Density Functional Theory of Bosons in a Trap

TL;DR

This paper develops a time-dependent Kohn-Sham-like theoretical framework for N bosons in traps, enabling calculation of excitation energies and accurately describing one-dimensional impenetrable boson condensates in dynamic harmonic traps.

Contribution

It introduces a novel time-dependent Kohn-Sham-like approach for bosons in traps, with rigorous proof of its validity for large N one-dimensional condensates.

Findings

Derivation of coupled equations for excitation energies

Rigorous proof of the approach's accuracy for 1D impenetrable bosons

Applicability to general time-dependent harmonic traps

Abstract

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