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The Lyapunov Exponents for Schrödinger Operators with Slowly Oscillating Potentials

✍ Scribed by Barry Simon; Yunfeng Zhu

Publisher
Elsevier Science
Year
1996
Tongue
English
Weight
521 KB
Volume
140
Category
Article
ISSN
0022-1236

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✦ Synopsis

By studying the integrated density of states, we prove the existence of Lyapunov exponents and the Thouless formula for the Schro dinger operator &d 2 Âdx 2 +cos x & with 0<&<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.

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