Parametrically excited "Scars" in Bose-Einstein condensates

Parametric excitation of a Bose-Einstein condensate (BEC) can be realized by periodically changing the interaction strength between the atoms. Above some threshold strength, this excitation modulates the condensate density. We show that when the condensate is trapped in a potential well of irregular shape, density waves can be strongly concentrated ("scarred") along the shortest periodic orbits of a classical particle moving within the confining potential. While single-particle wave functions of systems whose classical counterpart is chaotic may exhibit rich scarring patterns, in BEC, we show that nonlinear effects select mainly those scars that are locally described by stripes. Typically, these are the scars associated with self retracing periodic orbits that do not cross themselves in real space. Dephasing enhances this behavior by reducing the nonlocal effect of interference

The rotational modes of relativistic stars: Numerical results

We study the inertial modes of slowly rotating, fully relativistic compact stars. The equations that govern perturbations of both barotropic and non-barotropic models are discussed, but we present numerical results only for the barotropic case. For barotropic stars all inertial modes are a hybrid mixture of axial and polar perturbations. We use a spectral method to solve for such modes of various polytropic models. Our main attention is on modes that can be driven unstable by the emission of gravitational waves. Hence, we calculate the gravitational-wave growth timescale for these unstable modes and compare the results to previous estimates obtained in Newtonian gravity (i.e. using post-Newtonian radiation formulas). We find that the inertial modes are slightly stabilized by relativistic effects, but that previous conclusions concerning eg. the unstable r-modes remain essentially unaltered when the problem is studied in full general relativity.Comment: RevTeX, 29 pages, 31 eps figure

Differential rotation of nonlinear r-modes

Differential rotation of r-modes is investigated within the nonlinear theory up to second order in the mode amplitude in the case of a slowly-rotating, Newtonian, barotropic, perfect-fluid star. We find a nonlinear extension of the linear r-mode, which represents differential rotation that produces large scale drifts of fluid elements along stellar latitudes. This solution includes a piece induced by first-order quantities and another one which is a pure second-order effect. Since the latter is stratified on cylinders, it cannot cancel differential rotation induced by first-order quantities, which is not stratified on cylinders. It is shown that, unlikely the situation in the linearized theory, r-modes do not preserve vorticity of fluid elements at second-order. It is also shown that the physical angular momentum and energy of the perturbation are, in general, different from the corresponding canonical quantities.Comment: 9 pages, revtex4; section III revised, comments added in Introduction and Conclusions, references updated; to appear in Phys. Rev.

A numerical study of the r-mode instability of rapidly rotating nascent neutron stars

The first results of numerical analysis of classical r-modes of {\it rapidly} rotating compressible stellar models are reported. The full set of linear perturbation equations of rotating stars in Newtonian gravity are numerically solved without the slow rotation approximation. A critical curve of gravitational wave emission induced instability which restricts the rotational frequencies of hot young neutron stars is obtained. Taking the standard cooling mechanisms of neutron stars into account, we also show the `evolutionary curves' along which neutron stars are supposed to evolve as cooling and spinning-down proceed. Rotational frequencies of $1.4M_{\odot}$ stars suffering from this instability decrease to around 100Hz when the standard cooling mechanism of neutron stars is employed. This result confirms the results of other authors who adopted the slow rotation approximation.Comment: 4 pages, 2 figures; MNRAS,316,L1(2000

Faraday spectroscopy of atoms confined in a dark optical trap

We demonstrate Faraday spectroscopy with high duty cycle and sampling rate using atoms confined to a blue-detuned optical trap. Our trap consists of a crossed pair of high-charge-number hollow laser beams, which forms a dark, box-like potential. We have used this to measure transient magnetic fields in a 500-micron-diameter spot over a 400 ms time window with nearly unit duty cycle at a 500 Hz sampling rate. We use these measurements to quantify and compensate time-varying magnetic fields to ~10 nT per time sample.Comment: 6 pages, 8 figures Accepted in Phys. Rev.

R-mode Instability of Slowly Rotating Non-isentropic Relativistic Stars

We investigate properties of $r$-mode instability in slowly rotating relativistic polytropes. Inside the star slow rotation and low frequency formalism that was mainly developed by Kojima is employed to study axial oscillations restored by Coriolis force. At the stellar surface, in order to take account of gravitational radiation reaction effect, we use a near-zone boundary condition instead of the usually imposed boundary condition for asymptotically flat spacetime. Due to the boundary condition, complex frequencies whose imaginary part represents secular instability are obtained for discrete $r$-mode oscillations in some polytropic models. It is found that such discrete $r$-mode solutions can be obtained only for some restricted polytropic models. Basic properties of the solutions are similar to those obtained by imposing the boundary condition for asymptotically flat spacetime. Our results suggest that existence of a continuous part of spectrum cannot be avoided even when its frequency becomes complex due to the emission of gravitational radiation.Comment: 10 pages, 4 figures, accepted for publlication in PR

Non-converging hysteretic cycles in random spin networks

Behavior of hysteretic trajectories for cyclical input is investigated as a function of the internal structure of a system modeled by the classical random network of binary spins. Different regimes of hysteretic behavior are discovered for different network connectivity and topology. Surprisingly, hysteretic trajectories which do not converge at all are observed. They are shown to be associated with the presence of specific topological elements in the network structure, particularly with the fully interconnected spin groups of size equal or greater than 4.Comment: 4 pages, 3 figure