Strange attractors in periodically-kicked degenerate Hopf bifurcations

We prove that spiral sinks (stable foci of vector fields) can be transformed into strange attractors exhibiting sustained, observable chaos if subjected to periodic pulsatile forcing. We show that this phenomenon occurs in the context of periodically-kicked degenerate supercritical Hopf bifurcations. The results and their proofs make use of a new multi-parameter version of the theory of rank one maps developed by Wang and Young.Comment: 16 page

Approach to equilibrium for the stochastic NLS

We study the approach to equilibrium, described by a Gibbs measure, for a system on a $d$-dimensional torus evolving according to a stochastic nonlinear Schr\"odinger equation (SNLS) with a high frequency truncation. We prove exponential approach to the truncated Gibbs measure both for the focusing and defocusing cases when the dynamics is constrained via suitable boundary conditions to regions of the Fourier space where the Hamiltonian is convex. Our method is based on establishing a spectral gap for the non self-adjoint Fokker-Planck operator governing the time evolution of the measure, which is {\it uniform} in the frequency truncation $N$. The limit $N\to\infty$ is discussed.Comment: 15 p

Optical afterglows from cylindrical jets of short gamma-ray bursts

Observations of extragalactic radio jets and young stellar jets show that the jets are cylindrical; i.e., they maintain a nearly constant cross section on large scales. It has been suggested that the afterglow behaviors of some long-duration gamma-ray bursts (GRBs) are consistent with the cylindrical jet model of GRBs. Here we study the afterglow emission of cylindrical jets from short-duration GRBs. For the usual conical jet geometry, it is argued that, because of the low fluence of short GRBs, the prospects of detecting the optical afterglow 10 hr after the burst are not promising. However, in the present work we find that if the jets are cylindrical, the chance for detecting the optical afterglow will be increased, even if the burst occurs in a low-density (n ∼ 10-3 cm-3) medium. Since the jets are expected to not be well collimated initially and the time when they change from conical to cylindrical is not exactly known, we discuss two cases for the afterglow of cylindrical jets: the jets becoming cylindrical (1) after the gamma-ray - emitting phase and (2) before the gamma-ray - emitting phase. In both cases, the light-curve behaviors, especially the peak time, are sensitive to the cross section radius of the cylindrical jet. In the former case we find that for viewing angles less than ∼0.03 rad relative to the jet axis, typical short GRBs have a late-time R-band afterglow with a maximum apparent magnitude of mR ≲ 23, given that the efficiency for producing gamma rays and the shock microphysical parameters of the afterglow are the same in short and long bursts. For the latter case the optical afterglows can always be readily detected with mR < 23 at 10 hr after the burst. Comparison between model light curves and observational upper limits of the optical afterglow flux of a few short GRBs are also made. © 2005. The American Astronomical Society. All rights reserved.published_or_final_versio

Stability of Quantum Motion: Beyond Fermi-golden-rule and Lyapunov decay

We study, analytically and numerically, the stability of quantum motion for a classically chaotic system. We show the existence of different regimes of fidelity decay which deviate from Fermi Golden rule and Lyapunov decay.Comment: 5 pages, 5 figure

Ballistic Spin Injection from Fe into ZnSe and GaAs with a (001), (111), and (110) orientation

We present first-principles calculations of ballistic spin injection in Fe/GaAs and Fe/ZnSe junctions with orientation (001), (111), and (110). We find that the symmetry mismatch of the Fe minority-spin states with the semiconductor conduction states can lead to extremely high spin polarization of the current through the (001) interface for hot and thermal injection processes. Such a symmetry mismatch does not exist for the (111) and (110) interfaces, where smaller spin injection efficiencies are found. The presence of interface states is found to lower the current spin polarization, both with and without a Schottky barrier. Finally, a higher bias can also affect the spin injection efficiency.Comment: 12 pages, 18 figure

Short time decay of the Loschmidt echo

The Loschmidt echo measures the sensitivity to perturbations of quantum evolutions. We study its short time decay in classically chaotic systems. Using perturbation theory and throwing out all correlation imposed by the initial state and the perturbation, we show that the characteristic time of this regime is well described by the inverse of the width of the local density of states. This result is illustrated and discussed in a numerical study in a 2-dimensional chaotic billiard system perturbed by various contour deformations and using different types of initial conditions. Moreover, the influence to the short time decay of sub-Planck structures developed by time evolution is also investigated.Comment: 7 pages, 7 figures, published versio

Timing Recollision in Nonsequential Double Ionization by Intense Elliptically Polarized Laser Pulses

We examine correlated electron and doubly charged ion momentum spectra from strong field double ionization of Neon employing intense elliptically polarized laser pulses. An ellipticity-dependent asymmetry of correlated electron and ion momentum distributions has been observed. Using a 3D semiclassical model, we demonstrate that our observations reflect the sub-cycle dynamics of the recollision process. Our work reveals a general physical picture for recollision-impact double ionization with elliptical polarization, and demonstrates the possibility of ultrafast control of the recollision dynamics.Comment: 6 pages, 5 figure

Factors controlling tropospheric O3, OH, NOx, and SO2 over the tropical Pacific during PEM-Tropics B

Observations over the tropical Pacific during the Pacific Exploratory Mission (PEM)-Tropics B experiment (March-April 1999) are analyzed. Concentrations of CO and long-lived nonmethane hydrocarbons in the region are significantly enhanced due to transport of pollutants from northern industrial continents. This pollutant import also enhances moderately O3 concentrations but not NOx concentrations. It therefore tends to depress OH concentrations over the tropical Pacific. These effects contrast to the large enhancements of O3 and NOx concentrations and the moderate increase of OH concentrations due to biomass burning outflow during the PEM-Tropics A experiment (September-October 1996). Observed CH3I concentrations, as in PEM-Tropics A, indicate that convective mass outflux in the middle and upper troposphere is largely independent of altitude over the tropical Pacific. Constraining a one-dimensiohal model with CH3I observations yields a 10-day timescale for convective turnover of the free troposphere, a factor of 2 faster than during PEM-Tropics A. Model simulated HO2, CH2O, H2O2, and CH3OOH concentrations are generally in agreement with observations. However, simulated OH concentrations are lower (∼25%) than observations above 6 km. Whereas models tend to overestimate previous field measurements, simulated HNO3 concentrations during PEM-Tropics B are too low (a factor of 2-4 below 6 km) compared to observations. Budget analyses indicate that chemical production of O3 accounts for only 50% of chemical loss; significant transport of O3 into the region appears to take place within the tropics. Convective transport of CH3OOH enhances the production of HOx and O3 in the upper troposphere, but this effect is offset by HOx loss due to the scavenging of H2O2. Convective transport and scavenging of reactive nitrogen species imply a necessary source of 0.4-1 Tg yr-1 of NOx in the free troposphere (above 4 km) over the tropics. A large fraction of the source could be from marine lightning. Oxidation of DMS transported by convection from the boundary layer could explain the observed free tropospheric SO2 concentrations over the tropical Pacific. This source of DMS due to convection, however, would imply in the model free tropospheric concentrations much higher than observed. The model overestimate cannot be reconciled using recent kinetics measurements of the DMS-OH adduct reaction at low pressures and temperatures and may reflect enhanced OH oxidation of DMS during convection. Copyright 2001 by the American Geophysical Union