Non-Adiabatic Dynamics in Single-Electron Tunneling Devices with Time-Dependent Density Functional Theory

We simulate the dynamics of a single-electron source, modeled as a quantum dot with on-site Coulomb interaction and tunnel coupling to an adjacent lead, in time-dependent density functional theory. Based on this system, we develop a time-nonlocal exchange-correlation potential by exploiting analogies with quantum-transport theory. The time non-locality manifests itself in a dynamical potential step. We explicitly link the time evolution of the dynamical step to physical relaxation time scales of the electron dynamics. Finally, we discuss prospects for simulations of larger mesoscopic systems.