Schroedinger difference equation with deterministic ergodic potentials

Details Schroedinger difference equation with deterministic ergodic potentials Schroedinger difference equation with deterministic ergodic potentials

2012-03-16

arxiv.org/abs/1203.3646v1

Beyond Quasicrystals, eds. F. Axel & D. Gratias, Springer-Verlag/Les Editions de Physique 1995, pp. 481-549

Physics

Mathematical Physics

51 pages

Scientific paper

We review the recent developments in the theory of the one-dimensional tight-binding Schr\"odinger equation for a class of deterministic ergodic potentials. In the typical examples the potentials are generated by substitutional sequences, like the Fibonacci or the Thue-Morse sequence. We concentrate on rigorous results which will be explained rather than proved. The necessary mathematical background is provided in the text.

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