Hydrodynamic Diffusion in Integrable Systems
Résumé
We show that hydrodynamic diffusion is generically present in many-body, one-dimensional interacting quantum and classical integrable models. We extend the recently developed generalized hydrodynamic (GHD) to include terms of Navier-Stokes type, which leads to positive entropy production and diffusive relaxation mechanisms. These terms provide the subleading diffusive corrections to Euler-scale GHD for the large-scale nonequilibrium dynamics of integrable systems, and arise due to two-body scatterings among quasiparticles. We give exact expressions for the diffusion coefficients. Our results apply to a large class of integrable models, including quantum and classical, Galilean and relativistic field theories, chains, and gases in one dimension, such as the Lieb-Liniger model describing cold atom gases and the Heisenberg quantum spin chain. We provide numerical evaluations in the Heisenberg XXZ spin chain, both for the spin diffusion constant, and for the diffusive effects during the melting of a small domain wall of spins, finding excellent agreement with time-dependent density matrix renormalization group numerical simulations.
Mots clés
General Physics: Statistical and Quantum Mechanics
Quantum Information
etc.
model: integrability
spin: chain
spin: diffusion
field theory: relativistic
entropy: production
dimension: 1
atom: gas
hydrodynamics
Heisenberg
numerical calculations
many-body problem
quasiparticle
domain wall
scattering
Galilei