Communications in Mathematical Physics

, Volume 233, Issue 1, pp 27-48

First online:

Delocalization in Random Polymer Models

  • S. JitomirskayaAffiliated withDepartment of Mathematics, University of California at Irvine, Irvine, CA, 92697, USA.
  • , H. Schulz-BaldesAffiliated withFachbereich Mathematik, Technische Universität Berlin, 10623, Berlin, Germany.
  • , G. StolzAffiliated withDepartment of Mathematics, University of Alabama at Birmingham, Birmingham, Al, 35294 USA.

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 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.