Noncommutative tori and universal sets of non-binary quantum gates

A problem of universality in simulation of evolution of quantum system and in theory of quantum computations is related with the possibility of expression or approximation of arbitrary unitary transformation by composition of specific unitary transformations (quantum gates) from given set. In an earlier paper (quant-ph/0010071) application of Clifford algebras to constructions of universal sets of binary quantum gates $U_k \in U(2^n)$ was shown. For application of a similar approach to non-binary quantum gates $U_k \in U(l^n)$ in present work is used rational noncommutative torus ${\Bbb T}^{2n}_{1/l}$. A set of universal non-binary two-gates is presented here as one example.Comment: 5 pages, REVTeX3.1, v2: spelling and misprints, 4 new ref

Mapping the optical properties of slab-type two-dimensional photonic crystal waveguides

We report on systematic experimental mapping of the transmission properties of two-dimensional silicon-on-insulator photonic crystal waveguides for a broad range of hole radii, slab thicknesses and waveguide lengths for both TE and TM polarizations. Detailed analysis of numerous spectral features allows a direct comparison of experimental data with 3D plane wave and finite-difference time-domain calculations. We find, counter-intuitively, that the bandwidth for low-loss propagation completely vanishes for structural parameters where the photonic band gap is maximized. Our results demonstrate that, in order to maximize the bandwidth of low-loss waveguiding, the hole radius must be significantly reduced. While the photonic band gap considerably narrows, the bandwidth of low-loss propagation in PhC waveguides is increased up to 125nm with losses as low as 8$\pm$2dB/cm.Comment: 10 pages, 8 figure

Interaction between superconducting vortices and Bloch wall in ferrite garnet film

Interaction between a Bloch wall in a ferrite-garnet film and a vortex in a superconductor is analyzed in the London approximation. Equilibrium distribution of vortices formed around the Bloch wall is calculated. The results agree quantitatively with magneto-optical experiment where an in-plane magnetized ferrite-garnet film placed on top of NbSe2 superconductor allows observation of individual vortices. In particular, our model can reproduce a counter-intuitive attraction observed between vortices and a Bloch wall having the opposite polarity. It is explained by magnetic charges appearing due to discontinuity of the in-plane magnetization across the wall.Comment: 4 pages, 5 figure

The Mean-Field Limit for a Regularized Vlasov-Maxwell Dynamics

The present work establishes the mean-field limit of a N-particle system towards a regularized variant of the relativistic Vlasov-Maxwell system, following the work of Braun-Hepp [Comm. in Math. Phys. 56 (1977), 101-113] and Dobrushin [Func. Anal. Appl. 13 (1979), 115-123] for the Vlasov-Poisson system. The main ingredients in the analysis of this system are (a) a kinetic formulation of the Maxwell equations in terms of a distribution of electromagnetic potential in the momentum variable, (b) a regularization procedure for which an analogue of the total energy - i.e. the kinetic energy of the particles plus the energy of the electromagnetic field - is conserved and (c) an analogue of Dobrushin's stability estimate for the Monge-Kantorovich-Rubinstein distance between two solutions of the regularized Vlasov-Poisson dynamics adapted to retarded potentials.Comment: 34 page

Torsional-flexural buckling of unevenly battened columns under eccentrical compressive loading

In this paper, an analytical model is developed to determine the torsional-flexural buckling load of a channel column braced by unevenly distributed batten plates. Solutions of the critical-buckling loads were derived for three boundary cases using the energy method in which the rotating angle between the adjacent battens was presented in the form of a piecewise cubic Hermite interpolation (PCHI) for unequally spaced battens. The validity of the PCHI method was numerically verified by the classic analytical approach for evenly battened columns and a finite-element analysis for unevenly battened ones, respectively. Parameter studies were then performed to examine the effects of loading eccentricities on the torsional-flexural buckling capacity of both evenly and unevenly battened columns. Design parameters taken into account were the ratios of pure torsional buckling load to pure flexural–buckling load, the number and position of battens, and the ratio of the relative extent of the eccentricity. Numerical results were summarized into a series of relative curves indicating the combination of the buckling load and corresponding moments for various buckling ratios.National Natural Science Foundation of China (NSFC) under grant number (No.) 51175442 and Sichuan International Cooperation Research Project under grant No. 2014HH002

