Enstrophy Dynamics of Stochastically Forced Large-Scale Geophysical Flows

Enstrophy is an averaged measure of fluid vorticity. This quantity is particularly important in {\em rotating} geophysical flows. We investigate the dynamical evolution of enstrophy for large-scale quasi-geostrophic flows under random wind forcing. We obtain upper bounds on the enstrophy, as well as results establishing its H\"older continuity and describing the small-time asymptotics

Trapped ion quantum computation with transverse phonon modes

We propose a scheme to implement quantum gates on any pair of trapped ions immersed in a large linear crystal, using interaction mediated by the transverse phonon modes. Compared with the conventional approaches based on the longitudinal phonon modes, this scheme is much less sensitive to ion heating and thermal motion outside of the Lamb-Dicke limit thanks to the stronger confinement in the transverse direction. The cost for such a gain is only a moderate increase of the laser power to achieve the same gate speed. We also show how to realize arbitrary-speed quantum gates with transverse phonon modes based on simple shaping of the laser pulses.Comment: 5 page

Generalized Stable Multivariate Distribution and Anisotropic Dilations

After having closely re-examined the notion of a L\'evy's stable vector, it is shown that the notion of a stable multivariate distribution is more general than previously defined. Indeed, a more intrinsic vector definition is obtained with the help of non isotropic dilations and a related notion of generalized scale. In this framework, the components of a stable vector may not only have distinct Levy's stability indices $\alpha$'s, but the latter may depend on its norm. Indeed, we demonstrate that the Levy's stability index of a vector rather correspond to a linear application than to a scalar, and we show that the former should satisfy a simple spectral property

Generally Covariant Conservative Energy-Momentum for Gravitational Anyons

We obtain a generally covariant conservation law of energy-momentum for gravitational anyons by the general displacement transform. The energy-momentum currents have also superpotentials and are therefore identically conserved. It is shown that for Deser's solution and Clement's solution, the energy vanishes. The reasonableness of the definition of energy-momentum may be confirmed by the solution for pure Einstein gravity which is a limit of vanishing Chern-Simons coulping of gravitational anyons.Comment: 12 pages, Latex, no figure

Robust active magnetic dearing control using stabilizing dynamical compensators

The robust control of active magnetic bearings, based on a linearised interval model, is considered. Through robust stability analysis, all the first-order robust stabilizing dynamical compensators for the interval system are obtained. Disturbance attenuation and minimum control effort are also addressed. The approach is applied to a high-speed flywheel supported by two active and two passive magnetic bearings. Simulation and experimental results both show that it is simple, effective, and robust

Topological Bose-Mott Insulators in a One-Dimensional Optical Superlattice

We study topological properties of the Bose-Hubbard model with repulsive interactions in a one-dimensional optical superlattice. We find that the Mott insulator states of the single-component (two-component) Bose-Hubbard model under fractional fillings are topological insulators characterized by a nonzero charge (or spin) Chern number with nontrivial edge states. For ultracold atomic experiments, we show that the topological Chern number can be detected through measuring the density profiles of the bosonic atoms in a harmonic trap.Comment: 5 pages, published versio

Thermalization and temperature distribution in a driven ion chain

We study thermalization and non-equilibrium dynamics in a dissipative quantum many-body system -- a chain of ions with two points of the chain driven by thermal bath under different temperature. Instead of a simple linear temperature gradient as one expects from the classical heat diffusion process, the temperature distribution in the ion chain shows surprisingly rich patterns, which depend on the ion coupling rate to the bath, the location of the driven ions, and the dissipation rates of the other ions in the chain. Through simulation of the temperature evolution, we show that these unusual temperature distribution patterns in the ion chain can be quantitatively tested in experiments within a realistic time scale.Comment: 5 pages, 5 figure