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

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

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

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

The Hydrogen Atom in Combined Electric and Magnetic Fields with Arbitrary Mutual Orientations

For the hydrogen atom in combined magnetic and electric fields we investigate the dependence of the quantum spectra, classical dynamics, and statistical distributions of energy levels on the mutual orientation of the two external fields. Resonance energies and oscillator strengths are obtained by exact diagonalization of the Hamiltonian in a complete basis set, even far above the ionization threshold. At high excitation energies around the Stark saddle point the eigenenergies exhibit strong level repulsions when the angle between the fields is varied. The large avoided crossings occur between states with the same approximately conserved principal quantum number, n, and this intramanifold mixing of states cannot be explained, not even qualitatively, by conventional perturbation theory. However, it is well reproduced by an extended perturbation theory which takes into account all couplings between the angular momentum and Runge-Lenz vector. The large avoided crossings are interpreted as a quantum manifestation of classical intramanifold chaos. This interpretation is supported by both classical Poincar\'e surfaces of section, which reveal a mixed regular-chaotic intramanifold dynamics, and the statistical analysis of nearest-neighbor-spacingComment: two-column version, 10 pages, REVTeX, 10 figures, uuencoded, submitted to Rhys. Rev.

Hydrogen atom in crossed electric and magnetic fields: Phase space topology and torus quantization via periodic orbits

A hierarchical ordering is demonstrated for the periodic orbits in a strongly coupled multidimensional Hamiltonian system, namely the hydrogen atom in crossed electric and magnetic fields. It mirrors the hierarchy of broken resonant tori and thereby allows one to characterize the periodic orbits by a set of winding numbers. With this knowledge, we construct the action variables as functions of the frequency ratios and carry out a semiclassical torus quantization. The semiclassical energy levels thus obtained agree well with exact quantum calculations

Semiclassical mechanics of a non-integrable spin cluster

We study detailed classical-quantum correspondence for a cluster system of three spins with single-axis anisotropic exchange coupling. With autoregressive spectral estimation, we find oscillating terms in the quantum density of states caused by classical periodic orbits: in the slowly varying part of the density of states we see signs of nontrivial topology changes happening to the energy surface as the energy is varied. Also, we can explain the hierarchy of quantum energy levels near the ferromagnetic and antiferromagnetic states with EKB quantization to explain large structures and tunneling to explain small structures.Comment: 9 pages. For related works see "http://www.msc.cornell.edu/~clh/clh.html

A Reduced Order Approach for the Embedded Shifted Boundary FEM and a Heat Exchange System on Parametrized Geometries

A model order reduction technique is combined with an embedded boundary finite element method with a POD-Galerkin strategy. The proposed methodology is applied to parametrized heat transfer problems and we rely on a sufficiently refined shape-regular background mesh to account for parametrized geometries. In particular, the employed embedded boundary element method is the Shifted Boundary Method (SBM), recently proposed in Main and Scovazzi, J Comput Phys [17]. This approach is based on the idea of shifting the location of true boundary conditions to a surrogate boundary, with the goal of avoiding cut cells near the boundary of the computational domain. This combination of methodologies has multiple advantages. In the first place, since the Shifted Boundary Method always relies on the same background mesh, there is no need to update the discretized parametric domain. Secondly, we avoid the treatment of cut cell elements, which usually need particular attention. Thirdly, since the whole background mesh is considered in the reduced basis construction, the SBM allows for a smooth transition of the reduced modes across the immersed domain boundary. The performances of the method are verified in two dimensional heat transfer numerical examples