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.