Symmetry breaking in plasmonic waveguides with metal nonlinearities

We studied nonlinear effects in plasmonic metal film waveguides and couplers stimulated by third-order optical response due to ponderomotive metal nonlinearities. We analyzed the structure and dispersion of nonlinear plasmonic guided modes and predicted the bifurcations and symmetry breaking of nonlinear modes for the critical powers, depending on the structure dimensions.     

A Hierarchical Model of Quantum Anharmonic Oscillators: Critical Point Convergence

We study the two-dimensional gauge theory of the symmetric group S_n describing the statistics of branched n-coverings of Riemann surfaces. We consider the theory defined on the disc and on the sphere in the large-n limit. A non trivial phase structure emerges, with various phases corresponding to different connectivity properties of the covering surface. We show that any gauge theory on a two-dimensional surface of genus zero is equivalent to a random walk on the gauge group manifold: in the case of S_n, one of the phase transitions we find can be interpreted as a cutoff phenomenon in the corresponding random walk. A connection with the theory of phase transitions in random graphs is also pointed out. Finally we discuss how our results may be related to the known phase transitions in Yang-Mills theory. We discover that a cutoff transition occurs also in two dimensional Yang-Mills theory on a sphere, in a large N limit where the coupling constant is scaled with N with an extra logN compared to the standard t Hooft scaling.     

On a Theorem of Høegh-Krohn

A theorem proved by R. Høegh-Krohn in Comm. Math. Phys. 38(1974), 195–224, which yields a possibility to define states of systems of quantum particles by their values on the products , where \mathfraka _t , t are time automorphisms and F _j are multiplication operators, is generalized and extended. In particular, it is shown that the algebras generated by such products with F _j taken from the families of multiplication operators satisfying certain conditions are dense in the algebras of observables in the -weak topology, in which normal states are continuous. This result was obtained for the systems with two types of kinetic energy: the usual one expressed by means of the Laplacian; the relativistic kinetic energy defined by a pseudo-differential operator.     

Predictions and experimental studies of the tail pipe noise of an automotive muffler using a one dimensional CFD model

The tail pipe noise from a commercial automotive muffler was studied experimentally and numerically under the condition of wide open throttle acceleration in the present research. The engine was accelerated from 1000 to 6000 rpm in 30 s at the warm up condition. The transient acoustic characteristics of its exhaust muffler were predicted using one dimensional computational fluid dynamics. To validate the results of the simulation, the transient acoustic characteristics of the exhaust muffler were measured in an anechoic chamber according to the Japanese Standard (JIS D 1616). It was found that the results of simulation are in good agreement with experimental results at the 2nd order of the engine rotational frequency. At the high order of engine speed, differences between the computational and experimental results exist in the high revolution range (from 5000 to 6000 rpm at the 4th order, and from 4200 to 6000 rpm at the 6th order). According to these results, the differences were caused by the flow noise which was not considered in the simulation. Based on the theory of one dimensional CFD model, a simplified model which can provide an acceptable accuracy and save more than 90% of execution time compared with the standard model was proposed for the optimization design to meet the demand of time to market.     

Four modes competition and chaos in a shell

Steady-state chaotic vibrations of a shallow shell as a system with a nonsymmetrical restoring force and one equilibrium state are considered. Mode interaction and its effect on a chaotic behavior of the shell is studied. The terms "natural" and "imposed" chaos are introduced for the response of resonant and nonresonant modes. It is shown that such a qualitative difference is important for better understanding of chaos in systems with distributed parameters, and may be very useful for numerical investigations. Some qualitative comparisons with previous papers on chaos in distributed mechanical systems are also made. (c) 1994 American Institute of Physics.     

U-statistics in danach spaces

U-statistics in Banach spaces are considered and thoroughly investigated. The martingale structure, estimates of moments, the law of large numbers, the central limit theorem, the invariance principle, estimates of the rate of convergence, and large deviations are established     

Number of revolutions of a particle around a black hole: Is it infinite or finite?

We consider a particle falling into a rotating black hole. Such a particle makes an infinite number of revolutions n from the viewpoint of a remote observer who uses the Boyer–Lindquist type of coordinates. We examine the behavior of n when it is measured with respect to a local reference frame that also rotates due to dragging effect of spacetime. The crucial point consists here in the observation that for a nonextremal black hole, the leading contributions to n from a particle itself and the reference frame have the same form being in fact universal, so that divergences mutually cancel. As a result, the relative number of revolutions turns out to be finite. For the extremal black hole this is not so, n can be infinite. Different choices of the local reference frame are considered, the results turn out to be the same qualitatively. For illustration, we discuss two explicit examples—rotation in the flat spacetime and in the Kerr metric.     

Translational cooling of doped nanocrystals by Raman pulses: Towards macroscopic quantum state

One of the most interesting problems of modern physics is the realization of nanoparticles in macroscopic quantum states, in which they behave as a quantum objects. These states can only be implemented at ultra-low translational temperatures that have not been achieved so far. Here we develop a novel method for optical cooling of CaF₂:Yb³⁺ nanocrystals, which is based on the coherent population transfer induced in the impurity ions by ultraviolet Raman pulses. A doped nanocrystal localized in a radio-frequency trap is cooled due to the photon recoil from the pulses of varied intensity. The proposed method allows to obtain nanocrystals with translational temperatures of the order of 10^?9 K, which indicates that the nanocrystal approaches a macroscopic quantum state.