Applications of integrable models in condensed matter and cold atom physics

This chapter starts with a discussion of approximate physical realizations of 1+1-dimensional integrable models in solids and systems of ultra-cold trapped atoms. It then turns to local properties of energy eigenstates away from the edges of the spectrum. In generic models these states are thermal, while in integrable models non-thermal states with finite entropy densities coexist with thermal states. It discusses how to construct these atypical states by means of the Bethe Ansatz in the Heisenberg model. Finally, it outlines the crucial role these states play in describing the stationary states reached at late times after quantum quenches to integrable theories.