Kohn-Sham approximation scheme for an interacting Bose-condensed gas

TL;DR

This paper develops a density functional theory framework for interacting bosons, introducing a Kohn-Sham approximation scheme that simplifies the many-body problem to a single-particle system with self-consistent potentials.

Contribution

It presents a systematic approximation scheme for interacting bosons based on the effective action approach, extending the Kohn-Sham idea to bosonic systems.

Findings

Formulation of a grand canonical density functional theory for bosons.

Development of a Kohn-Sham-like approximation scheme for bosonic systems.

Self-consistent determination of the potential, density, and order parameter.

Abstract

The grand canonical density functional theory for inhomogeneous systems of interacting bosons is developed in the effective action approach. The Legendre transform of the generating functional for Green's functions is used to define the effective action as a functional of both the particle density and the order parameter. Expanding the thermal effective action in powers of the Planck constant we obtain a systematic approximation scheme, which practically implements the Kohn-Sham idea: the problem of interacting bosons is reduced to a single-particle system in a fictitious external potential. The Kohn-Sham potential, the density and the order parameter have to be determined self-consistently in a given order approximation.