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We consider the homogeneous Bose gas on a unit torus in the mean-field regimewhen the interaction strength is proportional to the inverse of the particlenumber. In the limit when the number of particles becomes large, we derive atwo-term expansion of the one-body density matrix of the ground state. Theproof is based on a cubic correction to Bogoliubov's approximation of theground state energy and the ground state.

Two-term expansion of the ground state one-body density matrix of a mean-field Bose gas