We characterize the algebraic-geometric potentials for the Schrödinger and AKNS operators using the Weyl m-functions and the Floquet exponent for these operators. The characterization is this: among random ergodic Schrödinger operators, the alebraic-geometric potentials are those for which (i) the spectrum is a union of finitely many intervals (or bands); (ii) the Lyapounov exponent vanishes on the spectrum.
The algebraic-geometric AKNS potentials / R. Johnson; C. De Concini. - In: ERGODIC THEORY & DYNAMICAL SYSTEMS. - ISSN 0143-3857. - STAMPA. - 7:(1987), pp. 1-24. [10.1017/S0143385700003783]
The algebraic-geometric AKNS potentials
JOHNSON, RUSSELL ALLAN;
1987
Abstract
We characterize the algebraic-geometric potentials for the Schrödinger and AKNS operators using the Weyl m-functions and the Floquet exponent for these operators. The characterization is this: among random ergodic Schrödinger operators, the alebraic-geometric potentials are those for which (i) the spectrum is a union of finitely many intervals (or bands); (ii) the Lyapounov exponent vanishes on the spectrum.
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