Simulating generalised fluids via interacting wave packets evolution

TL;DR

This paper introduces a novel simulation method for generalized hydrodynamics in integrable and quasi-integrable systems, enabling efficient large-scale simulations and revealing long-lived correlations that challenge traditional thermalization assumptions.

Contribution

The authors develop a wave packet-based simulation framework for GHD that incorporates fluctuations and integrability-breaking effects efficiently.

Findings

Efficient simulation of quasi-integrable systems with perturbations.

Long-lived correlations persist despite apparent local thermalization.

The framework captures fluctuations and correlations beyond standard GHD.

Abstract

One-dimensional integrable and quasi-integrable systems display, on macroscopic scales, a universal form of transport known as Generalized Hydrodynamics (GHD). In its standard Euler-scale formulation, GHD mirrors the equations of a two-dimensional compressible fluid but ignores fluctuations and becomes numerically unwieldy as soon as integrability-breaking perturbations are introduced. We show that GHD can be efficiently simulated as a gas of semiclassical wave packets - a natural generalisation of hard-rod particles - whose trajectories are efficiently mapped onto those of point particles. This representation (i) provides a transparent route to incorporate integrability-breaking terms, and (ii) automatically embeds the exact fluctuating-hydrodynamics extension of GHD. The resulting framework enables fast, large-scale simulations of quasi-integrable systems even in the presence of complicated integrability-breaking perturbations. It also manifest the pivotal role of two-point correlations in systems confined by external potentials: we demonstrate that situations where local one-point observables appear thermalised can nevertheless sustain long-lived, far-from-equilibrium long-range correlations for arbitrarily long times, signaling that, differently from what previously stated, true thermalisation is not reached at diffusive time-scales.