it is shown that the KP equation allows the Burgers–STO(BSTO) decomposition, two types of reducible coupled BSTO decompositions and the BSTO–KdV decomposition. Furthermore, we concentrate ourselves on pointing out the main idea and result of B?cklund transformation of the KP equation based on a special superpositi...     

Is space-time symmetry a suitable generalization of parity-time symmetry?

We discuss space-time symmetric Hamiltonian operators of the form H=H₀+igH^′$H=H_0+ig{H}^{\prime }$, where H₀$H_0$ is Hermitian and g$g$ real. H₀$H_0$ is invariant under the unitary operations of a point group G$G$ while H^′$H^{\prime }$ is invariant under transformation by elements of a subgroup G^′$G^{\prime }$ of G$G$. If G$G$ exhibits irreducible representations of dimension greater than unity, then it is possible that H$H$ has complex eigenvalues for sufficiently small nonzero values of g$g$. In the particular case that H$H$ is parity-time symmetric then it appears to exhibit real eigenvalues for all 0<g<g_c$0<g<g_c$, where g_c$g_c$ is the exceptional point closest to the origin. Point-group symmetry and perturbation theory enable one to predict whether H$H$ may exhibit real or complex eigenvalues for g>0$g>0$. We illustrate the main theoretical results and conclusions of this paper by means of two- and three-dimensional Hamiltonians exhibiting a variety of different point-group symmetries.     

Coercivity enhancement of anisotropic Dy-free Nd–Fe–B powders by conventional HDDR process

Coercivity enhancement of Dy-free Nd–Fe–Co–B–Ga–Zr powders was studied using the conventional hydrogenation–decomposition–desorption–recombination (HDDR) process. It was found that the addition of Al together with the proper Nd content and the slow hydrogen desorption of the HDDR treatment can induce high coercivity in the powder. For example, the 14.0 at% Nd–2.0 at% Al powder exhibits H_cJ of 1560 kA/m, B_r of 1.22 T, and (BH)_max of 257 kJ/m³. The high coercivity inducement of the powder is thought to be attributed to the formation of Nd-rich phase, which continuously surrounds fine Nd₂Fe₁₄B grains.     

Fabrication of particular structures of hexagonal boron nitride and boron–carbon–nitrogen layers by anisotropic etching

Anisotropic etching of hexagonal boron nitride (h-BN) and boron–carbon–nitrogen (BCN) basal plane can be an exciting platform to develop well-defined structures with interesting properties. Here, we developed an etching process of atomically thin h-BN and BCN layers to fabricate nanoribbons (NRs) and other distinct structures by annealing in H₂ and Ar gas mixture. BCN and h-BN films are grown on Cu foil by chemical vapor deposition (CVD) using solid camphor and ammonia borane as carbon, nitrogen and boron source, respectively. Formation of micron size well-defined etched holes and NRs are obtained in both h-BN and BCN layers by the post growth annealing process. The etching process of h-BN and BCN basal plane to fabricate NRs and other structures with pronounced edges can open up new possibilities in 2D hybrid materials.     

Fierz bilinear formulation of the Maxwell–Dirac equations and symmetry reductions

We study the Maxwell–Dirac equations in a manifestly gauge invariant presentation using only the spinor bilinear scalar and pseudoscalar densities, and the vector and pseudovector currents, together with their quadratic Fierz relations. The internally produced vector potential is expressed via algebraic manipulation of the Dirac equation, as a rational function of the Fierz bilinears and first derivatives (valid on the support of the scalar density), which allows a gauge invariant vector potential to be defined. This leads to a Fierz bilinear formulation of the Maxwell tensor and of the Maxwell–Dirac equations, without any reference to gauge dependent quantities. We show how demanding invariance of tensor fields under the action of a fixed (but arbitrary) Lie subgroup of the Poincaré group leads to symmetry reduced equations. The procedure is illustrated, and the reduced equations worked out explicitly for standard spherical and cylindrical cases, which are coupled third order nonlinear PDEs. Spherical symmetry necessitates the existence of magnetic monopoles, which do not affect the coupled Maxwell–Dirac system due to magnetic terms cancelling. In this paper we do not take up numerical computations. As a demonstration of the power of our approach, we also work out the symmetry reduced equations for two distinct classes of dimension 4 one-parameter families of Poincaré subgroups, one splitting and one non-splitting. The splitting class yields no solutions, whereas for the non-splitting class we find a family of formal exact solutions in closed form.     

Bound states of two-dimensional relativistic harmonic oscillators

We give the exact normalized bound state wavefunctions and energy expressions of the Klein-Gordon and Dirac equations with equal scalar and vector harmonic oscillator potentials in the two-dimensional space.