Equilibrium and eigenfunctions estimates in the semi-classical regime

We establish eigenfunctions estimates, in the semi-classical regime, for critical energy levels associated to an isolated singularity. For Schr\"odinger operators, the asymptotic repartition of eigenvectors is the same as in the regular case, excepted in dimension 1 where a concentration at the critical point occurs. This principle extends to pseudo-differential operators and the limit measure is the Liouville measure as long as the singularity remains integrable.Comment: 13 pages, 1 figure, perhaps to be revise

Numerical simulation of prominence oscillations

We present numerical simulations, obtained with the Versatile Advection Code, of the oscillations of an inverse polarity prominence. The internal prominence equilibrium, the surrounding corona and the inert photosphere are well represented. Gravity and thermodynamics are not taken into account, but it is argued that these are not crucial. The oscillations can be understood in terms of a solid body moving through a plasma. The mass of this solid body is determined by the magnetic field topology, not by the prominence mass proper. The model also allows us to study the effect of the ambient coronal plasma on the motion of the prominence body. Horizontal oscillations are damped through the emission of slow waves while vertical oscillations are damped through the emission of fast waves.Comment: 12 pages, 14 figures, accepted by Astronomy and Astrophysic

Orientational transition in nematic liquid crystals under oscillatory Poiseuille flow

We investigate the orientational behaviour of a homeotropically aligned nematic liquid crystal subjected to an oscillatory plane Poiseuille flow produced by an alternating pressure gradient. For small pressure amplitudes the director oscillates within the flow plane around the initial homeotropic position, whereas for higher amplitudes a spatially homogeneous transition to out-of-plane director motion was observed for the first time. The orientational transition was found to be supercritical and the measured frequency dependence of the critical pressure amplitude in the range between 2 and 20 Hz was in quantitative agreement with a recent theory.Comment: 11 pages, 4 figures, submitted to Europhys. Let

Quantum ergodicity for restrictions to hypersurfaces

Quantum ergodicity theorem states that for quantum systems with ergodic classical flows, eigenstates are, in average, uniformly distributed on energy surfaces. We show that if N is a hypersurface in the position space satisfying a simple dynamical condition, the restrictions of eigenstates to N are also quantum ergodic.Comment: 22 pages, 1 figure; revised according to referee's comments. To appear in Nonlinearit

On the Azimuthal Stability of Shock Waves around Black Holes

Analytical studies and numerical simulations of time dependent axially symmetric flows onto black holes have shown that it is possible to produce stationary shock waves with a stable position both for ideal inviscid and for moderately viscous accretion disks. We perform several two dimensional numerical simulations of accretion flows in the equatorial plane to study shock stability against non-axisymmetric azimuthal perturbations. We find a peculiar new result. A very small perturbation seems to produce an instability as it crosses the shock, but after some small oscillations, the shock wave suddenly transforms into an asymmetric closed pattern, and it stabilizes with a finite radial extent, despite the inflow and outflow boundary conditions are perfectly symmetric. The main characteristics of the final flow are: 1) The deformed shock rotates steadily without any damping. It is a permanent feature and the thermal energy content and the emitted energy vary periodically with time. 2) This behavior is also stable against further perturbations. 3) The average shock is still very strong and well defined, and its average radial distance is somewhat larger than that of the original axially symmetric circular shock. 4) Shocks obtained with larger angular momentum exhibit more frequencies and beating phenomena. 5) The oscillations occur in a wide range of parameters, so this new effect may have relevant observational consequences, like (quasi) periodic oscillations, for the accretion of matter onto black holes. Typical time scales for the periods are 0.01 and 1000 seconds for black holes with 10 and 1 million solar mass, respectively.Comment: 15 pages, 7 figures, accepted by the Astrophysical Journa

Theory of correlations between ultra-cold bosons released from an optical lattice

In this paper we develop a theoretical description of the correlations between ultra-cold bosons after free expansion from confinement in an optical lattice. We consider the system evolution during expansion and give criteria for a far field regime. We develop expressions for first and second order two-point correlations based on a variety of commonly used approximations to the many-body state of the system including Bogoliubov, meanfield decoupling, and particle-hole perturbative solution about the perfect Mott-insulator state. Using these approaches we examine the effects of quantum depletion and pairing on the system correlations. Comparison with the directly calculated correlation functions is used to justify a Gaussian form of our theory from which we develop a general three-dimensional formalism for inhomogeneous lattice systems suitable for numerical calculations of realistic experimental regimes.Comment: 18 pages, 11 figures. To appear in Phys. Rev. A. (few minor changes made and typos fixed