Boris Altshuler, Scaling Theory of the Anderson Localization Revisited скачать в хорошем качестве

Boris Altshuler, Scaling Theory of the Anderson Localization Revisited

Title: Scaling Theory of the Anderson Localization Revisited Abstract: Scaling theory of the Anderson Localization proposed in 1979 by Abrahams, Anderson, Licciardello, and Ramakrishnan. Following a period of active development, this theory is now complete. It is a slightly modified version of the scaling theory of ordinary phase transitions. The field theoretical foundation of this theory is a non-linear sigma – model, which results in a single parameter scaling. One can justify this approach only in two dimensions, where arbitrary weak disorder localizes all quantum states and metal to insulator transition does not occur. Nevertheless, it is considered that the 2+ε expansion offers a qualitatively accurate description of the Anderson transition for dimensions greater than 2. Recently the interest in the Many-Body Localization initiated studies of the Anderson model on the lattices in dimensions higher than 3 as well as on the graphs such as Random Regular Graphs. It turned out that the conventional one-parameter scaling theory becomes insufficient in the critical region of the Anderson transition. I will discuss the critical behavior of the Anderson transition, the multifractality of the eigenstates in the critical regime and of the spectral properties of the critical states.