Abstract
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-stationary, inhomogeneous situations, when motion occurs at the Euler-scale of hydrodynamics. In such situations, in interacting systems, the simple correlations due to fluid modes propagating with the flow receive subtle corrections, which we test. 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.
Highlights
In non-integrable systems, on the one hand, where one assumes that only a finite number of quasi-local conserved quantities exist, including the Hamiltonian, chaotic motion causes relaxation to occur to a thermal state described by the Gibbs ensemble, with a finite number of thermodynamic potentials
We develop a numerical scheme for calculating dynamical two-point correlations in Euler-scale generalized hydrodynamics (GHD), in the full generality of the theory of Ref. [1]
To demonstrate properties of correlations at the Euler-scale we examine three different scenarios, whose hydrodynamical properties have already been well studied: First, we calculate the spreading of correlations from an homogeneous thermal state
Summary
With the advent of experimental realizations of cold gases in reduced dimensions, the study of many-body systems far from equilibrium has received a lot of attention [2,3,4,5,6,7,8,9,10,11,12,13,14]. In non-integrable systems, on the one hand, where one assumes that only a finite number of quasi-local conserved quantities exist, including the Hamiltonian, chaotic motion causes relaxation to occur to a thermal state described by the Gibbs ensemble, with a finite number of thermodynamic potentials. Thermalization in this framework may be understood within the eigenstate thermalization hypothesis, first proposed in Refs. We develop a numerical scheme for calculating dynamical two-point correlations in Euler-scale GHD, in the full generality of the theory of Ref. The technical aspects of the presentation are deferred to the Appendix
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