| Abstract: | Fermi liquid theory, together with the semiclassical Boltzmann formalism, allows us to decipher transport phenomena in most metals. However, there are many intriguing compounds which seem to violate the basic assumptions underlying such an explanation. In this talk, I will present several solvable, large-N models of interacting electrons, which display such exotic behavior. In particular, I will discuss an electron-phonon model with a high-temperature resistivity exceeding the Mott-Ioffe-Regel limit; such metallic compounds are known as bad metals. A variant of this model exhibits resistivity saturation. In addition, I will describe a model with strong electron-electron interactions, which at low temperatures forms a marginal Fermi liquid; such a theory has been argued to describe the normal state of the high-Tc cuprates. I will present several compelling properties of these solvable models, and discuss their implications on our understanding of strongly-coupled materials, in particular in terms of chaos and its relation to fundamental bounds on transport properties. |