S. Jitomirskaya, H. Schulz-Baldes, G. Stolz
Delocalization in random polymer models
(428K, postscipt)

ABSTRACT.  A random polymer model is a one-dimensional Jacobi matrix 
randomly composed of two finite building blocks. If the two 
associated transfer matrices commute, the corresponding energy is 
called critical. Such critical energies appear in physical models, an 
example being the widely studied random dimer model. It is proven that 
the Lyapunov exponent vanishes quadratically at a generic critical 
energy and that the density of states is positive there. Large 
deviation estimates around these asymptotics allow to prove optimal 
lower bounds on quantum transport, showing that it is almost surely 
overdiffusive even though the models are known to have pure-point 
spectrum with exponentially localized eigenstates for almost every 
configuration of the polymers. Furthermore, the level spacing is 
shown to be regular at the critical energy.