Markovian Dynamics in Many-Body Quantum Systems (B07)

在这个项目中，我们探索量子晶格自旋系统的静态和动态性质之间的相互作用。 我们重点研究了这类系统的四个性质，即相互作用的局部性、相关性的衰减、快速混合和马尔可夫性。给定一个马尔可夫演化模型的戴维斯映射，这个项目的主要长期目标是描述条件的衰减相关性的平衡吉布斯状态下，相关的戴维斯半群混合迅速。这将对有效制备拓扑有序相位和量子纠错码的设计产生影响。

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.