Markovian Dynamics in Many-Body Quantum Systems (B07)

• Subject Area: Mathematics
• Term: since 2023
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 470903074

In this project, we explore the interplay between static and dynamical properties of quantum lattice spin systems. We focus on the study of four properties of such systems, namely locality of interactions, decay of correlations, rapid mixing and Markovianity. Given a Markovian evolution modeled by a Davies map, the main long-term goal of this project is to characterize the conditions on the decay of correlations in the equilibrium Gibbs states under which the associated Davies semigroup mixes rapidly. This will have implications on efficient preparation of topologically ordered phases and design of quantum error-correcting codes.

• DFG Programme: CRC/Transregios
• Subproject of: TRR 352: Mathematics of Many-Body Quantum Systems and Their Collective Phenomena
• Applicant Institution: Ludwig-Maximilians-Universität München
• Project Heads: Professorin Dr. Angela Capel; Dr. Cambyse Rouzé