THE NUCLEAR SHELL-MODEL AS A TESTING GROUND FOR MANY-BODY QUANTUM CHAOS

Atomic nuclei analyzed in the framework of the shell model provide a g ood example of a many-body quantum system with strong interactions bet ween its constituents. As excitation energy and level density increase , the system evolves in the direction of very complicated (''stochasti c'') dynamics. Energy levels and stationary wave functions obtained in realistic shell-model calculations are studied from the viewpoint of signatures of quantum chaos and complexity. The standard characteristi cs of local level statistics, such as nearest level spacing distributi on or spectral rigidity, manifest chaoticity which agrees with the GOE predictions. Going beyond that, we analyze the structure of the eigen functions and the distribution function of the eigenvector components using basis-dependent quantitative criteria such as information entrop y. The degree of complexity is shown to be a smooth function of excita tion energy. The representation dependence provides additional physica l information on the interrelation between the eigenbasis and the repr esentation basis. The exceptional role of the mean field basis is disc ussed. The spreading width and the shape of the strength function of t he original simple states are also studied. The generic wave functions in the chaotic region have similar observable properties which can be characterized by the average single-particle occupation numbers. Agre ement with the Fermi-Dirac distribution manifests the correspondence b etween chaotic dynamics and thermalization. The information entropy in the mean held basis gives an equivalent temperature scale which confi rms this correspondence. Pairing correlations display a phase transiti on to the normal state with a long tail of fluctuational enhancement a bove the level expected for a heated Fermi gas.