Jitomirskaya, S.; Schulz-Baldes, H.; Stolz, G. Delocalization in random polymer models. (English) Zbl 1013.82027 Commun. Math. Phys. 233, No. 1, 27-48 (2003). Summary: 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. Cited in 54 Documents MSC: 82D60 Statistical mechanics of polymers 60H30 Applications of stochastic analysis (to PDEs, etc.) Keywords:random polymer model; random dimer model; large deviation estimates; quantum transport PDFBibTeX XMLCite \textit{S. Jitomirskaya} et al., Commun. Math. Phys. 233, No. 1, 27--48 (2003; Zbl 1013.82027) Full Text: DOI arXiv