Hamburg 2001 – scientific programme

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SYGS: 30 Jahre Gutzwiller Spurformel

SYGS VII: HV VII

SYGS VII.1: Invited Talk

Wednesday, March 28, 2001, 18:00–18:30, S6

The Gutzwiller Trace Formula for Quantum Systems With Spin — •Jens Bolte — Abteilung Theoretische Physik, Universität Ulm

The Gutzwiller trace formula provides a semiclassical approximation for the density of states of a quantum system in terms of classical periodic orbits. In its original form Gutzwiller derived the trace formula for quantum systems without spin. In this talk the modifications will be discussed that arise for quantum systems with both translational and spin degrees of freedom and which are either described by Pauli or Dirac operators. In addition, spectral densities weighted by expectation values of observables will be considered. It turns out that in all cases the semiclassical approximation yields sums over periodic orbits of the translational motion. Spin contributes via weight factors that take a spin precession along the translational orbits into account.