Uniform Positivity of the Lyapunov Exponent for Monotone Potentials Generated by the Doubling Map
Year: 2024
Type: article
Abstract: We show that for any doubling map generated $$C^1$$ C 1 monotone potential with derivative uniformly bounded away from zero and infinity, the Lyapunov exponent of the associated Schrödinger operators is bounded below by $$\log {\lambda }-C$$ log λ - C for all energies, where C depends only on the potential. In particular, it answers an open question [D, Problem 5] raised by D. Damanik.
Author: Zhenghe Zhang
Institution: University of California, Riverside
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $2,890
OpenAlex ID: W4402540400