Lyapunov exponents and localization phenomena in multi-coupled nearly periodic systems

Lyapunov exponents of a system wave transfer matrix are employed to analyze localization in multi-coupled (and as a special case, mono-coupled) disordered periodic linear systems. An algorithm due to Wolf et al. [1] is used to calculate the Lyapunov exponents numerically. Perturbation techniques are used to find approximate Lyapunov exponents for the case of weak disorder. Two examples are presented. The largest Lyapunov exponent is calculated for a representative mono-coupled system, and compared with localization factors found by Monte Carlo methods, as well as with the approximated localization factors. This example is used to discuss computational issues. The Lyapunov exponents are also calculated for an example of a bi-coupled system, and compared with wave amplitude decay found in a single realization of the disordered system. The physical significance of the Lyapunov exponents for a multi-coupled nearly periodic system is discussed.