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Quench dynamics in integrable systems

These notes cover in some detail lectures I gave at the Les Houches Summer School 2012. I describe here work done with Deepak Iyer with important contributions from Hujie Guan. I discuss some aspects of the physics revealed by quantum quenches and present a formalism for studying the quench dynamics of integrable systems. The formalism presented generalizes an approach by Yudson and is applied to Lieb-Liniger model which describes a gas of $N$ interacting bosons moving on the continuous infinite line while interacting via a short range potential. We carry out the quench from several initial states and for any number of particles and compute the evolution of the density and the noise correlations. In the long time limit the system dilutes and we find that for any value of repulsive coupling independently of the initial state the system asymptotes towards astrongly repulsive gas, 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. These results can be confronted with experiments. For much more detail see: Phys. Rev. A 87, 053628 (2013) on which these notes are based. Further applications of the approach to the Heisenberg model and to the Anderson model will be presented elsewhere.