 00203 Elliott H. Lieb, Robert Seiringer, Jakob Yngvason
 A Rigorous Derivation of the GrossPitaevskii Energy Functional
for a Twodimensional Bose Gas
(41K, latex 2e)
May 1, 00

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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 $\bar\rho a^2$ is small, where $\bar\rho$ 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
$g\sim 1/\ln(\bar\rho a^2)$. 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.
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