北京-圣彼得堡数学论坛——$\Phi^4_3$ Theory from many-body quantum Gibbs states
报告人：朱蓉禅 (北京理工大学)
时间：2025-05-08 20:00-21:00
地点：Online (VooV Meeting)
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, 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.
Bio: Rongchan Zhu is a Professor at Beijing Institute of Technology. She earned her Ph.D. in 2012 from both the Academy of Mathematics and Systems Science, Chinese Academy of Sciences, and Bielefeld University in Germany. Her research focuses on Stochastic Partial Differential Equations (SPDEs), with particular emphasis on singular SPDEs, stochastic fluid equations, and the study of quantum field models via stochastic quantization methods.
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