The positivity of the Lyapunov exponent and the absence of the absolutely continuous spectrum for the almost-Mathieu equation
1984; American Institute of Physics; Volume: 25; Issue: 4 Linguagem: Inglês
10.1063/1.526221
ISSN1527-2427
AutoresAlexander Figotin, L. А. Pastur,
Tópico(s)Quantum Mechanics and Non-Hermitian Physics
ResumoThis paper contains the rigorous proof of the formulated by Andre and Aubry following statement: the Cauchy solutions of the discrete Schrödinger equation with the potential qn=g cos(2πnθ+φ) grow exponentially for every irrational θ, g>1 and almost every φε[0,2π). According to known this fact implies the absence of the absolutely continuous component of the spectrum for the corresponding operator.
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