Abstract
A review of results concerning the Schrödinger equation with random and almost periodic potentials is given with special emphasis on rigorous results; some more speculative discussions about the upper critical dimension of the localization problem is however developped at the end. Applications of similar ideas to other problems of wave propagation in inhomogeneous media are also mentionned.
The question of electron propagation in disordered systems or more generally the problem of wave propagation in inhomogeneous media is an old one, which has been strongly revived by the concept of localization introduced by Anderson and by the works of Mott, Thouless and many others. On the other hand electron propagation in incommensurate structures has appeared as a very attractive subject with the works of Azbel and Aubry.
This text is included in the Proceedings for the sake of completeness, under the kind pressure of Giulio Casati. It is the summary of review I gave at theLes Houches workshop “Common trends in condensed matter and particle physics” (March 1983) the proceedings of which will appear in Physics Reports. The reader will find here most of the results and references quoted in my lectures at Como.
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References
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© 1985 Plenum Press, New York
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Souillard, B. (1985). Mathematical and Physical Properties of Schrodinger Equations with Random and Almost-Periodic Potentials. In: Casati, G. (eds) Chaotic Behavior in Quantum Systems. NATO ASI Series, vol 120. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-2443-0_1
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