Disorder plays an important role in two dimensions, and is responsible for striking phenomena such as metal-insulator transition and the integral and fractional quantum Hall effects. In this Letter, we investigate the role of disorder in the context of the recently discovered topological insulator, which possesses a pair of helical edge states with opposing spins moving in opposite directions a...

This is a survey on the intermittent behavior of the parabolic Anderson model, which is the Cauchy problem for the heat equation with random potential on the lattice Z. We first introduce the model and give heuristic explanations of the long-time behavior of the solution, both in the annealed and the quenched setting for time-independent potentials. We thereby consider examples of potentials st...

The interacting disordered electron problem is reviewed with emphasis on the quantum phase transitions that occur in a model system and on the field-theoretic methods used to describe them. An elementary discussion of conservation laws and diffusive dynamics is followed by a detai1ed derivation of the extended nonlinear sigma model, which serves as an effective field theory for the problem. A g...

thoughtfully, with good taste and, for the most part, with meticulous accuracy. In several passages, however, words and sentences are incorrectly translated (see for example, Nos. 13, 85, and 216, pp. 42, 100, and 210-212, respectively). A few titles of subdivisions, moreover, have been ignored or overlooked as in No. 95, p. 108, where a new paragraph should read: Dentifrices: 'The white dentif...

When a disordered array of coupled waveguides is illuminated with an extended coherent optical field, discrete speckle develops: partially coherent light with a granular intensity distribution on the lattice sites. The same paradigm applies to a variety of other settings in photonics, such as imperfectly coupled resonators or fibers with randomly coupled cores. Through numerical simulations and...