A rigorous derivation of the Gross-Pitaevskii energy functional for a two-dimensional Bose gas
Lieb, Élliott H
Robert Seiringer
Yngvason, Jakob
We consider the ground state properties of an inhomogeneous two-dimensional 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 Gross-Pitaevskii (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 Thomas-Fermi type functional is adequate.
Springer
2001
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https://research-explorer.app.ist.ac.at/record/2347
Lieb É, Seiringer R, Yngvason J. A rigorous derivation of the Gross-Pitaevskii energy functional for a two-dimensional Bose gas. <i>Communications in Mathematical Physics</i>. 2001;224(1):17-31. doi:<a href="https://doi.org/10.1007/s002200100533">10.1007/s002200100533</a>
info:eu-repo/semantics/altIdentifier/doi/10.1007/s002200100533
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