Historical remarks

The last 15–20 years has witnessed spectacular progress in the study of disordered metals and semiconductors. These systems are interesting not only from the point of view of different technical applications but also because they reveal new unusual physical properties that are very different from what one would expect in clean regular materials. Although very often thermodynamic characteristics are already quite influenced by disorder, the most remarkable effects are observed in kinetics. Of course, in many cases one may use the classical transport theory based on the Boltzmann equation for a description of electron motion. However, if the disorder is strong or temperature is low, quantum effects become important, and to construct a theory in this situation one has to start from the Schrödinger equation in a potential that is assumed to be random.

To get information about physical properties of the system one has to solve the Schrödinger equation for an arbitrary potential, calculate a physical quantity, and, at the end, average over the random potential. Sometimes it is important to have information not only about the average but also about fluctuations. In this case one has to calculate moments of the physical quantities and even an entire distribution function. Needless to say, generally speaking, this program cannot be carried out exactly even in the absence of electron–electron interaction and one should use different approximation schemes.