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Our review covers microscopic foundations of generalized hydrodynamics (GHD). As one generic approach we develop form factor expansions, for ground states and generalized Gibbs ensembles (GGE), and compare the so obtained results with predictions from GHD. One cornerstone of GHD is the GGE averaged microscopic currents. They can be obtained using form factors. Discussed is also a second, completely orthogonal approach based on the availability of a self-conserved current.
Using generalized hydrodynamics (GHD), we develop the Euler hydrodynamics of classical integrable field theory. Classical field GHD is based on a known formalism for Gibbs ensembles of classical fields, that resembles the thermodynamic Bethe ansatz o
We discuss several classes of integrable Floquet systems, i.e. systems which do not exhibit chaotic behavior even under a time dependent perturbation. The first class is associated with finite-dimensional Lie groups and infinite-dimensional generaliz
For quantum integrable systems the currents averaged with respect to a generalized Gibbs ensemble are revisited. An exact formula is known, which we call collision rate ansatz. While there is considerable work to confirm this ansatz in various models
We introduce a class of integrable dynamical systems of interacting classical matrix-valued fields propagating on a discrete space-time lattice, realized as many-body circuits built from elementary symplectic two-body maps. The models provide an effi
The generalized Gibbs ensemble (GGE), which involves multiple conserved quantities other than the Hamiltonian, has served as the statistical-mechanical description of the long-time behavior for several isolated integrable quantum systems. The GGE may