**题目：**Quantum Fokker-Planck dynamics

**报告人：**Louis Labuschagne

**报告人单位：**North-West University

**摘要：**The Fokker-Planck equation is a partial differential equation which is a key ingredient in many models in physics. Given that relevant models relate to the description of large systems, quantization of the Fokker-Planck equation should be done in a manner that respects this fact. With this in mind we develop a quantum counterpart of Fokker-Planck dynamics within the context of non-commutative analysis based on general von Neumann algebras. We achieve this by presenting a quantization of the generalized Laplace operator, and by also proposing a potential term conditioned to noncommutative analysis. We next obtain conditions under which the composite term generates Markov dynamics, before in closing examining the asymptotic behaviour of the Markov semigroup thus obtained. We also present a noncommutative Csiszar-Kullback inequality formulated in terms of a notion of relative entropy, and show that for more general systems, good behaviour with respect to this notion of entropy similarly ensures good asymptotic behaviour of the dynamics.

**时间：**2024年6月25日（星期二）, 14:00-15:00

**地点：**正心楼716

**报告人简介：**Louis Labuschagne obtained his PhD in 1988 in the field of Single Linear Operator theory. He started his professional academic career in the same year at Stellenbosch University, moving to the University of Pretoria in 1992. This move also coincided with a shift in his research focus to Operator Algebras and their application to Quantum Theory. After spending 19 years in Pretoria, first at the University of Pretoria and then UNISA from 2001, he took up an appointment at North-West University in January 2011, where he currently serves as the director of the Focus Area for Pure and Applied Analytics. He was also deeply involved in the genesis of the DSI-NRF Center of Excellence in Mathematical and Statistical Sciences, where he still serves on the steering committee.

He has built up a network of collaborators from Poland, France, China and the USA, and has supervised 4 PhD students. He is the author of 51 papers and 1 book. In his spare time he likes to jog, hike and study biblical theology.

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