Quirin Vogel

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math.PR2025

Off-diagonal long-range order for the free Bose gas via the Feynman--Kac formula

Wolfgang KÃ¶nig, Quirin Vogel, Alexander Zass

We consider the path-integral representation of the ideal Bose gas under various boundary conditions. We show that Bose--Einstein condensation occurs at the famous critical density…

math.PR2024

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

Tianyi Bai, Wolfgang KÃ¶nig, Quirin Vogel

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