Maram Akila

Getting a Foot into Many-Body Quantum Chaos

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.