TY - JOUR

T1 - Anderson localization for the almost Mathieu equation, III. Semi-uniform localization, continuity of gaps, and measure of the spectrum

AU - Jitomirskaya, Svetlana Ya

AU - Last, Yoram

PY - 1998

Y1 - 1998

N2 - We show that the almost Mathieu operator, (Hωλθψ)(η) = ψ(η+1) + ψ(η-1)+ λ cos(πωη+θ)ψ(η), has semi-uniform (and thus dynamical) localization for λ > 15 and a.e. ω, θ. We also obtain a new estimate on gap continuity (in ω) for this operator with λ > 29 (or λ < 4/29), and use it to prove that the measure of its spectrum is equal to |4 -2|λ|| for A in this range and all irrational ωs.

AB - We show that the almost Mathieu operator, (Hωλθψ)(η) = ψ(η+1) + ψ(η-1)+ λ cos(πωη+θ)ψ(η), has semi-uniform (and thus dynamical) localization for λ > 15 and a.e. ω, θ. We also obtain a new estimate on gap continuity (in ω) for this operator with λ > 29 (or λ < 4/29), and use it to prove that the measure of its spectrum is equal to |4 -2|λ|| for A in this range and all irrational ωs.

UR - http://www.scopus.com/inward/record.url?scp=0032121409&partnerID=8YFLogxK

U2 - 10.1007/s002200050376

DO - 10.1007/s002200050376

M3 - Article

AN - SCOPUS:0032121409

SN - 0010-3616

VL - 195

SP - 1

EP - 14

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

IS - 1

ER -