Speaker: 朱蓉禅教授，北京理工大学

Inviter: 流体力学方程研究中心

Title: Derivation of $\Phi^4_3$ theory from many-body quantum Gibbs states

Language: Chinese

Time & Venue: 2025.04.17 10:30-11:30 南楼N202

Abstract: We derive the $\Phi^4_3$ measure on the torus as a rigorous limit of the quantum Gibbs state of an interacting Bose gas just above the Bose-Einstein phase transition. The proof is based on two key ingredients: first, we approximate the local $\Phi^4_3$ theory by a Hartree measure with a nonlocal interaction using techniques from stochastic quantization and paracontrolled calculus; and then, we connect the Hartree theory to the quantum problem using correlation inequalities and a finite-dimensional semiclassical approximation. This result is inspired by previous works of Lewin-Nam-Rougerie and Fröhlich-Knowles-Schlein-Sohinger on the derivation of 3D Hartree and $\Phi^4_2$ theories. The talk is based on joint work with Phan Thanh Nam and Xiangchan Zhu.