2019/12/03 by Bambusi, Dario, Zhao, Zhiyan · 1 citation
#FOS: Physical sciences #Mathematical Physics (math-ph)
paper · doi:10.48550/arxiv.1912.01528
Consider the one-dimensional discrete Schrödinger operator Hθ: (Hθ q)n=-(qn+1+qn-1)+ V(θ+nω) qn , n∈ Z , with ω∈ Rd Diophantine, and V a real-analytic function on Td=( R/2πZ)d. For V sufficiently small, we prove the dispersive estimate: for every ϕ∈ℓ1( Z), ‖ e^-\rm itHθϕ‖ℓ^∞ ≤ K0 \frac |lnε0|a(lnln(2+⟨ t⟩))2 d ⟨ t⟩\frac13 ‖ϕ‖ℓ1 , ⟨ t ⟩:=√(1+t2) , with a and K0 two absolute constants and ε0 an analytic norm of V. The estimate holds for every θ∈ Td.