Markovian Dynamics in Many-Body Quantum Systems (B07)

在这个项目中，我们探索了量子晶格自旋系统的静态和动力学性质之间的相互作用。我们着重研究了这类系统的四个性质，即相互作用的局域性、相关性的衰减性、快速混合和马尔可夫性。给定一个由Davies映射模拟的马尔可夫演化，这个项目的主要长期目标是刻画在平衡Gibbs态下关联迅速混合的关联衰变的条件。这对于拓扑有序相的有效制备和量子纠错码的设计具有重要意义。

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.