Semiclassical Analysis of the Supershell Effect in Reflection-Asymmetric Superdeformed Oscillator

An oscillatory pattern in the smoothed quantum spectrum, which is unique for single-particle motions in a reflection-asymmetric superdeformed oscillator potential, is investigated by means of the semiclassical theory of shell structure. Clear correspondence between the oscillating components of the smoothed level density and the classical periodic orbits is found. It is shown that an interference effect between two families of the short periodic orbits, called supershell effect, develops with increasing reflection-asymmetric deformations. Possible origins of this enhancement phenomena as well as quantum signatures of period-multipling bifurcations are discussed in connection with stabilities of the classical periodic orbits.Comment: 27 pages, REVTeX, 12 postscript figures are available from the author upon reques

Microscopic chaos and diffusion

We investigate the connections between microscopic chaos, defined on a dynamical level and arising from collisions between molecules, and diffusion, characterized by a mean square displacement proportional to the time. We use a number of models involving a single particle moving in two dimensions and colliding with fixed scatterers. We find that a number of microscopically nonchaotic models exhibit diffusion, and that the standard methods of chaotic time series analysis are ill suited to the problem of distinguishing between chaotic and nonchaotic microscopic dynamics. However, we show that periodic orbits play an important role in our models, in that their different properties in chaotic and nonchaotic systems can be used to distinguish such systems at the level of time series analysis, and in systems with absorbing boundaries. Our findings are relevant to experiments aimed at verifying the existence of chaoticity and related dynamical properties on a microscopic level in diffusive systems.Comment: 28 pages revtex, 14 figures incorporated with epsfig; see also chao-dyn/9904041; revised to clarify the definition of chaos and include discussion of a mixed model with both square and circular scatterer

Magnetic edge states

Magnetic edge states are responsible for various phenomena of magneto-transport. Their importance is due to the fact that, unlike the bulk of the eigenstates in a magnetic system, they carry electric current along the boundary of a confined domain. Edge states can exist both as interior (quantum dot) and exterior (anti-dot) states. In the present report we develop a consistent and practical spectral theory for the edge states encountered in magnetic billiards. It provides an objective definition for the notion of edge states, is applicable for interior and exterior problems, facilitates efficient quantization schemes, and forms a convenient starting point for both the semiclassical description and the statistical analysis. After elaborating these topics we use the semiclassical spectral theory to uncover nontrivial spectral correlations between the interior and the exterior edge states. We show that they are the quantum manifestation of a classical duality between the trajectories in an interior and an exterior magnetic billiard.Comment: 170 pages, 48 figures (high quality version available at http://www.klaus-hornberger.de

Uniform approximation for diffractive contributions to the trace formula in billiard systems

We derive contributions to the trace formula for the spectral density accounting for the role of diffractive orbits in two-dimensional billiard systems with corners. This is achieved by using the exact Sommerfeld solution for the Green function of a wedge. We obtain a uniformly valid formula which interpolates between formerly separate approaches (the geometrical theory of diffraction and Gutzwiller's trace formula). It yields excellent numerical agreement with exact quantum results, also in cases where other methods fail.Comment: LaTeX, 41 pages including 12 PostScript figures, submitted to Phys. Rev.