School Colloquium——$\Phi^4_3$ Theory from many-body quantum Gibbs states
报告人：朱蓉禅 (北京理工大学)
时间：2025-02-28 14:00-15:00
地点：智华楼四元厅
报告摘要： We derive the $\Phi^4_3$ 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 $\Phi^4_3$ 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. The connection to the quantum problem is then established by applying the variational approach and deriving a quantitative convergence of the quantum correlation functions to those of the Hartree classical field.
个人简介：朱蓉禅，北京理工大学教授，博士生导师，2012年博士毕业于中科院数学与系统科学研究院和德国比勒菲尔德大学。研究方向随机偏微分方程，主要关注奇异随机偏微分方程和随机流体方程以及通过随机量子化方法研究量子场模型。
