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Published September 15, 1996 | public
Journal Article

The Lyapunov Exponents for Schrödinger Operators with Slowly Oscillating Potentials

Abstract

By studying the integrated density of states, we prove the existence of Lyapunov exponents and the Thouless formula for the Schrödinger operator –d^2/dx^2+cos x^ν with 0<ν<1 on L^2[0, ∞). This yields an explicit formula for these Lyapunov exponents. By applying rank one perturbation theory, we also obtain some spectral consequences.

Additional Information

© 1996 Academic Press. Received 14 August 1995, Accepted 2 November 1995. This material is based upon work supported by the National Science Foundation under Grant DMS-9401491. The Government has certain rights in this material.

Additional details

Created:
August 19, 2023
Modified:
October 26, 2023