This 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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© 1984 American Institute of Physics.
1984
American Institute of Physics
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