Transport in low-dimensional quantum systems is controlled by Fermi statistics or interactions. The nature of these forces causes transport to be non-linear. In its turn nonlinear effects develop into hydrodynamic instabilities. In a clean quantum many-body system any smooth density packet develop shock-wave type singularities. I present a theory which describes Fermi systems in terms of hydrodynamics modes, where nonlinear corrections and singularities they cause are taken into account.

University of Chicago