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.

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.

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

Overtraining or burnout : a training and psycho-behavioural case study

The aim of this article is to present case study data that challenges the popular conception that athlete burnout represents the ultimate outcome of overtraining. A young male triathlete (22 yrs) completed a comprehensive training diary, along with the Athlete Burnout Questionnaire (ABQ) and the Multi-component Training Distress Scale (MTDS) weekly from the commencement of pre-season training, until the end of the competitive season 45 weeks later. Results were analysed retrospectively upon completion of the season and followed up with semi-structured interviews with the coach and athlete. These longitudinal observations are the first to document an athlete who appears to have simultaneously become overtrained and developed athlete burnout as measured by the ABQ. Thus we are advocating a need for future research to clarify differences between these two training-stress syndromes, specifically in relation to their aetiology, to avoid misdiagnosis and to ensure appropriate treatment for athletes experiencing these conditions is provided

Complex genome evolution in Anopheles coluzzii associated with increased insecticide usage in Mali.

In certain cases, a species may have access to important genetic variation present in a related species via adaptive introgression. These novel alleles may interact with their new genetic background, resulting in unexpected phenotypes. In this study, we describe a selective sweep on standing variation on the X chromosome in the mosquito Anopheles coluzzii, a principal malaria vector in West Africa. This event may have been influenced by the recent adaptive introgression of the insecticide resistance gene known as kdr from the sister species Anopheles gambiae. Individuals carrying both kdr and a nearly fixed X-linked haplotype, encompassing at least four genes including the P450 gene CYP9K1 and the cuticular protein CPR125, have rapidly increased in relative frequency. In parallel, a reproductively isolated insecticide-susceptible A. gambiae population (Bamako form) has been driven to local extinction, likely due to strong selection from increased insecticide-treated bed net usage

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

Stressors, Recovery Processes, and Manifestations of Training Distress in Dance

Abstract Dancers are expected to maintain consistently high levels of performance capability and to perform on demand. To meet these expectations, they subject their bodies to long hours of intensive physical training. Such training regimens are often combined with tight rehearsal and performance schedules, which over time, can lead to persistent fatigue, psychological distress, performance decrements, and injury. A similar process has been observed as a consequence of high-intensity training in many different sports, and considerable sport-related research has been devoted to identifying the antecedents, the symptoms that are experienced, and the most cost-effective ways of monitoring symptom development. This paper presents a general heuristic framework for understanding this “training distress process” and discusses the framework with specific reference to dance

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

Enhanced Energy Dissipation in Stepped Chutes. (Discussion)

The contribution is a timely reminder that most research on stepped chute hydraulics has been narrowly limited to flat identical horizontal steps in straight prismatic rectangular channels (Chanson 2001). For completeness, the writer wishes to provide relevant information on early stepped spillways and related works. He also adds some pertinent comment