Many-body quantum dynamics from the density

¹ Lundbeck Center for Theoretical Chemistry, Department of Chemistry, Aarhus University, 8000 Aarhus C, Denmark, EU
² Department of Physics, Nanoscience Center, University of Jyväskylä - 40014 Jyväskylä, Finland, EU
³ Institut für Theoretische Physik, Universität Innsbruck - Technikerstraße 25, 6020 Innsbruck, Austria, EU
⁴ European Theoretical Spectroscopy Facility (ETSF)

Received: 10 December 2012
Accepted: 16 January 2013

Abstract

We present a local control scheme to construct the external potential v that, for a given initial state, produces a prescribed time-dependent density in an interacting quantum many-body system. This numerical method is efficient and stable even for large and rapid density variations irrespective of the initial state and the interactions. It can at the same time be used to answer fundamental v-representability questions in density functional theory. In particular, in the absence of interactions, it allows us to construct the exact time-dependent Kohn-Sham potential for arbitrary initial states. We illustrate the method in a correlated one-dimensional two-electron system with different interactions, initial states and densities. For a Kohn-Sham system with a correlated initial state we demonstrate the interplay between memory and initial-state dependence as well as the failure of any adiabatic approximation.