The CPA solution of the anomalous Lyapunov exponent for disordered binary chains

Abstract:

The Coherent Potential Approximation (CPA) self-consistent equation is calculated for a binary disordered chain introducing a simple transformation. The transformation reduces the CPA equation to a cubic polynomial whose complex roots are related to the Green function and their relation to the complex Lyapunov exponent is also established. This solution fruitfully captures essential aspects of the well-known anomalous scaling behaviors in a different and advantageous way. It is found that the anomalous behavior is strongly effected by the nature of these roots. A small disorder expansion is carried out for comparison with the previous weak disorder calculations. We found that the CPA reproduced the anomalous behavior of the exact calculations.