Coherence and interactions in diffusive systems

This lecture is a tutorial introduction to coherent effects in disordered electronic systems. Avoiding technicalities as most as possible, I present some personal points of view to describe well-known signatures of phase coherence like weak localization correction or universal conductance fluctuations. I show how these physical properties of phase coherent conductors can be simply related to the classical return probability for a diffusive particle. The diffusion equation is then solved in various appropriate geometries and in the presence of a magnetic field. The important notion of quantum crossing is developed, which is at the origin of the quantum effects. The analogy with optics is exploited and the relation between universal conductance fluctuations and speckle fluctuations in optics is explained. The last part concerns the effect of electron-electron interactions. Using the same simple description, I derive qualitatively the expressions of the Altshuler-Aronov anomaly of the density of states, and of the correction to the conductivity. The last part, slightly more technical, adresses the question of the lifetime of a quasiparticle in a disordered metal.