Year: 2025
Type: article
Abstract: We consider the Schrödinger operator on the quantum graph whose edges connect the points of $${{\mathbb {Z}}}$$ Z . The numbers of the edges connecting two consecutive points n and $$n+1$$ n + 1 are read along the orbits of a shift of finite type. We prove that the Lyapunov exponent is potitive for energies E that do not belong to a discrete subset of $$[0,\infty )$$ [ 0 , ∞ ) . The number of points E of this subset in $$[(\pi (j-1))^2, (\pi j)^2]$$ [ ( π ( j - 1 ) ) 2 , ( π j ) 2 ] is the same for all $$j\in {{\mathbb {N}}}$$ j ∈ N .
Author: Oleg Safronov
Institution: University of North Carolina at Charlotte
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,290
OpenAlex ID: W4413825928