Focus Event on Modified Logarithmic Sobolev Inequalities for Quantum Markov Semigroups

The evolution of a quantum spin system weakly coupled to a heat-bath can be modeled by a quantum Markov semigroup, and its velocity of convergence to equilibrium can be studied using modified logarithmic Sobolev inequalities.

The goal of this event is to study the existence of such inequalities for certain families of quantum Markov semigroups and derive applications in several contexts related to quantum information theory.

Participants:

Ivan Bardet (Inria, Paris)
Angela Capel (Universität Tübingen)
Cambyse Rouzé (Technische Universität München)
Daniel Stilck França (ENS Lyon)

Report:

The main goal of this focused event organized by A. Capel was to bring together experts in quantum Markov semigroups (I. Bardet, C. Rouze, D. Franca) for a week of joint work on the speed of convergence to equilibrium in quantum mechanical systems. A key tool in studying the speed of convergence is the modified logarithmic Sobolev inequality (MLSI). A great deal of progress has been made in establishing MLSI's for certain physically relevant quantum Markov semigroups and in exploring their applications in quantum information theory.