Tunneling Mechanism due to Chaos in a Complex Phase Space

We have revealed that the barrier-tunneling process in non-integrable systems is strongly linked to chaos in complex phase space by investigating a simple scattering map model. The semiclassical wavefunction reproduces complicated features of tunneling perfectly and it enables us to solve all the reasons why those features appear in spite of absence of chaos on the real plane. Multi-generation structure of manifolds, which is the manifestation of complex-domain homoclinic entanglement created by complexified classical dynamics, allows a symbolic coding and it is used as a guiding principle to extract dominant complex trajectories from all the semiclassical candidates.Comment: 4 pages, RevTeX, 6 figures, to appear in Phys. Rev.

Detection and mobility of hafnium in SiO2

High-angle annular dark-field imaging in scanning transmission electron microscopy and x-ray photoelectron spectroscopy were used to investigate thermal SiO2 layers doped with Hf by ion-implantation. Hf was mobile under the focused electron beam in the asimplanted samples. After annealing for 5 min at 1200 °C, clusters of crystalline HfO2 were observed that were a few nm in size and surrounded by residual Hf that had remained trapped in the SiO2. Hf was not mobile under the electron beam in the annealed samples. Further annealing caused an expansion of the SiO2 that was damaged by ionimplantation. Hf rearrangement was confined to the ion beam damaged regions of the SiO2 layer. No diffusion of Hf into the undamaged SiO2 was observed. The implications of the results for complementary metal-oxide-semiconductor transistors with HfO2 gate dielectrics are discussed

An efficient Fredholm method for calculation of highly excited states of billiards

A numerically efficient Fredholm formulation of the billiard problem is presented. The standard solution in the framework of the boundary integral method in terms of a search for roots of a secular determinant is reviewed first. We next reformulate the singularity condition in terms of a flow in the space of an auxiliary one-parameter family of eigenproblems and argue that the eigenvalues and eigenfunctions are analytic functions within a certain domain. Based on this analytic behavior we present a numerical algorithm to compute a range of billiard eigenvalues and associated eigenvectors by only two diagonalizations.Comment: 15 pages, 10 figures; included systematic study of accuracy with 2 new figures, movie to Fig. 4, http://www.quantumchaos.de/Media/0703030media.av

Fresnel filtering in lasing emission from scarred modes of wave-chaotic optical resonators

We study lasing emission from asymmetric resonant cavity (ARC) GaN micro-lasers. By comparing far-field intensity patterns with images of the micro-laser we find that the lasing modes are concentrated on three-bounce unstable periodic ray orbits, i.e. the modes are scarred. The high-intensity emission directions of these scarred modes are completely different from those predicted by applying Snell's law to the ray orbit. This effect is due to the process of ``Fresnel filtering'' which occurs when a beam of finite angular spread is incident at the critical angle for total internal reflection.Comment: 4 pages, 3 figures (eps), RevTeX 3.1, submitted to Phys. Rev. Lett; corrected a minor (transcription) erro

Structure and Sodium Ion Dynamics in Sodium Strontium Silicate Investigated by Multinuclear Solid-State NMR

© 2016 American Chemical Society.The high oxide ion conductivity of the proposed sodium strontium silicate ion conductors Sr0.55Na0.45SiO2.775 (>10-2 S·cm-1 at 525 °C) and its unusual alkali metal substitution strategy have been extensively questioned in the literature. Here, we present a comprehensive understanding of the structure of this material using a combination of XRD and multinuclear 17O, 23Na, and 29Si solid-state NMR spectroscopy data and a detailed investigation of the Na ion dynamics by high temperature 23Na NMR line shape analysis and relaxation rates measurements. Both 23Na and 29Si NMR spectra demonstrate the absence of Na doping in strontium silicate SrSiO3 and the presence of an amorphous phase identified as Na2O·2SiO2 glass as the Na-containing product. Devitrification at 800 °C yields crystallization of the Na2O·2SiO2 glass into the known crystalline α-Na2Si2O5 phase which was positively identified by its XRD pattern and the extensive and clear 17O, 23Na, and 29Si NMR fingerprints. High temperature 23Na NMR reveals that the Na ions are mobile in the Na2O·2SiO2 amorphous component below its glass transition temperature (∼450 °C). In contrast, 23Na NMR data obtained on the crystalline α-Na2Si2O5 shows limited Na dynamics below ∼650 °C, and this result explains the large discrepancy in the conductivity observed in the literature which strongly depends on the thermal history of the Sr0.55Na0.45SiO2.775 material. These insights demonstrate that the high conductivity observed in Sr0.55Na0.45SiO2.775 is due to Na conduction in the Na2O·2SiO2 glass, and this motivates the quest for the discovery of low temperature fast ion conductors in noncrystalline solids

Dynamical Tunneling in Mixed Systems

We study quantum-mechanical tunneling in mixed dynamical systems between symmetry-related phase space tori separated by a chaotic layer. Considering e.g. the annular billiard we decompose tunneling-related energy splittings and shifts into sums over paths in phase space. We show that tunneling transport is dominated by chaos-assisted paths that tunnel into and out of the chaotic layer via the ``beach'' regions sandwiched between the regular islands and the chaotic sea. Level splittings are shown to fluctuate on two scales as functions of energy or an external parameter: they display a dense sequence of peaks due to resonances with states supported by the chaotic sea, overlaid on top of slow modulations arising from resonances with states supported by the ``beaches''. We obtain analytic expressions which enable us to assess the relative importance of tunneling amplitudes into the chaotic sea vs. its internal transport properties. Finally, we average over the statistics of the chaotic region, and derive the asymptotic tail of the splitting distribution function under rather general assumptions concerning the fluctuation properties of chaotic states.Comment: 28 pages, Latex, 16 EPS figure