Time-dependent density-functional theory: Features and challenges, with a special view on matter under extreme conditions

Abstract

Time-dependent density-functional theory (TDDFT) is a universal quantum mechanical approach to the dynamical many-body problem which can be used to describe matter that is driven out of equilibrium by arbitrary time-dependent perturbations. TDDFT is often applied in the linear-response regime to obtain information about electronic excitations and spectral properties, but it also holds in the strongly nonlinear regime, where the perturbations compete with or even override the internal interactions that provide the structure and stability of matter. The purpose of this article is to give a brief overview of the basic formalism of TDDFT, and then to discuss the advantages, successes, and challenges of TDDFT for describing matter under extreme conditions of pressure and external fields. Two questions will be particularly emphasized: what are “easy” and what are “tough” problems for TDDFT (both from a fundamental and practical point of view), and how can TDDFT deal with dissipation? Some answers will be given, and needs and directions for future research will be pointed out.