Expansion of the energy of the ground state of the Gross-Pitaevskii equation in the Thomas-Fermi limit

Gallo, Clément
March 2013
Journal of Mathematical Physics;Mar2013, Vol. 54 Issue 3, p031507
Academic Journal
From the asymptotic expansion of the ground state of the Gross-Pitaevskii equation in the Thomas-Fermi limit given by Gallo and Pelinovsky ['On the Thomas-Fermi ground state in a harmonic potential,' Asymptot. Anal. 73(1-2), 53-96 (2011)], we infer an asymptotic expansion of the kinetic, potential, and total energy of the ground state. In particular, we give a rigorous proof of the expansion of the kinetic energy calculated by Dalfovo, Pitaevskii, and Stringari ['Order parameter at the boundary of a trapped Bose gas,' Phys. Rev. A 54, 4213-4217 (1996)] in the case where the space dimension is 3. Moreover, we calculate one more term in this expansion, and we generalize the result to space dimensions 1 and 2.


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