Photoabsorption spectra of the diamagnetic hydrogen atom in the transition regime to chaos: Closed orbit theory with bifurcating orbits

With increasing energy the diamagnetic hydrogen atom undergoes a transition from regular to chaotic classical dynamics, and the closed orbits pass through various cascades of bifurcations. Closed orbit theory allows for the semiclassical calculation of photoabsorption spectra of the diamagnetic hydrogen atom. However, at the bifurcations the closed orbit contributions diverge. The singularities can be removed with the help of uniform semiclassical approximations which are constructed over a wide energy range for different types of codimension one and two catastrophes. Using the uniform approximations and applying the high-resolution harmonic inversion method we calculate fully resolved semiclassical photoabsorption spectra, i.e., individual eigenenergies and transition matrix elements at laboratory magnetic field strengths, and compare them with the results of exact quantum calculations.Comment: 26 pages, 9 figures, submitted to J. Phys.

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

The hydrogen atom in an electric field: Closed-orbit theory with bifurcating orbits

Closed-orbit theory provides a general approach to the semiclassical description of photo-absorption spectra of arbitrary atoms in external fields, the simplest of which is the hydrogen atom in an electric field. Yet, despite its apparent simplicity, a semiclassical quantization of this system by means of closed-orbit theory has not been achieved so far. It is the aim of this paper to close that gap. We first present a detailed analytic study of the closed classical orbits and their bifurcations. We then derive a simple form of the uniform semiclassical approximation for the bifurcations that is suitable for an inclusion into a closed-orbit summation. By means of a generalized version of the semiclassical quantization by harmonic inversion, we succeed in calculating high-quality semiclassical spectra for the hydrogen atom in an electric field

Extracting Multidimensional Phase Space Topology from Periodic Orbits

We establish a hierarchical ordering of periodic orbits in a strongly coupled multidimensional Hamiltonian system. Phase space structures can be reconstructed quantitatively from the knowledge of periodic orbits alone. We illustrate our findings for the hydrogen atom in crossed electric and magnetic fields.Comment: 4 pages, 5 figures, accepted for publication in Phys. Rev. Let

XTE J1739-302: An Unusual New X-ray Transient

A new x-ray transient, designated XTE J1739-302, was discovered with the Proportional Counter Array (PCA) on the Rossi X-ray Timing Explorer (RXTE) in data from 12 August 1997. Although it was the brightest source in the Galactic Center region while active (about 3.0 x 10^-9 ergs/cm2/s from 2 to 25 keV), it was only observed on that one day; it was not detectable nine days earlier or two days later. There is no known counterpart at other wavelengths, and its proximity to the Galactic Center will make such an identification difficult due to source confusion and extinction. The x-ray spectrum and intensity suggest a giant outburst of a Be/neutron star binary, although no pulsations were observed and the outburst was shorter than is usual from these systems.Comment: 11 pages incorporating 6 figures, AAStex; accepted for The Astrophysical Journal, Part 2 (Letters

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

Bifurcations, order, and chaos in the Bose-Einstein condensation of dipolar gases

We apply a variational technique to solve the time-dependent Gross-Pitaevskii equation for Bose-Einstein condensates in which an additional dipole-dipole interaction between the atoms is present with the goal of modelling the dynamics of such condensates. We show that universal stability thresholds for the collapse of the condensates correspond to bifurcation points where always two stationary solutions of the Gross-Pitaevskii equation disappear in a tangent bifurcation, one dynamically stable and the other unstable. We point out that the thresholds also correspond to "exceptional points," i.e. branching singularities of the Hamiltonian. We analyse the dynamics of excited condensate wave functions via Poincare surfaces of section for the condensate parameters and find both regular and chaotic motion, corresponding to (quasi-) periodically oscillating and irregularly fluctuating condensates, respectively. Stable islands are found to persist up to energies well above the saddle point of the mean-field energy, alongside with collapsing modes. The results are applicable when the shape of the condensate is axisymmetric.Comment: 10 pages, 4 figures, minor changes in the text and additional reference adde

Molecules in external fields: a semiclassical analysis

We undertake a semiclassical analysis of the spectral properties (modulations of photoabsorption spectra, energy level statistics) of a simple Rydberg molecule in static fields within the framework of Closed-Orbit/Periodic-Orbit theories. We conclude that in addition to the usual classically allowed orbits one must consider classically forbidden diffractive paths. Further, the molecule brings in a new type of 'inelastic' diffractive trajectory, different from the usual 'elastic' diffractive orbits encountered in previous studies of atomic and analogous systems such as billiards with point-scatterers. The relative importance of inelastic versus elastic diffraction is quantified by merging the usual Closed Orbit theory framework with molecular quantum defect theory.Comment: 4 pages, 3 figure