Transport in nanoscale systems: hydrodynamics, turbulence, and local electron heating

Transport in nanoscale systems is usually described as an open-boundary scattering problem. This picture, however, says nothing about the dynamical onset of steady states, their microscopic nature, or their dependence on initial conditions [1]. In order to address these issues, I will first describe the dynamical many-particle state via an effective quantum hydrodynamic theory [2]. This approach allows us to predict a series of novel phenomena like turbulence of the electron liquid [2], local electron heating in nanostructures [3], and the effect of electron viscosity on resistance [4]. I will provide both analytical results and numerical examples of first-principles electron dynamics in nanostructures using the above approach. I will also discuss possible experimental tests of our predictions. Work supported in part by NSF and DOE. \newline \newline [1] N. Bushong, N. Sai and M. Di Ventra, ``Approach to steady-state transport in nanoscale systems'' Nano Letters, 5 2569 (2005); M. Di Ventra and T.N. Todorov, ``Transport in nanoscale systems: the microcanonical versus grand-canonical picture,'' J. Phys. Cond. Matt. 16, 8025 (2004). \newline [2] R. D'Agosta and M. Di Ventra, ``Hydrodynamic approach to transport and turbulence in nanoscale conductors,'' cond-mat/05123326; J. Phys. Cond. Matt., in press. \newline [3] R. D'Agosta, N. Sai and M. Di Ventra, ``Local electron heating in nanoscale conductors,'' cond-mat/0605312; Nano Letters, in press. \newline [4] N. Sai, M. Zwolak, G. Vignale and M. Di Ventra, ``Dynamical corrections to the DFT-LDA electron conductance in nanoscale systems,'' Phys. Rev. Lett. 94, 186810 (2005).