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.