Proof of off-diagonal long-range order in a mean-field trapped Bose gas via the Feynman--Kac formula

Tianyi Bai, Wolfgang König, Quirin Vogel

We consider the non-interacting Bose gas of $N$ bosons in dimension $d\ge 3$ in a trap in a mean-field setting with a vanishing factor $a_N$ in front of the kinetic energy. The ch…