### Getting a Foot into Many-Body Quantum Chaos

Mathematical Physics Seminar

23rd February 2018, 2:00 pm – 12:00 am

Howard House, 4th Floor Seminar Room

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.

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