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

Clément Gallo (1)

1 I3M - Institut de Mathématiques et de Modélisation de Montpellier

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.

Domaines: Equations aux dérivées partielles [math.AP]; Physique mathématique [math-ph]

Clément Gallo. Expansion of the energy of the ground state of the Gross-Pitaevskii equation in the Thomas-Fermi limit. Journal of Mathematical Physics, 2013, 54, pp.031507-1/13. ⟨10.1063/1.4795245⟩. ⟨hal-00802318⟩