Low-temperature resistance fluctuation in disordered conductors

At low temperatures the electron elastic mean free path in a disordered conductor can become much smaller than the inelastic mean free path (or more precisely the Thouless length) which in turn may be comparable with, or even larger than the sample size. In this quantum regime, the electrical resistance is dominated by the coherence effects that eventuallylead to the now well-known weak or strong localization. Yet another remarkable manifestation of the quantum coherence is that it makes the resistance non-additive in series and, more importantly, non-self averaging, thus replacing the classical Ohm's law with a quantum Ohm's law describing statistical fluctuations. In this paper, we report on some of our recent work on the statistics of these "Sinai" fluctuations of residual resistance for one and higher space dimensions (d). In particular we show that the physics at the mobility edge may be dominated by these fluctuations. We also show that an external electric field tends to harness these fluctuations. Some observational consequences such as l/$f-noise$ at low temperatures are discussed. Our approach is based on invariant imbedding extended by us for this purpose