Polynomial integrability of the Hamiltonian systems with homogeneous potential of degree − 3

In this paper, we study the polynomial integrability of natural Hamiltonian systems with two degrees of freedom having a homogeneous potential of degree k given either by a polynomial, or by an inverse of a polynomial. For k=−2,−1,…,3,4, their polynomial integrability has been characterized. Here, we have two main results. First, we characterize the polynomial integrability of those Hamiltonian systems with homogeneous potential of degree −3. Second, we extend a relation between the nontrivial eigenvalues of the Hessian of the potential calculated at a Darboux point to a family of Hamiltonian systems with potentials given by an inverse of a homogeneous polynomial. This relation was known for such Hamiltonian systems with homogeneous polynomial potentials. Finally, we present three open problems related with the polynomial integrability of Hamiltonian systems with a rational potential.     

Ion-beam analysis of the structure and composition of nanocomposite nc-TiC/a-C:H coatings

The structure and composition of nanocomposite nc-TiC/a-C:H thin films prepared by closed-field unbalanced reactive magnetron sputtering in an argon-acetylene atmosphere have been investigated. The concentrations of carbon and heavier elements have been obtained by Rutherford backscattering and nuclear backscattering. The hydrogen concentration in the films has been determined by elastic recoil detection analysis. Based on the data obtained, a scheme has been proposed to evaluate the C:H matrix mass density and the sp ³ and sp ² fractions in the matrix.     

Higher Spin Dirac Operators Between Spaces of Simplicial Monogenics in Two Vector Variables

The higher spin Dirac operator \(\mathcal{Q}_{k,l}\) acting on functions taking values in an irreducible representation space for \(\mathfrak{so}(m)\) with highest weight \((k+\frac{1}{2},l+\frac{1}{2},\frac{1}{2},\ldots,\frac{1}{2})\), with k, l?∈?\(\mathbb{N}\) and \(k\geqslant l\), is constructed. The structure of the kernel space containing homogeneous polynomial solutions is then also studied.     

Quantum readout and fast initialization of nuclear spin qubits with electric currents

Nuclear spin qubits have the longest coherence times in the solid state, but their quantum readout and initialization is a great challenge. We present a theory for the interaction of an electric current with the nuclear spins of donor impurities in semiconductors. The theory yields a sensitivity criterion for quantum detection of nuclear spin states using electrically detected magnetic resonance, as well as an all-electrical method for fast nuclear spin qubit initialization.     

Synthesis of carbon black/polystyrene conductive nanocomposite. Pickering emulsion effect characterized by TEM

In this study, carbon black/polystyrene electrically conductive composites were obtained by suspension polymerization technique. The composite was characterized using transmission electron microscopy, which indicated two outstanding features concerning to the carbon black; first, that the carbon particles were adsorbed onto the surface of the polystyrene particles, similarly as in the Pickering emulsion phenomenon and second, that the primary aggregate structure of the carbon black was significantly affected by the dispersion process. On the other hand, the composite resistivity was in the order of 200 Ωcm, which was attributed to the direct contact of primary carbon black particles (percolation) and not to the tunneling effect. The obtained composite was evaluated as the electrically conductive element in SBR matrix.     

Degenerate band edges in optical fiber with multiple grating: efficient coupling to slow light

Degenerate band edges (DBEs) of a photonic bandgap have the form (ω-ω(D)) ∝k(2m) for integers m>1, with ω(D) the frequency at the band edge. We show theoretically that DBEs lead to efficient coupling into slow-light modes without a transition region, and that the field strength in the slow mode can far exceed that in the incoming medium. A method is proposed to create a DBE of arbitrary order m by coupling m optical modes with multiple superimposed gratings. The enhanced coupling near a DBE occurs because of the presence of one or more evanescent modes, which are absent at conventional quadratic band edges. We furthermore show that the coupling can be increased or suppressed by varying the number of excited evanescent waves.