2025/02/07 by Phan Thành Nam, Nam, Phan Thành, Rongchan Zhu +3 · 1 citation
Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR) #Quantum many-body systems #Theoretical and Computational Physics
paper · pdf · doi:10.48550/arxiv.2502.04884
openalex publication_date 2025/02/07 · openalex created_date 2025/02/11 · openalex updated_date 2026/07/28
We derive the Φ43 measure on the torus as a rigorous limit of the quantum Gibbs state of an interacting Bose gas, where the limiting classical measure describes the critical behavior of the Bose gas just above the Bose--Einstein phase transition. Since the quantum problem is typically formulated using a nonlocal interaction potential, a key challenge is to approximate the local Φ43 theory by a Hartree measure with a nonlocal interaction. This requires uniform estimates on the Hartree measure, which are achieved using techniques from recent development on stochastic quantization and paracontrolled calculus from \citeGIP15. The connection to the quantum problem is then established by applying the variational approach in \citeLewNamRou-21, where using a recent correlation inequality from \citeDeuNamNap-25 we refine the analysis and derive a quantitative convergence of the quantum correlation functions to those of the Hartree classical field.