In the limit of small ħ, e.g. short wavelengths, semi-classical theory provides a connection between the spectrum of a quantum mechanical system and the periodic orbits of its classical counter part. While this is well established for systems with few degrees of freedom the extension to many-body systems is challenging as the system dimension N  turns into an additional large parameter. For a long chain of interacting kicked tops short time spectral information may be obtained using a duality relation between the temporal and spatial evolution. This allows a direct comparison to the classical periodic orbits of the system. It reveals that this class of system possesses non-isolated orbit manifolds whose contributions to the trace formula are strongly dominant. For large N their presence leads to remarkably strong spectral fluctuations, which are not recovered by conventional semi-classical theory.

* Maram Akila, Universität Duisburg-Essen