Information entropy, chaos and complexity of the shell model eigenvectors

The energies and wave functions of stationary many-body states are analyzed to look for the signatures of quantum chaos. Realistic shell model calculations are performed in the JT-scheme for 12 particles in the sd-shell. Local level statistics are in perfect agreement with the GOE predictions whereas the eigenvectors show evidence for non-complete energy dependent chaoticity. The information entropy of individual eigenvectors turns out to be a convenient measure of degree of complexity of individual wave functions. We discuss the representation dependence and the sensitivity to the interaction strength. The exceptional role of the mean field basis is stressed.