Markovsche Dynamik in Vielteilchen-Quantensystemen

01.01.2023 bis 31.12.2026

The interplay between static and dynamical properties of classical lattice spin systems is by now largely understood. For example, the equivalence between decay of correlations of a Gibbs state and the rapid convergence of its corresponding Glauber dynamics has been established in high generality on mathematical grounds. However, the quantum counterpart of the theory remains largely unexplored. The long-term goal of the proposed project is to gain a better mathematical understanding of intrinsically quantum properties of local dissipative evolutions over generic spin many-body quantum systems. We will focus on four main properties of such systems, namely locality of interactions, decay of correlations, rapid mixing and Markovianity.