On the possibility of experimentally testing some predictions of the theory of localization

Spatial nonlocality (dispersion) of transport equations leads to a nonlinear dependence of the voltage drop $U$ on the distance between the points of voltage measurement. For this reason, the results of conventional two-probe measurements of conductivity substantially depend on the relationship between the linear dimensions of the sample $L$ and the characteristic length of spatial dispersion $R$ of the generalized diffusion coefficient $D(q, \omega)$. This makes it possible to obtain information on the character of spatial nonlocality of $D(q, \omega)$ in the vicinity of the Anderson transition and, in particular, on the magnitude of the correlation multifractal dimension $D_2$ of electron wave functions near the mobility edge.