Finger patterns produced by thermomagnetic instability in superconductors

A linear analysis of thermal diffusion and Maxwell equations is applied to study the thermomagnetic instability in a type-II superconducting slab. It is shown that the instability can lead to formation of spatially nonuniform distributions of magnetic field and temperature. The distributions acquire a finger structure with fingers perpendicular to the screening current direction. We derive the criterion for the instability, and estimate its build-up time and characteristic finger width. The fingering instability emerges when the background electric field is larger than a threshold field, $E>E_c$, and the applied magnetic field exceeds a value $H_fing \propto 1/\sqrt{E}$. Numerical simulations support the analytical results, and allow to follow the development of the fingering instability beyond the linear regime. The fingering instability may be responsible for the nucleation of dendritic flux patterns observed in superconducting films using magneto-optical imaging.Comment: 8 pages, 6 figures, accepted to Phys. Rev. B; (new version: minor changes

Negaton and Positon solutions of the soliton equation with self-consistent sources

The KdV equation with self-consistent sources (KdVES) is used as a model to illustrate the method. A generalized binary Darboux transformation (GBDT) with an arbitrary time-dependent function for the KdVES as well as the formula for $N$-times repeated GBDT are presented. This GBDT provides non-auto-B\"{a}cklund transformation between two KdV equations with different degrees of sources and enable us to construct more general solutions with $N$ arbitrary $t$-dependent functions. By taking the special $t$-function, we obtain multisoliton, multipositon, multinegaton, multisoliton-positon, multinegaton-positon and multisoliton-negaton solutions of KdVES. Some properties of these solutions are discussed.Comment: 13 pages, Latex, no figues, to be published in J. Phys. A: Math. Ge

Effect of iron doping on the properties of nanopowders and coatings on the basis of Al2O3 produced by pulsed electron beam evaporation

Multiphase nanopowders (NPs) and amorphous/amorphous-nanocrystalline coatings (A-NC) have been prepared by the evaporation of ceramic targets of Al2O3-Fe2O3 (0.1, 3, 5 Fe2O3 mass %) by a pulsed electron beam in vacuum. The specific surface area of NP Al2O3-Fe2O3 reached 277 m2/g. The α and γ phases Al2O3 and other nonidentified phases have been found in the composition of NP Al2O3-Fe2O3. All coatings contained an insignificant fraction of the crystalline γ phase. No secondary phases on the basis of iron have been revealed. According to transmission electron microscopy, the fine fraction of NP Al2O3-Fe2O3 consists of amorphous nanoparticles of an irregular and quasispherical shape no more than 10 nm in size which form agglomerates reaching 1.5 μm. A large fraction of NPs consists of crystal spherical nanoparticles with preferential sizes of about 10-20 nm. All NP Al2O3-Fe2O3 showed ferromagnetic behavior at room temperature. The maximum magnetic response has been established in NPs with a minimum iron content (1.1 mass %). The pulsed cathode luminescence spectra of coatings and NP Al2O3-Fe2O3 have been presented by a wide band in the wavelength range of 300-900 nm regardless of their phase composition. Phase transformations into NP AL2O3-1.1% Fe and coatings from undoped Al2O3 heated to 1400°C occur according to the following scheme: amorphous phase → γ → δ → θ → α, regardless of their initial phase composition. The threshold of thermal stability of the Γ phase in NPs and the coating of undoped Al2O3 does not exceed 830°C. For the first time, the increased thermo and optically stimulated luminescent response comparable with the response of the leading TLD-500K thermoluminescent dosimeter has been reached in A-NC coatings of undoped Al2O3. © 2013 Pleiades Publishing, Ltd

Effectiveness of BaTiO3 dielectric patches on YBa2Cu3O7 thin films for MEM switches

A micro-electro-mechanical (MEM) switch built on a superconducting microstrip filter will be utilized to investigate BaTiO3 dielectric patches for functional switching points of contact. Actuation voltage resulting from the MEM switch provokes static friction between the bridge membrane and BaTiO3 insulation layer. The dielectric patch crystal structure and roughness affect the ability of repetitively switching cycles and lifetime. A series of experiments have been performed using different deposition methods and RF magnetron sputtering was found to be the best deposition process for the BaTiO3 layer. The effect examination of surface morphology will be presented using characterization techniques as x-ray diffraction, SEM and AFM for an optimum switching device. The thin film is made of YBa2Cu3O7 deposited on LaAlO3 substrate by pulsed laser deposition. For this work, the dielectric material sputtering pressure is set at 9.5x10-6 Torr. The argon gas is released through a mass-flow controller to purge the system prior to deposition. RF power is 85 W at a distance of 9 cm. The behavior of Au membranes built on ultimate BaTiO3 patches will be shown as part of the results. These novel surface patterns will in turn be used in modelling other RF MEM switch devices such as distributed-satellite communication system operating at cryogenic temperatures