Speaker: Un Cig Ji (池雲植) 教授，Chungbuk National University, Korea

Inviter: 骆顺龙研究员

Title: Quantum Evolution Families Induced by Gaussian Generalized Mehler Semigroups

Language: English

Time & Venue: 2025.12.23 10:00-11:00 数学院南楼N620

Abstract: In this talk, based on classical and quantum white noise theory, we discuss a canonical construction of quantum evolution families on white noise operators. For this purpose, we first study time-inhomogeneous Gaussian generalized Mehler semigroups on white noise functionals. Then, utilizing canonical topological isomorphisms between the space of white noise operators and the space of two-variable white noise functionals, we construct quantum evolution families induced by these time-inhomogeneous Gaussian generalized Mehler semigroups. By establishing a notion of positivity for generalized operators, we introduce the concept of quantum Markov families of operators acting on the space of white noise operators. This construction of quantum evolution families leads to a more general notion of quantum evolution families on generalized operators.