Chaos and Localisation

This thesis investigates quantum transport in the energy space of two paradigm systems of quantum chaos theory. These are highly excited hydrogen atoms subject to a microwave field, and kicked atoms which mimic the delta-kicked rotor model. Both of these systems show a complex dynamical evolution arising from the interaction with an external time-periodic driving force. In particular two quantum phenomena, which have no counterpart on the classical level, are studied: the suppression of classical diffusion, known as dynamical localisation, and quantum resonances as a regime of enhanced transport for the delta-kicked rotor. The first part of the thesis provides new support for the quantitative analogy between energy transport in strongly driven highly excited atoms and particle transport in Anderson-localised solids. A comprehensive numerical analysis of the atomic ionisation rates shows that they obey a universal power-law distribution, in agreement with Anderson localisation theory. This is demonstrated for a one-dimensional model as well as for the real three-dimensional atom. We also discuss the implications of the universal decay-rate distributions for the asymptotic time-decay of the survival probability of the atoms. The second part of the thesis clarifies the effect of decoherence, induced by spontaneous emission, on the quantum resonances which have been observed in a recent experiment with delta-kicked atoms. Scaling laws are derived, based on a quasi-classical approximation of the quantum evolution. These laws describe the shape of the resonance peaks in the mean energy of an experimental ensemble of kicked atoms. Our analytical results match perfectly numerical computations and explain the initially surprising experimental observations. Furthermore, they open the door to the study of the competing effects of decoherence and chaos on the stability of the time evolution of kicked atoms. This stability may be characterised by the overlap of two identical initial states which are subject to different time evolutions. This overlap, called fidelity, is investigated in an experimentally accessible situation.In dieser Arbeit untersuchen wir quantalen Transport im Energieraum anhand zweier Paradebeispiele der Quantenchaostheorie: hoch angeregte Wasserstoffatome im Mikrowellenfeld, und gekickte Atome, die das Modellsystem des delta-gekickten Rotors simulieren. Beide Systeme unterliegen aufgrund des aeusseren, zeitlich periodischen Antriebs einer komplexen Zeitentwicklung. Insbesondere werden zwei Quantenphenomaene untersucht, die kein klassisches Analogon besitzen: die Unterdrueckung klassischer Diffusion, bekannt unter dem Schlagwort dynamischer Lokalisierung, und die Quantenresonanzen als dynamisches Regime, das sich durch beschleunigten Transport im delta-gekickten Rotor auszeichnet. Der erste Teil der Arbeit belegt auf neue Weise die quantitative Analogie zwischen dem Energietransport in stark getriebenen, hoch angeregten Atomen und dem Teilchentransport im Anderson-lokalisierten Festkoerper. Eine umfassende numerische Analyse der atomaren Ionisationsraten zeigt in Uebereinstimmung mit der Lokalisierungstheorie nach Anderson, dass die Ratenverteilungen einem universellen Potenzgesetz unterliegen. Dies wird sowohl fuer ein eindimensionales Modell als auch fuer das reale dreidimensionale Atom demonstriert. Ausserdem werden die Konsequenzen aus der universellen Verteilung der Ionisationsraten fuer die asymptotische Zeitabhaengigkeit der Ueberlebenswahrscheinlichkeit der Atome diskutiert. Der zweite Teil der Arbeit klaert den Einfluss von Dekohaerenz -- induziert durch Spontanemission -- auf die kuerzlich im Experiment mit delta-gekickten Atomen beobachteten Quantenresonanzen. Wir leiten Skalierungsgesetze ab, die auf einer quasiklassischen Naeherung der Quantendynamik beruhen und die Form von Resonanzpeaks beschreiben, welche in der mittleren Energie eines atomaren Ensembles im Experiment beobachtet wurden. Unsere analytischen Resultate stimmen mit numerischen Rechnungen ausgezeichnet ueberein und erklaeren die zunaechst ueberraschenden experimentellen Befunde. Darueberhinaus weisen sie den Weg zur Untersuchung des wechselseitig konkurrierenden Einflusses von Dekohaerenz und Chaos auf die Stabilitaet der quantenmechanischen Zeitentwicklung gekickter Atome. Die Stabilitaet laesst sich mittels des Ueberlapps zweier anfaenglich gleicher, aber unterschiedlich propagierter Zustaende charakterisieren. Dieser Ueberlapp, bekannt als ,,Fidelity'', wird hier fuer eine experimentell realisierbare Situation untersucht

MS FT-2-2 7 Orthogonal polynomials and quadrature: Theory, computation, and applications

Quadrature rules find many applications in science and engineering. Their analysis is a classical area of applied mathematics and continues to attract considerable attention. This seminar brings together speakers with expertise in a large variety of quadrature rules. It is the aim of the seminar to provide an overview of recent developments in the analysis of quadrature rules. The computation of error estimates and novel applications also are described

Internationales Kolloquium über Anwendungen der Informatik und Mathematik in Architektur und Bauwesen : 04. bis 06.07. 2012, Bauhaus-Universität Weimar

The 19th International Conference on the Applications of Computer Science and Mathematics in Architecture and Civil Engineering will be held at the Bauhaus University Weimar from 4th till 6th July 2012. Architects, computer scientists, mathematicians, and engineers from all over the world will meet in Weimar for an interdisciplinary exchange of experiences, to report on their results in research, development and practice and to discuss. The conference covers a broad range of research areas: numerical analysis, function theoretic methods, partial differential equations, continuum mechanics, engineering applications, coupled problems, computer sciences, and related topics. Several plenary lectures in aforementioned areas will take place during the conference. We invite architects, engineers, designers, computer scientists, mathematicians, planners, project managers, and software developers from business, science and research to participate in the conference

Goddard Visiting Scientist Program for the Space and Earth Sciences Directorate

A visiting scientist program was conducted in the space and earth sciences at GSFC. Research was performed in the following areas: astronomical observations; broadband x-ray spectral variability; ground-based spectroscopic and photometric studies; Seyfert galaxies; active galactic nuclei (AGN); massive stellar black holes; the differential microwave radiometer (DMR) onboard the cosmic background explorer (COBE); atmospheric models; and airborne and ground based radar observations. The specific research efforts are detailed by tasks