Quench dynamics in interacting quantum systems in 1-d

In this talk I will describe the quench dynamics of  isolated interacting systems in 1-d,  governed  by integrable Hamiltonians . I shall study the time evolution of a gas of interacting bosons moving on the continuous infinite line and interacting via a short range potential (the  Lieb-Liniger  model).  For a system with a finite number of bosons  we find that independently of the initial state the system asymptotes towards a strongly repulsive gas for any value of repulsive coupling, while for any value of attractive coupling, the system forms a maximal bound state that dominates at longer times. In either case the system equilibrates but does not thermalize, an effect that is consistent with prethermalization.  For an infinite system  we find that the system  equilibrates to a generalized Gibbs ensemble.  If time permits I shall discuss also the quench dynamics of the XXZ Heisenberg chain and of a mobile impurity in an interacting Bose gas (quantum  Brownian motion).