Long Time Behavior of Time-Dependent Density Functional Theory*

We investigate whether real-time TDDFT calculations can capture internal equilibration of an electronic system by performing multi-picosecond TDDFT simulations of aluminum. We monitor the system by calculating the projections of the TDDFT states into the Kohn-Sham eigenvectors of the system. For a system of non-interacting Fermions at equilibrium, the ensemble average of these projections would follow a Fermi distribution, but for interacting systems (e.g., a Fermi liquid), the distribution can be modified. Using a recently published algorithm (Modine and Hatcher, JCP 142, 204111 (2014)), we construct initial TDDFT states whose average projections match a Fermi distribution. During TDDFT propagation of these states, the calculated projections are observed to evolve away from the Fermi distribution to a modified distribution with a sharper drop at the Fermi level and longer tails at high and low energies.