• DOI:10.21468/SciPostPhys.6.4.049
• Corpus ID: 102486781

Diffusion in generalized hydrodynamics and quasiparticle scattering

@article{Nardis2019DiffusionIG,
  title={Diffusion in generalized hydrodynamics and quasiparticle scattering},
  author={Jacopo de Nardis and Denis Bernard and Benjamin Doyon},
  journal={SciPost Physics},
  year={2019}
}

• J. D. Nardis, D. Bernard, B. Doyon
• Published 3 December 2018
• Physics, Mathematics
• SciPost Physics

We extend beyond the Euler scales the hydrodynamic theory for quantum
and classical integrable models developed in recent years, accounting
for diffusive dynamics and local entropy production. We review how the
diffusive scale can be reached via a gradient expansion of the
expectation values of the conserved fields and how the coefficients of
the expansion can be computed via integrated steady-state two-point
correlation functions, emphasising that {\mathcal PT}𝒫T-symmetry
can fully fix the inherent ambiguity in the definition of conserved
fields at the diffusive scale. We develop a form factor expansion to
compute such correlation functions and we show that, while the dynamics
at the Euler scale is completely determined by the density of single
quasiparticle excitations on top of the local steady state, diffusion is
due to scattering processes among quasiparticles, which are only present
in truly interacting systems. We then show that only two-quasiparticle
scattering processes contribute to the diffusive dynamics. Finally we
employ the theory to compute the exact spin diffusion constant of a
gapped XXZ spin-1/2−1/2
chain at finite temperature and half-filling, where we show that spin
transport is purely diffusive.