Geometric and Spectral Functional Analysis of Quantum Markov Semigroups on Lie Groups

Key Points

• This research aims to explore the geometric and spectral properties of quantum Markov semigroups on lie groups using curvature-dimension criteria and optimal transport.
• Application of curvature-dimension criteria to analyze quantum markov semigroups.
• Utilization of optimal transport frameworks to assess spectral properties.
• Examination of the thermodynamic limit in the context of the studied semigroups.
• Establishment of linkages between geometric properties and transport effects within quantum markov semigroups.
• Identification of optimal transport structures in the thermodynamic limit.
• Demonstration of implications for physical systems modeled by these semigroups.

Abstract