Winter 2004–2005

Ma 191b - Ergodic Schrödinger Operators
12:30 - 2:00 T // 257 Sloan
3:00 - 4:30 R // 253b Sloan
David Damanik

This course will cover Schrödinger operators with ergodic potentials, mainly in one dimension. The primary examples are potentials generated by i.i.d. random variables or almost periodic functions. The following topics will be discussed: Lyapunov exponent and IDS, Kotani theory, Furstenberg's theorem, various ways of proving localization, examples with Cantor spectrum, quantum dynamics.

Main Texts:

• L. Pastur, A. Figotin: Spectra of random and almost-periodic operators. Springer-Verlag, Berlin, 1992
• R. Carmona, J. Lacroix: Spectral theory of random Schrödinger operators. Birkhäuser, Boston, 1990
• H. Cycon, R. Froese, W. Kirsch, B. Simon: Schrödinger operators withapplication to quantum mechanics and global geometry. Springer-Verlag, Berlin, 1987
• P. Bougerol, J. Lacroix: Products of random matrices with applications toSchrödinger operators. Birkhäuser, Boston, 1985