A rigorous derivation of the Gross-Pitaevskii energy functional for a two-dimensional Bose gas

É. Lieb, R. Seiringer, J. Yngvason, Communications in Mathematical Physics 224 (2001) 17–31.


Journal Article | Published
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Abstract
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.
Publishing Year
Date Published
2001-11-01
Journal Title
Communications in Mathematical Physics
Volume
224
Issue
1
Page
17 - 31
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Lieb É, Seiringer R, Yngvason J. A rigorous derivation of the Gross-Pitaevskii energy functional for a two-dimensional Bose gas. Communications in Mathematical Physics. 2001;224(1):17-31. doi:10.1007/s002200100533
Lieb, É., Seiringer, R., & Yngvason, J. (2001). A rigorous derivation of the Gross-Pitaevskii energy functional for a two-dimensional Bose gas. Communications in Mathematical Physics, 224(1), 17–31. https://doi.org/10.1007/s002200100533
Lieb, Élliott, Robert Seiringer, and Jakob Yngvason. “A Rigorous Derivation of the Gross-Pitaevskii Energy Functional for a Two-Dimensional Bose Gas.” Communications in Mathematical Physics 224, no. 1 (2001): 17–31. https://doi.org/10.1007/s002200100533.
É. Lieb, R. Seiringer, and J. Yngvason, “A rigorous derivation of the Gross-Pitaevskii energy functional for a two-dimensional Bose gas,” Communications in Mathematical Physics, vol. 224, no. 1, pp. 17–31, 2001.
Lieb É, Seiringer R, Yngvason J. 2001. A rigorous derivation of the Gross-Pitaevskii energy functional for a two-dimensional Bose gas. Communications in Mathematical Physics. 224(1), 17–31.
Lieb, Élliott, et al. “A Rigorous Derivation of the Gross-Pitaevskii Energy Functional for a Two-Dimensional Bose Gas.” Communications in Mathematical Physics, vol. 224, no. 1, Springer, 2001, pp. 17–31, doi:10.1007/s002200100533.

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