3 papers
math.PR2024
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 bosons in dimension in a trap in a mean-field setting with a vanishing factor in front of the kinetic energy. The ch…
math.PR2023
Off-diagonal long-range order for the free Bose gas via the Feynman--Kac formula
Wolfgang König, 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.PR2022
Gibbs measures for the repulsive Bose gas
Tianyi Bai, Quirin Vogel
We prove the existence of Gibbs measures for the Feynman representation of the Bose gas with non-negative interaction in the grand-canonical ensemble. Our results are valid for all…