4,008 research outputs found
Semiclassical quantization with bifurcating orbits
Bifurcations of classical orbits introduce divergences into semiclassical
spectra which have to be smoothed with the help of uniform approximations. We
develop a technique to extract individual energy levels from semiclassical
spectra involving uniform approximations. As a prototype example, the method is
shown to yield excellent results for photo-absorption spectra for the hydrogen
atom in an electric field in a spectral range where the abundance of
bifurcations would render the standard closed-orbit formula without uniform
approximations useless. Our method immediately applies to semiclassical trace
formulae as well as closed-orbit theory and offers a general technique for the
semiclassical quantization of arbitrary systems
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.
Sound propagation over uneven ground and irregular topography
Theoretical, computational, and experimental techniques for predicting the effects of irregular topography on long range sound propagation in the atmosphere was developed. Irregular topography here is understood to imply a ground surface that is not idealized as being perfectly flat or that is not idealized as having a constant specific acoustic impedance. The interest focuses on circumstances where the propagation is similar to what might be expected for noise from low altitude air vehicles flying over suburban or rural terrain, such that rays from the source arrive at angles close to grazing incidence
Open circular billiards and the Riemann hypothesis
A comparison of escape rates from one and from two holes in an experimental
container (e.g. a laser trap) can be used to obtain information about the
dynamics inside the container. If this dynamics is simple enough one can hope
to obtain exact formulas. Here we obtain exact formulas for escape from a
circular billiard with one and with two holes. The corresponding quantities are
expressed as sums over zeroes of the Riemann zeta function. Thus we demonstrate
a direct connection between recent experiments and a major unsolved problem in
mathematics, the Riemann hypothesis.Comment: 5 pages, 4 embedded postscript figures; v2: more explicit on how the
Reimann Hypothesis arises from a comparison of one and two hole escape rate
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
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
Emotional and Adrenocortical Responses of Infants to the Strange Situation: The Differential Function of Emotional Expression
The aim of the study was to investigate biobehavioural organisation in infants with different qualities of attachment. Quality of attachment (security and disorganisation), emotional expression, and adrenocortical stress reactivity were investigated in a sample of 106 infants observed during Ainsworth’s Strange Situation at the age of 12 months. In addition, behavioural inhibition was assessed from maternal reports. As expected, securely attached infants did not show an adrenocortical response. Regarding the traditionally defined insecurely attached groups, adrenocortical activation during the strange situation was found for the ambivalent group, but not for the avoidant one. Previous ndings of increased adrenocortical activity in disorganised infants could not be replicated. In line with previous ndings, adrenocortical activation was most prominent in insecure infants with high behavioural inhibition indicating the function of a secure attachment relationship as a social buffer against less adaptive temperamental dispositions. Additional analyses indicated that adrenocortical reactivity and behavioural distress were not based on common activation processes. Biobehavioural associations within the different attachment groups suggest that biobehavioural processes in securely attached infants may be different from those in insecurely attached and disorganised groups. Whereas a coping model may be applied to describe the biobehavioural organisation of secure infants, an arousal model explanation may be more appropriate for the other groups
2-(1,4-Dioxo-1,4-dihydro-2-naphthyl)-2-methylpropanoic acid
The sterically crowded title compound, C₁₄H₁₂O₄, crystallizes as centrosymmetric hydrogen-bonded dimers involving the carboxyl groups. The naphthoquinone ring system is folded by 11.5 (1)° about a vector joining the 1,4-C atoms, and the quinone O atoms are displaced from the ring plane, presumably because of steric interactions with the bulky substituent
Decimation and Harmonic Inversion of Periodic Orbit Signals
We present and compare three generically applicable signal processing methods
for periodic orbit quantization via harmonic inversion of semiclassical
recurrence functions. In a first step of each method, a band-limited decimated
periodic orbit signal is obtained by analytical frequency windowing of the
periodic orbit sum. In a second step, the frequencies and amplitudes of the
decimated signal are determined by either Decimated Linear Predictor, Decimated
Pade Approximant, or Decimated Signal Diagonalization. These techniques, which
would have been numerically unstable without the windowing, provide numerically
more accurate semiclassical spectra than does the filter-diagonalization
method.Comment: 22 pages, 3 figures, submitted to J. Phys.
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