Peculiarities in the Formation of X-Ray Fluxes by Waveguide–Resonators of Different Construction

The phenomenon of total external reflection (TER) of quasi-monochromatic X-ray radiation fluxes on a material interface and the effect of waveguide–resonator propagation of these fluxes in nanosize extended slit clearance, as well as a device operating on the basis of this effect—a planar X-ray waveguide–resonator—are briefly described. Experimental data on the formation of an X-ray flux by a composite X-ray waveguide–resonator are presented, and a model describing the decrease in the angular divergence of the formed flux without a decrease in the integral intensity is proposed. The model is based on the conception of partial angular tunneling of the radiation flux in the gap between two consequently mounted and mutually adjusted waveguide–resonators; the tunneling is implemented due to the interaction between interference fields of standing X-ray waves excited by the radiation transported by the slit clearance of these waveguide–resonators.     

Spin Ensembles Coupled to Superconducting Resonators：A Scalable Architecture for Solid-State Quantum Computing

A design is proposed for scalable solid-state quantum computing, which is based on collectively enhanced magnetic coupling between nitrogen-vacancy center ensembles and superconducting transmission line resonators interconnected by current-biased Josephson junction superconducting phase qubit. In this hybrid system, we realize distant multi-qubit controlled phase gate operations and generate distant multi-qubit entangled W-like states, being indispensable resource to quantum computation. Our proposed architecture consists of solid-state spin ensembles and circuit QED, and could achieve quantum computing in a solid-state environment with high-fidelity and scalable way. The experimental feasibility is discussed, and the implementation efficiency is demonstrated numerically.     

Analysis of Frequency Spectrum of Laser-Induced Vibration of Microbeam Resonators

The vibration phenomenon during pulsed laser heating of micro-beams is investigated. The beam is made of silicon and is heated by a laser pulse with a non-Gaussian temporal profile and with an ultrashort pulse duration of 2ps, which incites vibration due to the thermoelastic damping effect. This coupled thermoelastic problem is solved using an analytical-numerical technique based on the Laplace transformation. The damping ratio and resonant frequency shift ratio of beams due to the air damping effect and the thermoelastic damping effect are also examined and discussed.     

Behaviour of Hexagon Split Ring Resonators and Left-Handed Metamaterials

We used a rectangular waveguide system to measure the X-band (8-12 GHz) transmission of hexagon split ring resonators (SRRs) alone and the left-handed metamaterials (LHMs) consisting of hexagon SRR array and wire array. The experimental results show that for an individual SRR, the resonance frequency increases with the azimuthal gap, but decreases with the radial gap. For two identical SRRs, the resonance peak has a shift because of the electromagnetic interaction, and the resonance frequency and the strength decrease with the separation distance. Finally, we demonstrate the left-handed effect of the LHMs.     

Coupled longitudinal–transverse dynamics of an axially accelerating beam

The coupled longitudinal–transverse nonlinear dynamics of an axially accelerating beam is numerically investigated; this problem is classified as a parametrically excited gyroscopic system. The axial speed is assumed to be comprised of a constant mean value along with harmonic fluctuations. Hamilton’s principle is employed to derive the equations of motion of the system which are in the form of two coupled partial differential equations. The equations are discretized using the Galerkin method, which yields a set of coupled second-order nonlinear ordinary differential equations with time-dependent coefficients. The sub-critical dynamics of the system is examined via the pseudo-arclength continuation technique, while the global dynamics is investigated using direct time integration. The mean axial speed and the amplitude of the speed variations are varied so as to construct the bifurcation diagrams of Poincaré maps. The vibration specifications of the system are investigated more detailed via plotting time histories, phase-plane portraits, and fast Fourier transforms (FFTs).     

