Hydrodynamic approach to transport and quantum turbulence in nanoscale conductors

The description of electron-electron interactions in transport problems is both analytically and numerically difficult. Here we show that a much simpler description of electron transport in the presence of interactions can be achieved in nanoscale systems. In particular, we show that the electron flow in nanoscale conductors can be described by Navier-Stokes type of equations with an effective electron viscosity, i.e., on a par with the dynamics of a viscous and compressible classical fluid. By using this hydrodynamic approach we derive the conditions for the transition from laminar to turbulent flow in nanoscale systems and discuss possible experimental tests of our predictions.