Transport of electrical charge across a nanoscale system is accompanied by many effects related to the interaction among electrons, and electrons and ions [1]. After a critical introduction of the transport problem I will discuss relatively unexplored phenomena that occur in these systems like turbulence of the electron liquid, local electron heating and the effect of electron viscosity on resistance. I will provide both analytical results and numerical examples of electron dynamics in nanoscale systems, and discuss experimental tests of our predictions.

[1] M. Di Ventra, Electrical transport in nanoscale systems, Cambridge University Press, Cambridge, 2008.