We devise an iterative scheme for numerically calculating dynamical two-point correlation functions in integrable many-body systems, in the Eulerian scaling limit. Expressions for these were originally derived in Ref. [1] by combining the fluctuation-dissipation principle with generalized hydrodynamics. Crucially, the scheme is able to address non-stationarity, inhomogeneous situations, when motion occurs at the Euler scale of hydrodynamics. Using our scheme, we study the spreading of correlations in several integrable models from inhomogeneous initial states. For the classical hard rod model we compare our results with Monte-Carlo simulations and observe excellent agreement at long time scales, thus providing the first demonstration of validity for the expressions derived in Ref. [1]. We also observe the onset of the Euler-scale limit for the dynamical correlations.


F. S. Møller, G. Perfetto, B. Doyon, J. Schmiedmayer, “Euler-scale dynamical correlations in integrable systems with fluid motion”, SciPost Phys. Core 3, 16 (2020).


Related to Project A03