Quantum chaos in many-body systems: what can we learn from the Ce atom?

Results of an extensive study of a real quantum chaotic many-body system – the Ce atom – are presented. We discuss the origins of the quantum chaotic behaviour of the system, analyse statistical and dynamical properties of the multi-particle chaotic eigenstates and consider matrix elements or transition amplitudes between them. We show that based on the universal properties of the chaotic eigenstates a statistical theory of finite few-particle systems with strong interaction can be developed. We also discuss such important physical effects as enhancement of weak perturbations in many-body quantum chaotic systems, distribution of single-particle occupation numbers and its deviations from the standard Fermi–Dirac shape, and ways of introducing statistical temperature-based description in such systems.