Diffusive hydrodynamics from integrability breaking

TL;DR

This paper derives a general diffusion equation describing how conserved quantities in nearly integrable systems transition from ballistic to diffusive transport when integrability is weakly broken, linking diffusion constants to hydrodynamic data.

Contribution

It introduces a unified framework for understanding the crossover from generalized to conventional hydrodynamics in nearly integrable systems, including explicit formulas for diffusion constants.

Findings

Diffusive transport emerges when integrability is broken.

Diffusion constants depend on the matrix elements of perturbations.

The framework applies to long-range interactions and relates to hydrodynamic data.

Abstract

We describe the crossover from generalized hydrodynamics to conventional hydrodynamics in nearly integrable systems. Integrable systems have infinitely many conserved quantities, which spread ballistically in general. When integrability is broken, only a few of these conserved quantities survive. The remaining conserved quantities are generically transported diffusively; we derive a compact and general diffusion equation for these. The diffusion constant depends on the matrix elements of the integrability-breaking perturbation; for a certain class of integrability-breaking perturbations, including long-range interactions, the diffusion constant can be expressed entirely in terms of generalized hydrodynamic data.