Numerical study of scars in a chaotic billiard

We study numerically the scaling properties of scars in stadium billiard. Using the semiclassical criterion, we have searched systematically the scars of the same type through a very wide range, from ground state to as high as the 1 millionth state. We have analyzed the integrated probability density along the periodic orbit. The numerical results confirm that the average intensity of certain types of scars is independent of $\hbar$ rather than scales with $\sqrt{\hbar}$. Our findings confirm the theoretical predictions of Robnik (1989).Comment: 7 pages in Revtex 3.1, 5 PS figures available upon request. To appear in Phys. Rev. E, Vol. 55, No. 5, 199

Elliptic Quantum Billiard

The exact and semiclassical quantum mechanics of the elliptic billiard is investigated. The classical system is integrable and exhibits a separatrix, dividing the phasespace into regions of oscillatory and rotational motion. The classical separability carries over to quantum mechanics, and the Schr\"odinger equation is shown to be equivalent to the spheroidal wave equation. The quantum eigenvalues show a clear pattern when transformed into the classical action space. The implication of the separatrix on the wave functions is illustrated. A uniform WKB quantization taking into account complex orbits is shown to be adequate for the semiclassical quantization in the presence of a separatrix. The pattern of states in classical action space is nicely explained by this quantization procedure. We extract an effective Maslov phase varying smoothly on the energy surface, which is used to modify the Berry-Tabor trace formula, resulting in a summation over non-periodic orbits. This modified trace formula produces the correct number of states, even close to the separatrix. The Fourier transform of the density of states is explained in terms of classical orbits, and the amplitude and form of the different kinds of peaks is analytically calculated.Comment: 33 pages, Latex2e, 19 figures,macros: epsfig, amssymb, amstext, submitted to Annals of Physic

Structure of Quantum Chaotic Wavefunctions: Ergodicity, Localization, and Transport

We discuss recent developments in the study of quantum wavefunctions and transport in classically ergodic systems. Surprisingly, short-time classical dynamics leaves permanent imprints on long-time and stationary quantum behavior, which are absent from the long-time classical motion. These imprints can lead to quantum behavior on single-wavelength or single-channel scales which are very different from random matrix theory expectations. Robust and quantitative predictions are obtained using semiclassical methods. Applications to wavefunction intensity statistics and to resonances in open systems are discussed.Comment: 8 pages, including 2 figures; talk given at `Dynamics of Complex Systems' workshop in Dresden, 1999 and submitted for conference proceedings to appear in Physica

New Iridopteridalean from the Devonian of Venezuela

The first permineralized Devonian plant fossil is reported here from the Middle or lowermost Upper Devonian of western Venezuela. Two orders of branching plus dichotomous ultimate appendages are known from compressions. A branch of the first order contains a mesarch actinostele with six primary xylem ribs, each with a protoxylem strand near the rib tip (peripheral edge). Compressions of first‐order branches demonstrate three equally spaced lateral organs (higher‐order branches and dichotomous ultimate appendages) attached in whorls, with every other whorl displaying laterals placed in identical orientations and intermediate whorls with laterals offset exactly halfway between. The permineralized specimen partly confirms the presence of whorls and indicates that vascular traces are derived from every other primary xylem rib in each whorl, with intervening ribs producing traces in whorls above and below. Second‐order branches have only ultimate appendages that are attached in a nonwhorled, three‐dimensional, or alternate arrangement. Sterile ultimate appendages dichotomize up to six times and terminate in recurved tips. Fertile ultimate appendages have paired sporangia distally; these sporangia are often upright but are otherwise similar to sterile examples. The stelar anatomy demonstrates an iridopteridalean affinity for these plants, resembling Arachnoxylon kopfii Read in arrangement and number of xylem ribs although it is smaller in size. Among iridopteridaleans, the branching pattern and mode of trace departure is unique, and we therefore name the plant Compsocradus laevigatus gen. et sp. nov

A tree without leaves

The puzzle presented by the famous stumps of Gilboa, New York, finds a solution in the discovery of two fossil specimens that allow the entire structure of these early trees to be reconstructed

Global versus local billiard level dynamics: The limits of universality

Level dynamics measurements have been performed in a Sinai microwave billiard as a function of a single length, as well as in rectangular billiards with randomly distributed disks as a function of the position of one disk. In the first case the field distribution is changed globally, and velocity distributions and autocorrelation functions are well described by universal functions derived by Simons and Altshuler. In the second case the field distribution is changed locally. Here another type of universal correlations is observed. It can be derived under the assumption that chaotic wave functions may be described by a random superposition of plane waves

Incorporating ecological and evolutionary processes into continental-scale conservation planning

Systematic conservation planning research has focused on designing systems of conservation areas that efficiently protect a comprehensive and representative set of species and habitats. Recently, there has been an emphasis on improving the adequacy of conservation area design to promote the persistence and future generation of biodiversity. Few studies have explored incorporating ecological and evolutionary processes into conservation planning assessments. Biodiversity in Australia is maintained and generated by numerous ecological and evolutionary processes at various spatial and temporal scales. We accommodated ecological and evolutionary processes in four ways: (1) using sub-catchments as planning units to facilitate the protection of the integrity and function of ecosystem processes occurring on a sub-catchment scale; (2) targeting one type of ecological refugia, drought refugia, which are critical for the persistence of many species during widespread drought; (3) targeting one type of evolutionary refugia which are important for maintaining and generating unique biota during long-term climatic changes; and (4) preferentially grouping priority areas along vegetated waterways to account for the importance of connected waterways and associated riparian areas in maintaining processes. We identified drought refugia, areas of relatively high and regular herbage production in arid and semiarid Australia, from estimates of gross primary productivity derived from satellite data. In this paper, we combined the novel incorporation of these processes with a more traditional framework of efficiently representing a comprehensive sample of biodiversity to identify spatial priorities across Australia. We explored the trade-offs between economic costs, representation targets, and connectivity. Priority areas that considered ecological and evolutionary processes were more connected along vegetated waterways and were identified for a small increase in economic cost. Priority areas for conservation investment are more likely to have long-term benefits to biodiversity if ecological and evolutionary processes are considered in their identification

On Nonlinear Functionals of Random Spherical Eigenfunctions

We prove Central Limit Theorems and Stein-like bounds for the asymptotic behaviour of nonlinear functionals of spherical Gaussian eigenfunctions. Our investigation combine asymptotic analysis of higher order moments for Legendre polynomials and, in addition, recent results on Malliavin calculus and Total Variation bounds for Gaussian subordinated fields. We discuss application to geometric functionals like the Defect and invariant statistics, e.g. polyspectra of isotropic spherical random fields. Both of these have relevance for applications, especially in an astrophysical environment.Comment: 24 page