Local Control and v-Representability of Correlated Quantum Dynamics

TL;DR

This paper introduces an efficient local control method to determine external potentials that generate prescribed densities in interacting quantum systems, advancing density-functional theory and Kohn-Sham approaches.

Contribution

The authors develop a stable numerical scheme for constructing external potentials in correlated quantum dynamics, enabling exact Kohn-Sham potential construction for arbitrary initial states.

Findings

Method works efficiently for large, rapid density changes

Can construct exact Kohn-Sham potentials for correlated initial states

Demonstrates limitations of adiabatic approximations in correlated systems

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. The numerical method is efficient and stable even for large and rapid density variations irrespective of the initial state and the interactions. The method 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.