Phase recurrences and metastability in a one-dimensional solid

The inverse localization length α (and hence resistance) of a one-dimensional disordered solid can be expressed in terms of a cumulative phase ε which obeys a nonlinear finite-difference equation. We examine this equation in the limit of zero disorder and obtain an expression for probability distribution P(ε). In the band-gap region, there is a stable fixed point leading to a nonzero α. At discrete points within a band there are metastable attractors with period ≥ 2 which for a small amount of disorder can lead to anomalies in α