Using the quantized mean-field method to model Joule heating in a short nano-conductor

The quantized mean-field method (QMF) is an extension of the traditional mean-field method for simulating quantum mechanical systems with electrons and ions. It adds the quantum nature of the ions to the simulations. Here we transform the QMF equations from wave function form to density operator form, study the connection between QMF and the recent correlated electron-ion dynamics (CEID) method, and show that QMF is a special case of CEID. Our simulations show that QMF fails to produce correct Joule heating in a nano-conductor. This is due to the mean-field approximation for the electrons. However, quantum properties of the ions, such as zero point energy, are conserved