Statistics of rare events in disordered conductors

Asymptotic behavior of the distribution functions of eigenstate intensities and current relaxation times in disordered conductors is studied in the weak disorder limit by means of an optimal fluctuation method. It is argued that this method is more appropriate for the study of rare events in three-dimensional conductors than the approaches based on nonlinear {σ} models because it is capable of correctly handling fluctuations of the random potential with large amplitude as well as the short-scale structure of the corresponding solutions of the Schr\"odinger equation. It also helps to clarify the physical picture of such events in one and two dimensions. For two- and three-dimensional conductors, the asymptotics of the distribution functions obtained by this method differ, in some cases significantly, from previously established results.