Fomenko–Mischenko Theory, Hessenberg Varieties, and Polarizations

The symmetric algebra ${S(\mathfrak{g})}$ over a Lie algebra ${\mathfrak{g}}$ has the structure of a Poisson algebra. Assume ${\mathfrak{g}}$ is complex semisimple. Then results of Fomenko–Mischenko (translation of invariants) and Tarasov construct a polynomial subalgebra ${{\mathcal {H}} = {\mathbb C}[q_1,\ldots,q_b]}$ of ${S(\mathfrak{g})}$ which is maximally Poisson commutative. Here b is the dimension of a Borel subalgebra of ${\mathfrak{g}}$ . Let G be the adjoint group of ${\mathfrak{g}}$ and let ? = rank ${\mathfrak{g}}$ . Using the Killing form, identify ${\mathfrak{g}}$ with its dual so that any G-orbit O in ${\mathfrak{g}}$ has the structure (KKS) of a symplectic manifold and ${S(\mathfrak{g})}$ can be identified with the affine algebra of ${\mathfrak{g}}$ . An element ${x\in \mathfrak{g}}$ will be called strongly regular if ${\{({\rm d}q_i)_x\},\,i=1,\ldots,b}$ , are linearly independent. Then the set ${\mathfrak{g}^{\rm{sreg}}}$ of all strongly regular elements is Zariski open and dense in ${\mathfrak{g}}$ and also ${\mathfrak{g}^{\rm{sreg}}\subset \mathfrak{g}^{\rm{ reg}}}$ where ${\mathfrak{g}^{\rm{reg}}}$ is the set of all regular elements in ${\mathfrak{g}}$ . A Hessenberg variety is the b-dimensional affine plane in ${\mathfrak{g}}$ , obtained by translating a Borel subalgebra by a suitable principal nilpotent element. Such a variety was introduced in Kostant (Am J Math 85:327–404, 1963). Defining Hess to be a particular Hessenberg variety, Tarasov has shown that ${{\rm{Hess}}\subset \mathfrak{g}^{\rm{sreg}}}$ . Let R be the set of all regular G-orbits in ${\mathfrak{g}}$ . Thus if ${O\in R}$ , then O is a symplectic manifold of dimension 2n where n = b ? ?. For any ${O\in R}$ let ${O^{\rm{sreg}} = \mathfrak{g}^{\rm{sreg}} \cap O}$ . One shows that O ^sreg is Zariski open and dense in O so that O ^sreg is again a symplectic manifold of dimension 2n. For any ${O\in R}$ let ${{\rm{Hess}}(O) = {\rm{Hess}}\cap O}$ . One proves that Hess(O) is a Lagrangian submanifold of O ^sreg and that $${\rm{Hess}} = \sqcup_{O\in R}{\rm{Hess}}(O).$$ The main result of this paper is to show that there exists simultaneously over all ${O\in R}$ , an explicit polarization (i.e., a “fibration” by Lagrangian submanifolds) of O ^sreg which makes O ^sreg simulate, in some sense, the cotangent bundle of Hess(O).     

Spectral Analysis of Weakly Coupled Stochastic Lattice Ginzburg–Landau Models

We consider the relaxation to equilibrium of solutions , t>0, , of stochastic dynamical Langevin equations with white noise and weakly coupled Ginzburg–Landau interactions. Using a Feynman–Kac formula, which relates stochastic expectations to correlation functions of a spatially non-local imaginary time quantum field theory, we obtain results on the joint spectrum of H, , where H is the self-adjoint, positive, generator of the semi-group associated with the dynamics, and P ^j , j= 1, …, d are the self-adjoint generators of the group of lattice spatial translations. We show that the low-lying energy-momentum spectrum consists of an isolated one-particle dispersion curve and, for the mass spectrum (energy-momentum at zero-momentum), besides this isolated one-particle mass, we show, using a Bethe–Salpeter equation, the existence of an isolated two-particle bound state if the coefficient of the quartic term in the polynomial of the Ginzburg–Landau interaction is negative and d= 1, 2; otherwise, there is no two-particle bound state. Asymptotic values for the masses are obtained. Received: 27 September 2000 / Accepted: 16 January 2001     

Features of the Coupled Nuclear–Electron Spin Precession in the Bose–Einstein Condensate of Magnons

JETP Letters - The experimental detection of the Bose-Einstein condensate of magnons in coupled nuclear-electron spin precession in antiferromagnets brings the prospect of its use for magnonics and...     

Soliton Solutions of Coupled KdV System from Hirota＇s Bilinear Direct Method

With Hirota＇s bilinear direct method, we study the special coupled KdV system to obtain its new soliton solutions. Then we further discuss soliton evolution, corresponding structures, and interesting interactive phenomena in detail with plot. As a result, we find that after the interaction, the solitons make elastic collision and there are no exchanges of their physical quantities including energy, velocity and shape except the phase shift.     

Dynamics of Coupled Quantum-Classical Oscillators

The dynamics of systems consisting of coupled quantum-classical oscillators is numerically investigated. It is shown that, under certain conditions, the quantum oscillator exhibits chaos. When the mass of the classical oscillator increases, the chaos will be suppressed; if the energy of the system and/or the coupling strength between the two oscillators increases, chaotic behaviour of the system appears. This result will be helpful to understand the probability of the emergence of quantum chaos and may be applied to explain the spectra of complex atoms qualitatively.     

Inverse Scattering Transform of the Coupled Sasa–Satsuma Equation by Riemann–Hilbert Approach

The inverse scattering transform of a coupled Sasa–Satsuma equation is studied via Riemann–Hilbert approach. Firstly, the spectral analysis is performed for the coupled Sasa–Satsuma equation, from which a Riemann–Hilbert problem is formulated. Then the Riemann–Hilbert problem corresponding to the reflection-less case is solved.As applications, multi-soliton solutions are obtained for the coupled Sasa–Satsuma equation. Moreover, some figures are given to describe the soliton behaviors, including breather types, single-hump solitons, double-hump solitons, and two-bell solitons.     

