Anomalous diffusion in phase space of electron and electron-phonon fluids*

We study non-local hydrodynamic response of electron and combined electron-phonon fluids. This hydrodynamic regime is governed by infinite set of kinetic modes that describe scattering events in different angular harmonic channels. The scattering rates of these modes leads to anomalous, Lévy-flight-like phase space diffusion and allows us to obtain expressions for the non-local heat and charge conductivities. We discuss Dirac, Fermi, and electron-phonon fluids, including the crossover from hydrodynamic to ballistic transport.