2017/10/12 by András Sütö, Andras Suto, Suto, Andras
Mathematics · Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #FOS: Physical sciences #Mathematical Physics (math-ph) #Physics of Superconductivity and Magnetism #Quantum Gases (cond-mat.quant-gas) #Quantum, superfluid, helium dynamics #cond-mat.quant-gas #math-ph #math.MP
paper · pdf · doi:10.48550/arxiv.1710.04441
proof of main theorems corrected, simplified
openalex publication_date 2017/10/12 · arxiv created 2017/12/05 · arxiv updated 2017/12/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Using the rigorous path integral formalism of Feynman and Kac we prove London's eighty years old conjecture that during the superfluid transition in liquid helium Bose-Einstein condensation (BEC) takes place. The result is obtained by proving first that at low enough temperatures macroscopic permutation cycles appear in the system, and then showing that this implies BEC. We find also that in the limit of zero temperature the infinite cycles cover the whole system, while BEC remains partial. For the Bose-condensed fluid at rest we define a macroscopic wave function. Via the equivalence of 1/2 spins and hard-core bosons the method extends to lattice models. We show that at low enough temperatures the spin-1/2 axially anisotropic Heisenberg models, including the isotropic ferro- and antiferromagnet and the XY model, undergo magnetic ordering.