LYAPUNOV EXPONENTS AND LOCALIZATION PHENOMENA IN MULTI-COUPLED NEARLYPERIODIC-SYSTEMS

Lyapunov exponents of a system wave transfer matrix are employed to an alyze localization in multi-coupled (and as a special case, mono-coupl ed) disordered periodic linear systems. An algorithm due to Wolf et al . [1] is used to calculate the Lyapunov exponents numerically. Perturb ation techniques are used to find approximate Lyapunov exponents for t he case of weak disorder. Two examples are presented. The largest Lyap unov exponent is calculated for a representative mono-coupled system, and compared with localization factors found by Monte Carlo methods, a s 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 hi-coupled system, and compared with wa ve amplitude decay found in a single realization of the disordered sys tem. The physical significance of the Lyapunov exponents for a multi-c oupled nearly periodic system is discussed.