Delocalization in random polymer models

Jitomirskaya S, Schulz-Baldes H, Stolz G (2003)

Publication Type: Journal article

Publication year: 2003

Journal

Communications in Mathematical Physics Springer Verlag (Germany)

Publisher: Springer Verlag (Germany)

Book Volume: 233

Pages Range: 27-48

URI: http://de.arxiv.org/abs/math-ph/0405024

DOI: 10.1007/s00220-002-0757-5

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.

Authors with CRIS profile

Hermann Schulz-Baldes Professur für Mathematik (Mathematische Physik)

Involved external institutions

University of California Irvine US United States (USA) (US) University of Alabama at Birmingham (UAB) US United States (USA) (US)

How to cite

APA:

Jitomirskaya, S., Schulz-Baldes, H., & Stolz, G. (2003). Delocalization in random polymer models. Communications in Mathematical Physics, 233, 27-48. https://dx.doi.org/10.1007/s00220-002-0757-5

MLA:

Jitomirskaya, Svetlana, Hermann Schulz-Baldes, and Gunter Stolz. "Delocalization in random polymer models." Communications in Mathematical Physics 233 (2003): 27-48.

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