Nearly Localised States in Weakly Disordered Conductors. II. Beyond Diffusion Approximation

We use optimal fluctuation method for a new ballistic $\sigma$-model to study the long time dispersion of conductance $G(t)$ of a mesoscopic sample. In the long time limit the conductance of a $d$-dimensional sample decays as $\exp (-A \ln^d t )$. At shorter times the new results match those in our previous paper. It is found that at very long times the diffraction effects are important and the ballistic treatment is not valid. We also suggest a physical picture of trapping.