Semiclassical Quantisation Using Diffractive Orbits

Diffraction, in the context of semiclassical mechanics, describes the manner in which quantum mechanics smooths over discontinuities in the classical mechanics. An important example is a billiard with sharp corners; its semiclassical quantisation requires the inclusion of diffractive periodic orbits in addition to classical periodic orbits. In this paper we construct the corresponding zeta function and apply it to a scattering problem which has only diffractive periodic orbits. We find that the resonances are accurately given by the zeros of the diffractive zeta function.Comment: Revtex document. Submitted to PRL. Figures available on reques

Semiclassical Quantization by Pade Approximant to Periodic Orbit Sums

Periodic orbit quantization requires an analytic continuation of non-convergent semiclassical trace formulae. We propose a method for semiclassical quantization based upon the Pade approximant to the periodic orbit sums. The Pade approximant allows the re-summation of the typically exponentially divergent periodic orbit terms. The technique does not depend on the existence of a symbolic dynamics and can be applied to both bound and open systems. Numerical results are presented for two different systems with chaotic and regular classical dynamics, viz. the three-disk scattering system and the circle billiard.Comment: 7 pages, 3 figures, submitted to Europhys. Let

Decimation and Harmonic Inversion of Periodic Orbit Signals

We present and compare three generically applicable signal processing methods for periodic orbit quantization via harmonic inversion of semiclassical recurrence functions. In a first step of each method, a band-limited decimated periodic orbit signal is obtained by analytical frequency windowing of the periodic orbit sum. In a second step, the frequencies and amplitudes of the decimated signal are determined by either Decimated Linear Predictor, Decimated Pade Approximant, or Decimated Signal Diagonalization. These techniques, which would have been numerically unstable without the windowing, provide numerically more accurate semiclassical spectra than does the filter-diagonalization method.Comment: 22 pages, 3 figures, submitted to J. Phys.

Molecules in external fields: a semiclassical analysis

We undertake a semiclassical analysis of the spectral properties (modulations of photoabsorption spectra, energy level statistics) of a simple Rydberg molecule in static fields within the framework of Closed-Orbit/Periodic-Orbit theories. We conclude that in addition to the usual classically allowed orbits one must consider classically forbidden diffractive paths. Further, the molecule brings in a new type of 'inelastic' diffractive trajectory, different from the usual 'elastic' diffractive orbits encountered in previous studies of atomic and analogous systems such as billiards with point-scatterers. The relative importance of inelastic versus elastic diffraction is quantified by merging the usual Closed Orbit theory framework with molecular quantum defect theory.Comment: 4 pages, 3 figure

Créatinine plasmatique et sensibilité du porc au syndrome d'hyperthermie maligne-Relations avec deux enzymes du globule rouge (PHI et 6-PGD)

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Dilatonic global strings

We examine the field equations of a self-gravitating global string in low energy superstring gravity, allowing for an arbitrary coupling of the global string to the dilaton. Massive and massless dilatons are considered. For the massive dilaton the spacetime is similar to the recently discovered non-singular time-dependent Einstein self-gravitating global string, but the massless dilaton generically gives a singular spacetime, even allowing for time-dependence. We also demonstrate a time-dependent non-singular string/anti-string configuration, in which the string pair causes a compactification of two of the spatial dimensions, albeit on a very large scale.Comment: 18 pages RevTeX, 3 figures, references amende