Heidelberg 1999 – scientific programme

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MP: Theoretische und Mathematische Grundlagen der Physik

MP 4: Hauptvortr
äge IV

MP 4.1: Invited Talk

Thursday, March 18, 1999, 14:00–14:45, MA1

Semiclassical methods in mixed systems and systems with diffraction — •Martin Sieber — Max-Planck-Institut für Physik komplexer Systeme, Noethnitzer Str. 38, 01187 Dresden

Semiclassical methods belong to the main tools for the investigation of highly excited quantum systems. They allow to approximate wave functions, energy spectra or scattering resonances in terms of classical trajectories. Besides yielding an accurate quantitative description they often allow simple physical interpretations of quantum phenomena.

Semiclassical approximations have been developed in detail for integrable or chaotic systems. In many systems these methods are, however, not sufficient. They have to be extended, for example, for the treatment of mixed system, that can show regular as well as chaotic behaviour, or for systems in which diffraction plays a role, for example in systems with magnetic flux lines. In these systems uniform approximations have to be applied that describe collective contributions of two or more trajectories. This is similar to the modification of geometrical optics in the vicinity of caustics. In my talk I want to give an overview on the application of uniform approximations for energy spectra in mixed systems and systems with diffractive effects.