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Lyapunov exponent of the random Schrödinger operator with short-range correlated noise potential

✍ Scribed by Godin, Y. A.; Molchanov, S.; Vainberg, B.

Book ID
121587804
Publisher
SP MAIK Nauka/Interperiodica
Year
2013
Tongue
English
Weight
487 KB
Volume
20
Category
Article
ISSN
1061-9208

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✍ Barry Simon; Yunfeng Zhu 📂 Article 📅 1996 🏛 Elsevier Science 🌐 English ⚖ 521 KB

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 al