UC San Diego

In this dissertation we discuss the dynamical behavior of electrons on the nanoscopic scale. We begin by presenting a view of electron transport which an alternative to that due to Landauer, in which the flow of electrons across a junction is framed as the discharge of a large but finite capacitor. The benefit of this construction is that time- dependent calculations can be framed in a conceptually simple and well-defined way. We characterize the conductance of a quasi-one-dimensinal chain of gold atoms, as well as a quantity which is similar to the distribution functions of classical statistical mechanics. We go on to the quasi-two-dimensional case and characterize the flow patterns of electrons emerging from a nanoscopic junction. We discuss the dynamic angular pattern of electron flow, as well as the movement of charge at the surface of the electrodes near the junction. We continue by considering the hydrodynamic form of the many-body Schrödinger equation and demonstrate that the electron liquid develops turbulent eddy-like structures in experimentally attainable regimes. We provide the demonstration using both an ab-initio formalism, as well as an approximate Navier-Stokes calculation. We go on to describe an experiment whereby the turbulence of the electron liquid could be detected through the use of a Superconducting Quantum Interference Device (SQUID), by measuring the asymmetry in the magnetic flux produced as a result of current flow near the nanoscopic junction. In addition, we characterize the turbulent eddies by considering the velocity correlation tensor Finally, we discuss the stochastic extension to current density functional theory and demonstrate the decay of a Helium atom which is effectively coupled to an external reservoir. We demonstrate the utility of the stochastic Schrödinger formalism as compared to the master equation approach, and discuss the relevance of the stochastic Shrödinger equation to quantum measurement theory