Critical energies in random palindrome models

We investigate the occurrence of critical energies - where the Lyapunov exponent vanishes--in random Schroedinger operators when the potentials have some local order, which we call random palindrome models. We give necessary and sufficient conditions for the presence of such critical energies: the commutativity of finite word elliptic transfer matrices. Finally, we perform some numerical calculations of the Lyapunov exponents showing their behavior near the critical energies and the respective time evolution of an initially localized wave packet, obtaining the exponent ruling the algebraic growth of the second momentum. We also consider special random palindrome models with one-letter bounded gap property; the transport effects of such long range order are showed numerically