Energy and Vorticity in Fast Rotating Bose-Einstein Condensates

Details Energy and Vorticity in Fast Rotating Bose-Einstein Condensates Energy and Vorticity in Fast Rotating Bose-Einstein Condensates

2008-06-19

arxiv.org/abs/0806.3191v2

J. Phys. A: Math. Theor. 41 (2008), 445002.

Physics

Mathematical Physics

19 pages, LaTeX; typos corrected, clarifying remarks added, some rearrangements in the text

Scientific paper

10.1088/1751-8113/41/44/445002

We study a rapidly rotating Bose-Einstein condensate confined to a finite trap in the framework of two-dimensional Gross-Pitaevskii theory in the strong coupling (Thomas-Fermi) limit. Denoting the coupling parameter by $1/\eps^2$ and the rotational velocity by $\Omega$, we evaluate exactly the next to leading order contribution to the ground state energy in the parameter regime $|\log\eps|\ll \Omega\ll 1/(\eps^2|\log\eps|)$ with $\eps\to 0$. While the TF energy includes only the contribution of the centrifugal forces the next order corresponds to a lattice of vortices whose density is proportional to the rotational velocity.

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