Jacopo de Nardis (Université de Gand, Belgique)
Diffusion and super-diffusion in quantum and classical chains
I will review the recent progresses in extracting an emergent hydrodynamic description of interacting many-body quantum integrable systems valid at large time and space scales from the underlying microscopic unitary time evolution. In particular, I will show how to extract non-trivial hydrodynamic quantities characterising transport dynamics as such as diffusion constants and Drude weights. I will then focus on those cases where the diffusion constant of the charge associated with non-abelian symmetries (i.e. SU(2) symmetry) diverges at finite temperatures, leading to anomalous super-diffusive transport in isotropic spin chains with charge fluctuations falling within the KPZ universality class. This puzzling phenomena has been nowadays detected in different integrable quantum and classical interacting chains but also non-integrable quantum chains and an accurate and general understanding is still under research.