Tulio O. Carvalho and Cesar R. de Oliveira
Critical energies in random palindrome models
(540K, ps)

ABSTRACT.  We investigate the occurrence of critical energies -- where the Lyapunov exponent vanishes -- 
in random Schr\"odinger operators when the potential have some local order, which we call {\em 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 behaviour 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.