A Short Introduction to Anderson Localization

Abstract

Abstract Anderson localization is another physical problem that has spurred much mathematical research. The issue here is how disorder, such as random changes in the spacing of a crystal, influences the movement of electrons and thus the crystal's conductivity. In 1977, Anderson was awarded the Nobel prize for his investigations on this subject. This chapter introduces the physical model, based on a random Schrodinger operator, and carefully reviews different notions of localization as well as rigorous proofs of localization. A very readable introduction to finite-volume criteria for localization via percolation arguments is followed by an elegant proof of localization for large disorder.

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