In the quantum many-body systems that have a dense spectra of excited states (compound nuclei, rare-earth atoms, molecules, clusters, ''quantum dots'' in solids, spin systems) weak perturbation can be strongly enhanced. An example of a compound nucleus is considered in detail. The factor of enhancement of parity nonconserving (PNC) effects in neutron-nucleus reactions exceeds 100. Calculations of the mean square value of the matrix element between compound states show that the statistical mechanism explains the ''random'' part of the dynamical enhancement. Possible mechanisms of regular effect are considered. It is shown that the valence mechanism (PNC effect due to single-particle component of compound states and potential scattering) contradicts the results of measurements of PNC effects in low level density nuclei (n + 124Sn, Pb-207, etc.). Calculations show also that the contribution of the valence mechanism is 100 times smaller than the observed PNC effect in Th-232. Any enhancement due to collective excitations (giant resonances) is also excluded. The limit on the strength of the neutron PNC weak potential is extracted from the measurements of neutron spin rotation in 124Sn: \g(n)\ less-than-or-equal-to 1 or \epsilon\ less-than-or-equal-to 10(-8). Possible mechanism of correlations among compound states components (''quasielastic'' mechanism) is considered.
