We discuss the notion of integrability in quantum mechanics. Starting from a review of some definitions commonly used in the literature, we propose a different set of criteria, leading to a classification of models in terms of different integrability classes. We end by highlighting some of the expected physical properties associated to models fulfilling the proposed criteria.

We consider the extension of the thermodynamic Bethe Ansatz (TBA) to cases in which additional terms involving higher conserved charges are added to the Hamiltonian, or in which a distinction is made between the Hamiltonian used for time evolution and that used for defining the density matrix. Writing down equations describing the saddle-point (pseudoequilibrium) state of the infinite system, we prove the existence and uniqueness of solutions provided simple requirements are met. We show how a knowledge of the saddle-point rapidity distribution is equivalent to that of all generalized inverse temperatures, and how the standard equilibrium equations for e.g. excitations are simply generalized.

We consider the non-equilibrium dynamics of the interacting Lieb-Liniger gas after instantaneously switching the interactions off. The subsequent time evolution of the space-and time-dependent correlation functions is computed exactly. Different relaxation behavior is observed for different correlation functions. The long time average is compared with the predictions of several statistical ensembles. The generalized Gibbs ensemble restricted to a fixed number of particles is shown to give correct results at large times for all length scales.

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Abstract. We consider the transverse dynamical structure factor of the anisotropic Heisenberg spin-1/2 chain (XXZ model) in the gapped antiferromagnetic regime (∆ > 1). Specializing to the case of zero field, we use two independent approaches based on integrability (one valid for finite size, the other for the infinite lattice) to obtain the exact two-spinon part of this correlator. We discuss in particular its asymmetry with respect to the π/2 momentum line, its overall anisotropy dependence, and its contribution to sum rules.The two-spinon transverse structure factor of the gapped Heisenberg AFM chain 2