Symbolic dynamics I. Finite dispersive billiards

Orbits in different dispersive billiard systems, e.g. the 3 disk system, are mapped into a topological well ordered symbol plane and it is showed that forbidden and allowed orbits are separated by a monotone pruning front. The pruning front can be approximated by a sequence of finite symbolic dynamics grammars.Comment: CYCLER Paper 93Jan00

Room-temperature near-infrared silicon carbide nanocrystalline emitters based on optically aligned spin defects

Bulk silicon carbide (SiC) is a very promising material system for bio-applications and quantum sensing. However, its optical activity lies beyond the near infrared spectral window for in-vivo imaging and fiber communications due to a large forbidden energy gap. Here, we report the fabrication of SiC nanocrystals and isolation of different nanocrystal fractions ranged from 600 nm down to 60 nm in size. The structural analysis reveals further fragmentation of the smallest nanocrystals into ca. 10-nm-size clusters of high crystalline quality, separated by amorphization areas. We use neutron irradiation to create silicon vacancies, demonstrating near infrared photoluminescence. Finally, we detect, for the first time, room-temperature spin resonances of these silicon vacancies hosted in SiC nanocrystals. This opens intriguing perspectives to use them not only as in-vivo luminescent markers, but also as magnetic field and temperature sensors, allowing for monitoring various physical, chemical and biological processes.Comment: 5 pages, 4 figure

Resonance-Assisted Tunneling

We present evidence that tunneling processes in near-integrable systems are enhanced due to the manifestation of nonlinear resonances and their respective island chains in phase space. A semiclassical description of this "resonance-assisted" mechanism is given, which is based on a local perturbative description of the dynamics in the vicinity of the resonances. As underlying picture, we obtain that the quantum state is coupled, via a succession of classically forbidden transitions across nonlinear resonances, to high excitations within the well, from where tunneling occurs with a rather large rate. The connection between this description and the complex classical structure of the underlying integrable dynamics is furthermore studied, giving ground to the general coherence of the description as well as guidelines for the identification of the dominant tunneling paths. The validity of this mechanism is demonstrated within the kicked Harper model, where good agreement between quantum and semiclassical (resonance-assisted) tunneling rates is found.Comment: 52 pages, 16 figures, submitted to Annals of Physic

Local structure of self-affine sets

The structure of a self-similar set with open set condition does not change under magnification. For self-affine sets the situation is completely different. We consider planar self-affine Cantor sets E of the type studied by Bedford, McMullen, Gatzouras and Lalley, for which the projection onto the horizontal axis is an interval. We show that within small square neighborhoods of almost each point x in E, with respect to many product measures on address space, E is well approximated by product sets of an interval and a Cantor set. Even though E is totally disconnected, the limit sets have the product structure with interval fibres, reminiscent to the view of attractors of chaotic differentiable dynamical systems.Comment: 10 pages, 2 figure

Symmetries and collective excitations in large superconducting circuits

The intriguing appeal of circuits lies in their modularity and ease of fabrication. Based on a toolbox of simple building blocks, circuits present a powerful framework for achieving new functionality by combining circuit elements into larger networks. It is an open question to what degree modularity also holds for quantum circuits -- circuits made of superconducting material, in which electric voltages and currents are governed by the laws of quantum physics. If realizable, quantum coherence in larger circuit networks has great potential for advances in quantum information processing including topological protection from decoherence. Here, we present theory suitable for quantitative modeling of such large circuits and discuss its application to the fluxonium device. Our approach makes use of approximate symmetries exhibited by the circuit, and enables us to obtain new predictions for the energy spectrum of the fluxonium device which can be tested with current experimental technology