Density-functional theory of bosons in a trap

Abstract

A time-dependent Kohn-Sham-(KS-)like theory is presented for N bosons in three- and lower-dimensional traps. We derive coupled equations, which allow us to calculate the energies of elementary excitations. A rigorous proof is given to show that the KS-like equation correctly describes the properties of one-dimensional impenetrable bosons in a general time-dependent harmonic trap in the large-N limit.