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We demonstrate that a completely integrable classical mechanical model,namely the lattice Landau-Lifshitz classical spin chain, supports diffusivespin transport with a finite diffusion constant in the easy-axis regime, whilein the easy-plane regime it displays ballistic transport in the absence of anyknown relevant local or quasi-local constant of motion in the symmetry sectorof the spin current. This surprising finding should open the way towardsanalytical computation of diffusion constants for integrable interactingsystems and hints on existence of new quasi-local classical conservation lawsbeyond the standard soliton theory.

Macroscopic Diffusive Transport in a Microscopically Integrable Hamiltonian System