Mathematics

The past few years have witnessed an increasing interest in the study of the non-equilibrium dynamics of closed many-body quantum systems, a prominent setting of investigation being that of a quantum quench (i.e., the process of taking a system out of equilibrium by a sudden change in one of the parameters in the Hamiltonian). The main questions arising in this field, regarding the relaxation dynamics and the characterization of the eventual stationary state, are typically extremely hard to address, even numerically, for interacting systems. Recently, analytical methods based on the Bethe ansatz have proved to be successful in the study of quantum quenches in experimentally relevant one-dimensional integrable systems. After a pedagogical introduction to Bethe ansatz integrable models, I will explain how the mathematical results coming from Bethe ansatz methods have been employed in the recent literature to obtain significant physical results in the study of quantum quenches.