Higher-order <Emphasis Type="Bold">?</Emphasis> corrections in the semiclassical quantization of chaotic billiards

In the periodic orbit quantization of physical systems, usually only the leading-order ? contribution to the density of states is considered. Therefore, by construction, the eigenvalues following from semiclassical trace formulae generally agree with the exact quantum ones only to lowest order of ?. In different theoretical work the trace formulae have been extended to higher orders of ?. The problem remains, however, how to actually calculate eigenvalues from the extended trace formulae since, even with ? corrections included, the periodic orbit sums still do not converge in the physical domain. For lowest-order semiclassical trace formulae the convergence problem can be elegantly, and universally, circumvented by application of the technique of harmonic inversion. In this paper we show how, for general scaling chaotic systems, also higher-order ? corrections to the Gutzwiller formula can be included in the harmonic inversion scheme, and demonstrate that corrected semiclassical eigenvalues can be calculated despite the convergence problem. The method is applied to the open three-disk scattering system, as a prototype of a chaotic system. Received 10 September 2001 and Received in final form 3 January 2002     

Coaxial configuration of the dielectric Cherenkov maser

The linearized Lorentz force, continuity equation, and Maxwell's equations are used to calculate the system dispersion relation for a coaxial configuration of the dielectric Cherenkov maser. The system consists of two coaxial conductors lined with dielectric and an annular relativistic electron beam, which propagates between the two liners. The dispersion relation for the beam and dielectric-lined coaxial waveguide structure and the no-beam system that describes the dependence of the generated frequency on the coaxial waveguide parameters are presented. Using the linearized dispersion relation, the growth rate for the beam-TM_0n waveguide mode instability is calculated in the strong-coupling tenuous beam limit     

Cell scale self-organisation in the OFC model for earthquake dynamics

We examine the cell scale self organising mechanisms in the Olami Feder Christensen (OFC) model that have the potential to generate critical behaviour. In particular we demonstrate how spatial organisation and quantisation of strain distributions occurs, why temporal strain fluctuations are minimised as the local strain conservation factor, β → 1.0, and how the strain distributions are dependent upon the lattice geometry employed. The origin of the self-organising behaviour can be divided into two regimes; at low β where no re-rupturing of cells occurs and for higher β where the probability of re-rupturing becomes increasingly significant. The presence or absence of the re-rupturing mechanism leads to different system optimisations, tending from spatially well ordered strain domains at intermediate β to a spatially rough strain field but a temporally stationary, memory less strain distribution at β = 1. The construction of the Markov chain demonstrates that degeneracy of the transitions is a primary control on transition probabilities at β = 1. The stationary state occupation is controlled by transition degeneracy, local correlations and mean residence times.     

Resonance widths in open microwave cavities studied by harmonic inversion

From the measurement of a reflection spectrum of an open microwave cavity, the poles of the scattering matrix in the complex plane have been determined. The resonances have been extracted by means of the harmonic inversion method. By this, it became possible to resolve the resonances in a regime where the linewidths exceed the mean level spacing up to a factor of 10, a value inaccessible in experiments up to now. The obtained experimental distributions of linewidths were found to be in perfect agreement with predictions from random matrix theory when wall absorption and fluctuations caused by couplings to additional channels are considered.