Author(s):

Lieb, Élliott H; Seiringer, Robert; Yngvason, Jakob

Article Title: 
A rigorous derivation of the GrossPitaevskii energy functional for a twodimensional Bose gas

Affiliation 

Abstract: 
We consider the ground state properties of an inhomogeneous twodimensional Bose gas with a repulsive, short range pair interaction and an external confining potential. In the limit when the particle number N is large but ρ̄a2 is small, where ρ̄ is the average particle density and a the scattering length, the ground state energy and density are rigorously shown to be given to leading order by a GrossPitaevskii (GP) energy functional with a coupling constant g ∼ 1/ 1n(ρ̄a2). In contrast to the 3D case the coupling constant depends on N through the mean density. The GP energy per particle depends only on Ng. In 2D this parameter is typically so large that the gradient term in the GP energy functional is negligible and the simpler description by a ThomasFermi type functional is adequate.

Journal Title:

Communications in Mathematical Physics

Volume: 
224

Issue 
1

ISSN:

14320916

Publisher:

Springer

Date Published:

20011101

Start Page: 
17

End Page:

31

URL: 

DOI: 
10.1007/s002200100533

Open access: 
yes (repository) 