Berry's ansatz in Fock space: beyond random matrix theory for many-body quantum chaos

Berry's ansatz of random superposition of vector basis to mimic the statistical properties of quantum states in classically chaotic systems, has been highly successfull for one-body systems. It is at the heart of the original justification for the eigenstate thermalisation hypothesis (ETH) for many-body quantum systems. We detail its use in many-body Fock space using recent developments in many-body semiclassical techniques for Bose Hubbard models. Quantitative predicitions for 2-point correlations in Fock space are given, which agree very well with numerics. This study highlights how semiclassical techniques can be efficient for many-body chaos beyond the universal regime of random matrix theory.