Localization of Chaotic Resonance States due to a Partial Transport Barrier

Chaotic eigenstates of quantum systems are known to localize on either side of a classical partial transport barrier if the flux connecting the two sides is quantum mechanically not resolved due to Heisenberg's uncertainty. Surprisingly, in open systems with escape chaotic resonance states can localize even if the flux is quantum mechanically resolved. We explain this using the concept of conditionally invariant measures from classical dynamical systems by introducing a new quantum mechanically relevant class of such fractal measures. We numerically find quantum-to-classical correspondence for localization transitions depending on the openness of the system and on the decay rate of resonance states.Comment: 5+1 pages, 4 figure

Visualization and comparison of classical structures and quantum states of 4D maps

For generic 4D symplectic maps we propose the use of 3D phase-space slices which allow for the global visualization of the geometrical organization and coexistence of regular and chaotic motion. As an example we consider two coupled standard maps. The advantages of the 3D phase-space slices are presented in comparison to standard methods like 3D projections of orbits, the frequency analysis, and a chaos indicator. Quantum mechanically, the 3D phase-space slices allow for the first comparison of Husimi functions of eigenstates of 4D maps with classical phase space structures. This confirms the semi-classical eigenfunction hypothesis for 4D maps.Comment: For videos with rotated view of the 3D phase-space slices in high resolution see http://www.comp-phys.tu-dresden.de/supp

Hierarchical Fractal Weyl Laws for Chaotic Resonance States in Open Mixed Systems

In open chaotic systems the number of long-lived resonance states obeys a fractal Weyl law, which depends on the fractal dimension of the chaotic saddle. We study the generic case of a mixed phase space with regular and chaotic dynamics. We find a hierarchy of fractal Weyl laws, one for each region of the hierarchical decomposition of the chaotic phase-space component. This is based on our observation of hierarchical resonance states localizing on these regions. Numerically this is verified for the standard map and a hierarchical model system.Comment: 5 pages, 3 figure

Resonance eigenfunction hypothesis for chaotic systems

A hypothesis about the average phase-space distribution of resonance eigenfunctions in chaotic systems with escape through an opening is proposed. Eigenfunctions with decay rate $\gamma$ are described by a classical measure that $(i)$ is conditionally invariant with classical decay rate $\gamma$ and $(ii)$ is uniformly distributed on sets with the same temporal distance to the quantum resolved chaotic saddle. This explains the localization of fast-decaying resonance eigenfunctions classically. It is found to occur in the phase-space region having the largest distance to the chaotic saddle. We discuss the dependence on the decay rate $\gamma$ and the semiclassical limit. The hypothesis is numerically demonstrated for the standard map

Geometrical theory of diffraction and spectral statistics

We investigate the influence of diffraction on the statistics of energy levels in quantum systems with a chaotic classical limit. By applying the geometrical theory of diffraction we show that diffraction on singularities of the potential can lead to modifications in semiclassical approximations for spectral statistics that persist in the semiclassical limit $\hbar \to 0$. This result is obtained by deriving a classical sum rule for trajectories that connect two points in coordinate space.Comment: 14 pages, no figure, to appear in J. Phys.

Design Guidelines for interlocked stator cores made of CoFe sheets

CoFe lamination stacks used for high-performance electric motors can be manufactured economically in high volumes by interlocking. In order to ensure sufficient joint strength with minimized sheet thickness, a comprehensive knowledge of the influences of various process parameters, such as embossing depth, clearance and counter punch force, is essential. To analyze these parameters, which also influence the magnetic properties, experiments are carried out and resulting joint strengths are determined in top tensile tests. The negative influences of the cutting process on magnetic conductivity and thus hysteresis losses due to residual stresses and plastic deformation are well known. In the subsequent stacking step, an influence of embossing and pre-stresses on the material properties is expected. In addition, local electrical contacts between the sheets may occur due to the interlocking process, causing additional eddy currents. Loss measurements are conducted to investigate the effect of the joining process on the magnetic properties of the stack. In doing so, the influence of process parameters such as the embossing depth and clearance on eddy current power losses is analyzed

The exposure of the hybrid detector of the Pierre Auger Observatory

The Pierre Auger Observatory is a detector for ultra-high energy cosmic rays. It consists of a surface array to measure secondary particles at ground level and a fluorescence detector to measure the development of air showers in the atmosphere above the array. The "hybrid" detection mode combines the information from the two subsystems. We describe the determination of the hybrid exposure for events observed by the fluorescence telescopes in coincidence with at least one water-Cherenkov detector of the surface array. A detailed knowledge of the time dependence of the detection operations is crucial for an accurate evaluation of the exposure. We discuss the relevance of monitoring data collected during operations, such as the status of the fluorescence detector, background light and atmospheric conditions, that are used in both simulation and reconstruction.Comment: Paper accepted by Astroparticle Physic

The Pierre Auger Observatory III: Other Astrophysical Observations

Astrophysical observations of ultra-high-energy cosmic rays with the Pierre Auger ObservatoryComment: Contributions to the 32nd International Cosmic Ray Conference, Beijing, China, August 201

Ultrahigh energy neutrinos at the pierre auger observatory

The observation of ultrahigh energy neutrinos (UHEs) has become a priority in experimental astroparticle physics. UHEs can be detected with a variety of techniques. In particular, neutrinos can interact in the atmosphere (downward-going ) or in the Earth crust (Earth-skimming ), producing air showers that can be observed with arrays of detectors at the ground. With the surface detector array of the Pierre Auger Observatory we can detect these types of cascades. The distinguishing signature for neutrino events is the presence of very inclined showers produced close to the ground (i.e., after having traversed a large amount of atmosphere). In this work we review the procedure and criteria established to search for UHEs in the data collected with the ground array of the Pierre Auger Observatory.This includes Earth-skimming as well as downward-going neutrinos. No neutrino candidates have been found, which allows us to place competitive limits to the diffuse flux of UHEs in the EeV range and above

The Pierre Auger Observatory II: Studies of Cosmic Ray Composition and Hadronic Interaction models

Studies of the composition of the highest energy cosmic rays with the Pierre Auger Observatory, including examination of hadronic physics effects on the structure of extensive air showers.Comment: Contributions to the 32nd International Cosmic Ray Conference, Beijing, China, August 201