Friday, December 26, 2014

How Electronic Dynamics with Pauli Exclusion Produces Fermi-Dirac Statistics.

Triet S. Nguyen, Ravindra Nanguneri, and John Parkhill, arxiv:14115324v1 (2014)
Contributed by Alán Aspuru-Guzik

A very interesting preprint by John Parkhill from the University of Notredame and his group provides a solution for a long-standing theoretical problem: Many of the quantum master equations that treat electron-phonon interactions fail to reach a Fermi-Dirac distribution at long times. For example, Ehrenfest dynamics is one of the usual suspects for this behavior. By employing a combination of time-dependent perturbation theory and the extended normal ordering theory of Kutzelnigg and Mukherjee, Parkhill and his co-workers arrive to a novel master equation.

The results from this work show that the Pauli principle "blocks" electron relaxation and slows it down, and in addition it leads to a time-dependent relaxation rate. The plot below shows the correct asymptotic relaxation of a double excitation in a model system and the plot in the right shows a time-dependent relaxation rate.

The paper says that "A paper using these new formulas in a useful all-electron dynamics code is
an immediate follow up.". The contributor is looking forward to it.