A note on Lyapunov exponents of deterministic strongly mixing potentials

Jean Bourgain, Eric Bourgain-Chang

Type: Article

Publication Date: 2015-04-20

Citations: 6

DOI: https://doi.org/10.4171/jst/89

Abstract

In this Note, we consider 1D lattice Schrödinger operators with deterministic strongly mixing potentials as studied in [3] and [2] with very small coupling. We describe a scheme to establish positivity of the Lyapunov exponent from a statement at some fixed scale. The required input may then be derived from Furstenberg theory, if the underlying dynamics are sufficiently mixing, or verified directly by numerical means.

Locations

Journal of Spectral Theory - View - PDF
arXiv (Cornell University) - View - PDF

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