2000/05/15 by Vadim Kostrykin, Robert Schrader · 1 citation
Mathematics · Physics and Astronomy · #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #Spectral Theory in Mathematical Physics #math-ph #math.MP #msc:34F05 #msc:60H25 #msc:82B44
paper · pdf · doi:10.1088/0305-4470/33/46/306
published as J. Phys. A: Math. Gen. 33 (2000) 8231 - 8240 · 9 pages
arxiv created 2000/05/15 · openalex publication_date 2000/11/09 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30
In this paper we prove an upper bound for the Lyapunov exponent γ( E ) and a two-sided bound for the integrated density of states N ( E ) at an arbitrary energy E >0 of random Schrödinger operators in one dimension. These Schrödinger operators are given by potentials of identical shape centred at every lattice site but with non-overlapping supports and with randomly varying coupling constants. Both types of bounds only involve scattering data for the single-site potential. They show, in particular, that both γ( E ) and N ( E )-( E ) 1/2 /π decay at infinity at least like 1/( E ) 1/2 . As an example we consider the random Kronig-Penney model.