Abstract
We prove an upper bound for the ground state energy of a Bose gas consisting of N hard spheres with radius mathfrak {a}/N, moving in the three-dimensional unit torus Lambda . Our estimate captures the correct asymptotics of the ground state energy, up to errors that vanish in the limit N rightarrow infty . The proof is based on the construction of an appropriate trial state, given by the product of a Jastrow factor (describing two-particle correlations on short scales) and of a wave function constructed through a (generalized) Bogoliubov transformation, generating orthogonal excitations of the Bose–Einstein condensate and describing correlations on large scales.
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