Phase recurrences and metastability in a one-dimensional solid

The inverse localization length ± (and hence resistance) of a one-dimensional disordered solid can be expressed in terms of a cumulative phase 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(). In the band-gap region, there is a stable fixed point leading to a nonzero ±. 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 ±.