Comment on "Recurrences without closed orbits"

In a recent paper Robicheaux and Shaw [Phys. Rev. A 58, 1043 (1998)] calculate the recurrence spectra of atoms in electric fields with non-vanishing angular momentum not equal to 0. Features are observed at scaled actions ``an order of magnitude shorter than for any classical closed orbit of this system.'' We investigate the transition from zero to nonzero angular momentum and demonstrate the existence of short closed orbits with L_z not equal to 0. The real and complex ``ghost'' orbits are created in bifurcations of the ``uphill'' and ``downhill'' orbit along the electric field axis, and can serve to interpret the observed features in the quantum recurrence spectra.Comment: 2 pages, 1 figure, REVTE

Rupture cascades in a discrete element model of a porous sedimentary rock

We investigate the scaling properties of the sources of crackling noise in a fully-dynamic numerical model of sedimentary rocks subject to uniaxial compression. The model is initiated by filling a cylindrical container with randomly-sized spherical particles which are then connected by breakable beams. Loading at a constant strain rate the cohesive elements fail and the resulting stress transfer produces sudden bursts of correlated failures, directly analogous to the sources of acoustic emissions in real experiments. The source size, energy, and duration can all be quantified for an individual event, and the population analyzed for their scaling properties, including the distribution of waiting times between consecutive events. Despite the non-stationary loading, the results are all characterized by power law distributions over a broad range of scales in agreement with experiments. As failure is approached temporal correlation of events emerge accompanied by spatial clustering.Comment: 5 pages, 4 figure

Semiclassical quantization of the hydrogen atom in crossed electric and magnetic fields

The S-matrix theory formulation of closed-orbit theory recently proposed by Granger and Greene is extended to atoms in crossed electric and magnetic fields. We then present a semiclassical quantization of the hydrogen atom in crossed fields, which succeeds in resolving individual lines in the spectrum, but is restricted to the strongest lines of each n-manifold. By means of a detailed semiclassical analysis of the quantum spectrum, we demonstrate that it is the abundance of bifurcations of closed orbits that precludes the resolution of finer details. They necessitate the inclusion of uniform semiclassical approximations into the quantization process. Uniform approximations for the generic types of closed-orbit bifurcation are derived, and a general method for including them in a high-resolution semiclassical quantization is devised

Long-Term X-ray Monitoring of 1E 1740.7-2942 and GRS 1758-258

We report on long-term observations of the Galactic-bulge black hole candidates 1E 1740.7-2942 and GRS 1758-258 with the Rossi X-Ray Timing Explorer. 1E 1740.7-2942 has been observed 77 times and GRS 1758-258 has been observed 82 times over the past 1000 days. The flux of each object has varied by no more than a factor of 2.5 during this period, and the indices of the energy spectra have varied by no more than 0.4. The power spectra are similar to other black-hole candidates: flat-topped noise, breaking to a power law. Each object has exhibited a brightening that lasted for several months, and we have a found a time lag between the photon power-law index and the count rate. In both sources, the spectrum is softest during the decline from the brightening. This behavior can be understood in the context of thin-disk and advection-dominated accretion flows coexisting over a wide range of radii, with the implication that both sources have low-mass companions and accrete via Roche-lobe overflow.Comment: Accepted for publication in The Astrophysical Journa

Contribution of forbidden orbits in the photoabsorption spectra of atoms and molecules in a magnetic field

In a previous work [Phys. Rev. A \textbf{66}, 0134XX (2002)] we noted a partial disagreement between quantum R-matrix and semiclassical calculations of photoabsorption spectra of molecules in a magnetic field. We show this disagreement is due to a non-vanishing contribution of processes which are forbidden according to the usual semiclassical formalism. Formulas to include these processes are obtained by using a refined stationary phase approximation. The resulting higher order in $\hbar$ contributions also account for previously unexplained ``recurrences without closed-orbits''. Quantum and semiclassical photoabsorption spectra for Rydberg atoms and molecules in a magnetic field are calculated and compared to assess the validity of the first-order forbidden orbit contributions.Comment: 12 pages, 6 figure