Maximal fluctuations — A new phenomenon in disordered systems

Rigorous results for 1D systems combined with more intuitive results for higher dimensions indicate that there is a universal theorem on fluctuations in the transmission coefficient of disordered systems. Recognising that the transmission coefficient for waves traversing a disordered system can be no greater than unity, and no less than zero, the theorem states that in each channel either |t|2≈1 or |t|2≈0, with the probability set by the conductance. This is the most extreme excursion of the distribution possible, hence the name “maximal fluctuations”. The effect is distinct from the universal fluctuations which refer to the sensitivity of t to changes in the medium.