Form factors and generalized hydrodynamics for integrable systems

Abstract

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). In the latter case the so obtained results are compared with predictions from GHD. One cornerstone of GHD are the GGE averaged microscopic currents, which can also be obtained through employing form factors. Discussed is a second, completely orthogonal approach based on the availability of a self-conserved current.

arXiv commentReview article. v1: 39 pages, 2 figures. v2: 50 pages, 2 figures, presentation substantially improved, references added

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• Correlation functions and transport coefficients in generalised hydrodynamics
• Generalized Hydrodynamics in the 1D Bose gas: theory and experiments
• Ballistic macroscopic fluctuation theory
• Generalized hydrodynamics of the KdV soliton gas
• Fragmentation and emergent integrable transport in the weakly tilted Ising chain
• Generalized Hydrodynamics of the attractive Non-Linear Schroedinger Equation
• Subdiffusive hydrodynamics of nearly-integrable anisotropic spin chains
• Out-of-equilibrium dynamics of the XY spin chain from form factor expansion
• The Space of Integrable Systems from Generalised $T\bar{T}$-Deformations
• The dissipative Generalized Hydrodynamic equations and their numerical solution
• Benchmarks of Generalized Hydrodynamics for 1D Bose Gases
• Generalised Gibbs Ensemble for spherically constrained harmonic models