A rigorous derivation of the Gross-Pitaevskii energy functional for a two-dimensional Bose gas
published
Élliott
Lieb
author
Robert
Seiringer
author 4AFD0470-F248-11E8-B48F-1D18A9856A87
Jakob
Yngvason
author
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.
Springer2001
Communications in Mathematical Physics10.1007/s002200100533
224117 - 31
yes
Lieb, Élliott, Robert Seiringer, and Jakob Yngvason. “A Rigorous Derivation of the Gross-Pitaevskii Energy Functional for a Two-Dimensional Bose Gas.” <i>Communications in Mathematical Physics</i> 224, no. 1 (2001): 17–31. <a href="https://doi.org/10.1007/s002200100533">https://doi.org/10.1007/s002200100533</a>.
É. Lieb, R. Seiringer, J. Yngvason, Communications in Mathematical Physics 224 (2001) 17–31.
Lieb, É., Seiringer, R., & Yngvason, J. (2001). A rigorous derivation of the Gross-Pitaevskii energy functional for a two-dimensional Bose gas. <i>Communications in Mathematical Physics</i>, <i>224</i>(1), 17–31. <a href="https://doi.org/10.1007/s002200100533">https://doi.org/10.1007/s002200100533</a>
É. Lieb, R. Seiringer, and J. Yngvason, “A rigorous derivation of the Gross-Pitaevskii energy functional for a two-dimensional Bose gas,” <i>Communications in Mathematical Physics</i>, 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.” <i>Communications in Mathematical Physics</i>, vol. 224, no. 1, Springer, 2001, pp. 17–31, doi:<a href="https://doi.org/10.1007/s002200100533">10.1007/s002200100533</a>.
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>
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