Anderson Localization: Looking Forward
Prof. Boris Altshuler, Columbia University, USA
In particular, we will see that the ideas developed for understanding quantum mechanics of a single particle can be extended to attack many-body problems that include disorder. As an example we will discuss weakly interacting bosons in one-dimensions (1D) in the presence of a random potential. It is commonly accepted that there are no phase transitions in one- dimensional (1D) systems at a finite temperature T, because long-range correlations are destroyed by thermal fluctuations. It turns out, however, that the 1D gas of short-range interacting disordered bosons undergoes a finite T phase transition between two distinct states: fluid and insulator. None of these states has long-range spatial correlations, but this is a true albeit non-conventional phase transition: transport properties are singular at the transition point. In the fluid phase the mass transport is possible, whereas in the insulator it is completely blocked even at T>0.