Ttitle: Quantum Markov Semigroups and Complete Logarithmic Sobolev Inequalities
Speaker: Li Gao, Texas A&M University
Abstract: Quantum Markov semigroups were introduced in the seventies to model the evolution of irreversible open quantum systems. Mathematically, they are generalization of classical Markov semigroups where the underlying function space is replaced by a non-commutative operator algebra. For classical Markov semigroup, logarithmic Sobolev inequality is a basic and powerful tool in the study of the time to the equilibrium. When moving to the quantum world, a major difference and challenge is the presence of entanglement. In this talk, we will explore the situation that the open quantum system is entangled with another system. This leads to a ``complete'' log-Sobolev inequality that is stable under tensorization (which in quantum case is no longer automatic). In particular, we will focus on semigroups on matrix algebras and finite graphs. Based on joint works with Marius Junge and Nicholas LaRacuente.
Time: 15:00-16:00, 26, Dec, 2018. Place: Room 522, Gewu Building（格物楼）
