2,129 research outputs found
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
Symmetry-breaking thermally induced collapse of dipolar Bose-Einstein condensates
We investigate a Bose-Einstein condensate with additional long-range dipolar
interaction in a cylindrically symmetric trap within a variational framework.
Compared to the ground state of this system, little attention has as yet been
payed to its unstable excited states. For thermal excitations, however, the
latter is of great interest, because it forms the "activated complex" that
mediates the collapse of the condensate. For a certain value of the s-wave
scatting length our investigations reveal a bifurcation in the transition
state, leading to the emergence of two additional and symmetry-breaking excited
states. Because these are of lower energy than their symmetric counterpart, we
predict the occurrence of a symmetry-breaking thermally induced collapse of
dipolar condensates. We show that its occurrence crucially depends on the trap
geometry and calculate the thermal decay rates of the system within leading
order transition state theory with the help of a uniform rate formula near the
rank-2 saddle which allows to smoothly pass the bifurcation.Comment: 6 pages, 3 figure
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
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.
Recognition of geochemical footprints of mineral systems in the regolith at regional to continental scales
Understanding the character of Australia's extensive regolith cover is crucial to the continuing success of mineral exploration. We hypothesise that the regolith contains geochemical fingerprints of processes related to the development and preservation of mineral systems at a range of scales. We test this hypothesis by analysing the composition of surface sediments within greenfield regional-scale (southern Thomson Orogen) and continental-scale (Australia) study areas. In the southern Thomson Orogen area, the first principal component (PC1) derived in our study [Ca, Sr, Cu, Mg, Au and Mo at one end; rare earth elements (REEs) and Th at the other] is very similar to the empirical vector used by a local company (enrichment in Sr, Ca and Au concomitant with depletion in REEs) to successfully site exploration drill holes for Cu-Au mineralisation. Mapping of the spatial distribution of PC1 in the region reveals several areas of elevated values and possible mineralisation potential. One of the strongest targets in the PC1 map is located between Brewarrina and Bourke in northern New South Wales. Here, exploration drilling has intersected porphyry Cu-Au mineralisation with up to 1 wt% Cu, 0.1 g/t Au, and 717ppm Zn. The analysis of a comparable geochemical dataset at the continental scale yields a compositionally similar PC1 (Ca, Sr, Mg, Cu, Au and Mo at one end; REEs and Th at the other) to that of the regional study. Mapping PC1 at the continental scale shows patterns that (1) are spatially compatible with the regional study and (2) reveal several geological regions of elevated values, possibly suggesting an enhanced potential for porphyry Cu-Au mineralisation. These include well-endowed mineral provinces such as the Curnamona and Capricorn regions, but also some greenfield regions such as the Albany-Fraser/western Eucla, western Murray and Eromanga geological regions. We conclude that the geochemical composition of Australia's regolith may hold critical information pertaining to mineralisation within/beneath it.The studies reported here would not have been possible without Commonwealth
funding through the Cooperative Research Centre Program,
the Onshore Energy Security Program, and Geoscience Australia appropriation
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 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
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
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