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We report on the comprehensive numerical study of the fluctuation andcorrelation properties of wave functions in three-dimensional mesoscopicdiffusive conductors. Several large sets of nanoscale samples with finitemetallic conductance, modeled by an Anderson model with different strengths ofdiagonal box disorder, have been generated in order to investigate both smalland large deviations (as well as the connection between them) of thedistribution function of eigenstate amplitudes from the universal prediction ofrandom matrix theory. We find that small, weak localization-type, deviationscontain both diffusive contributions (determined by the bulk and boundaryconditions dependent terms) and ballistic ones which are generated by electrondynamics below the length scale set by the mean free path ell. By relating theextracted parameters of the functional form of nonperturbative deviations(``far tails'') to the exactly calculated transport properties of mesoscopicconductors, we compare our findings based on the full solution of theSchrodinger equation to different approximative analytical treatments. We findthat statistics in the far tail can be explained by the exp-log-cubeasymptotics (convincingly refuting the log-normal alternative), but withparameters whose dependence on ell is linear and, therefore, expected to bedominated by ballistic effects. It is demonstrated that both small deviationsand far tails depend explicitly on the sample size--the remaining puzzle thenis the evolution of the far tail parameters with the size of the conductorsince short-scale physics is supposedly insensitive to the sample boundaries.Comment: 13 pages, 9 embedded EPS figures, expanded discussion (with extra one  figure) on small size effec

Structure of quantum disordered wave functions: weak localization, far tails, and mesoscopic transport