2,944 research outputs found
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 rather than scales with
. 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
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