论文标题
马尔可夫政权以外的动力地图
Dynamical maps beyond Markovian regime
论文作者
论文摘要
量子动态图提供了量子演变的合适数学表示。这是完全阳性的概念，它提供了量子演化的适当数学表示，并引起了封闭的哈密顿系统的统一演变的强大概括。开放系统的量子演变的一个突出的例子是马尔可夫半群。在接下来的内容中，我们分析了正面和完全积极地图的两个半群。在后一种情况下，动力学由著名的Gorini-Kossakowski-Lindblad-Sudarshan（GKLS）主程式支配。然而，马尔可夫半群仅提供了一般量子进化的大致描述。我们分析的主要主题是超出该制度的动态图。近年来，非马克维亚量子进化引起了很多关注，并且有很多专门的文献。在本报告中，我们分析了由时间局部发电机和/或非本地记忆内核控制的量子动力学。特别关注{\ em crovisibility}的概念，该概念通常用作马尔可道的定义。特别是，所谓的CP-划分性（与P-差异性相反）的概念被广泛接受为量子马尔可道性的适当定义。我们讨论分裂性的许多重要的物理含义。我们还简要讨论了动态图以外的马尔可维亚性的概念，也就是说，当人们可以访问“系统 +环境”的演变时。整个博览会更多地集中在它们之间的一般概念和复杂的联系上，而不是研究特定系统。我们通过开放量子系统（例如振幅阻尼和相阻尼模型）的范式模型来说明分析的概念。
Quantum dynamical maps provide suitable mathematical representation of quantum evolutions. It is the very notion of complete positivity which provides a proper mathematical representation of quantum evolution and gives rise to the powerful generalization of unitary evolution of closed Hamiltonian systems. A prominent example of quantum evolution of an open system is a Markovian semigroup. In what follows, we analyze both the semigroups of positive and completely positive maps. In the latter case the dynamics is governed by the celebrated Gorini-Kossakowski-Lindblad-Sudarshan (GKLS) Master Equation. Markovian semigroups, however, provide only an approximate description of general quantum evolution. The main topic of our analysis are dynamical maps beyond this regime. Non-Markovian quantum evolution attracted a lot of attention in recent years and there is a vast literature dedicated to it. In this report we analyze quantum dynamics governed by time-local generators and/or non-local memory kernels. A special attention is devoted to the concept of {\em divisibility} which is often used as a definition of Markovianity. In particular, the concept of so called CP-divisibility (in contrast to P-divisibility) is widely accepted as a proper definition of quantum Markovianity. We discuss a number of important physical implications of divisibility. We also briefly discuss the notion of Markovianity beyond the dynamical map, that is, when one has an access to the evolution of `system + environment'. The entire exposition is concentrated more on the general concepts and intricate connections between them than on studying particular systems. We illustrate the analyzed concepts by paradigmatic models of open quantum systems like the amplitude damping and phase damping models.