Energy Band and Josephson Dynamics of Spin-Orbit Coupled Bose–Einstein Condensates

We theoretically investigate the energy band structure and Josephson dynamics of a spin-orbit coupled Bose–Einstein condensate in a double-well potential. We study the energy band structure and the corresponding tunneling dynamics of the system by properly adjusting the SO coupling, Raman coupling, Zeeman field and atomic interactions.The coupled effects of SO coupling, Raman coupling, Zeeman field and atomic interactions lead to the appearance of complex energy band structure including the loop structure. Particularly, the emergence of the loop structure in energy band also depends on SO coupling, Raman coupling, Zeeman field and atomic interactions. Correspondingly,the Josephson dynamics of the system are strongly related to the energy band structure. Especially, the emergence of the loop structure results in complex tunneling dynamics, including suppression-revival transitions and self-trapping of atoms transfer between two spin states and two wells. This engineering provides a possible means for studying energy level and corresponding dynamics of two-species SO coupled BECs.     

Coupled flexural–longitudinal vibration of delaminated composite beams with local stability analysis

A novel analytical model is developed to solve the problem of free vibration of delaminated composite beams. The beam with a single delamination was modelled by six equivalent single layers by establishing the kinematic continuity in the undelaminated portion of the system. In the delaminated region the layers were captured by the traditional theories. First, Timoshenko beam theory is applied to solve the problem, then by reducing the model, the corresponding Euler–Bernoulli solution is presented. Both the free and constrained models were considered. The most important aspect of the present analysis is that the beams of the delaminated region are subjected to normal forces, as well. That is the essential reason for leading to a coupled flexural–longitudinal vibration problem. It is also concluded that delamination buckling can take place if the normal force is compressive in one of the half-periods of the vibration and reaches a critical value. The problem was also investigated experimentally by modal hammer and sweep excitation tests on beams made of E-glass/polyester in order to measure the natural frequencies and mode shapes. The comparison of the analytical and experimental results indicates the importance of the independent rotations provided by Timoshenko beams over the simple beam theory. The delamination buckling of the beams was captured based on the static stability analysis in the first step. Further results show that the problem is more complex than it was thought before, e.g., some nonlinearity, time-dependent stiffness as well as parametric excitation aspects were discovered during the present analysis.     

Review of Spin–Orbit Coupled Semimetal SrIrO3 in Thin Film Form

Spin–orbit coupling, locking the momentum of an electron to its spin, has been shown essential for giving rise to many novel physical behaviors. SrIrO₃ is a typical metallic member of the strong spin–orbit coupling iridate family. Its orthorhombic phase has been confirmed as a paramagnetic semimetal resulted from the interplay among spin–orbit coupling, electron correlation, and crystal field, and was theoretically predicted to host versatile topological phases. This article reviews the current knowledge on the preparation and the tunable properties of orthorhombic SrIrO₃ films. Experiments have demonstrated that orthorhombic SrIrO₃ can be successfully synthesized as films under substrate lattice constraint without high pressure, and the films frequently display metal-insulator transition due to disorder and weak-antilocalization owing to spin-orbit coupling. The properties of orthorhombic SrIrO₃ film are sensitive to the rotation and tilting of the IrO₆ octahedral, and consequently can be significantly tuned through strain engineering. Simultaneously, thickness-dependent size effect is also remarkable in SrIrO₃ films. The accumulated research on SrIrO₃ films suggests an urgent demand for research on superlattices constructed with orthorhombic SrIrO₃, to better understand the mechanism of the electron structure evolution, and thus the relevant magnetic states and topological phases in orthorhombic SrIrO₃ and its family.     

Invariant Solutions of the Yang–Mills Field Equations Coupled to a Scalar Doublet

The Yang–Mills system of field equations which includes coupling to an SU(2) scalar matter doublet is developed. It is shown that an SU(2) current for a scalar matter doublet can be developed. The basic structure which fits the Yang–Mills system is somewhat different from the case of the scalar triplet. Using this form for the scalar current, it is possible to write down the Yang–Mills system which couples to the scalar matter doublet. It is shown that several sets of solutions to this system of equations can be obtained.     

Magnetic Circular Dichroism of Cyclic π-Electron Systems

Abstract

While the simple PPP model accounts for the absolute signs of low-energy π? transitions in cyclic π-electron chromophores (numerous new examples of application to heterocycles are given), its greatest contribution lies in the formulation of simple general rules. The previously known mirror-image pairing theorem for charged alternant hydrocarbons and the soft-hard rule for substituent and heteroatom effects on cyclic π-systems are now complemented by a ΔHOMO-ΔLUMO rule which permits prediction of the absolute sign of the lowest energy B term in cyclic π-systems which are formally related to an annulene containing 4N+2 electrons.