Euler-scale dynamical correlations in integrable systems with fluid motion

TL;DR

This paper introduces a numerical scheme to compute dynamical correlations in integrable systems at the Euler scale, capable of handling non-stationary, inhomogeneous conditions, and validates it through classical models and simulations.

Contribution

It presents a novel iterative numerical method for calculating Euler-scale dynamical correlations in inhomogeneous integrable systems, extending previous theoretical expressions.

Findings

Excellent agreement with Monte-Carlo simulations for the hard-rod model

First validation of the derived correlation expressions in non-stationary settings

Observation of the onset of the Euler-scale limit in dynamical correlations

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.