Correlated electron-ion dynamics with open boundaries:: formalism

We extend a new formalism, which allows correlated electron-ion dynamics to be applied to the problem of open boundary conditions. We implement this at the first moment level (allowing heating of ions by electrons) and observe the expected cooling in the classical part of the ionic kinetic energy and current-induced heating in the quantum contribution. The formalism for open boundaries should be easily extended to higher moments of the correlated electron-ion fluctuations.