标题： 量子更新过程 显示英文标题

标题： Quantum renewal processes

摘要： 我们引入了一种广义主方程的构造方法，其解由完全正且迹保留的映射给出。这些超越林布兰德（Lindblad）范式的动力学是基于经典的更新过程获得的，因此被称为量子更新过程。它们可以通过半群动力学与跳跃事件结合描述，跳跃事件之间的时间间隔服从独立分布，并遵循适当的等待时间分布。 在此框架下，还可以进一步引入修正过程，在该过程中前几次事件遵循不同的分布。 一个关键因素是算符排序，这标志着与经典情况的重要区别。事实上，对于相同的量子变换选择，会得到不同的量子动力学。特别是对于修正过程的情况，考虑时间反转的算符排序是自然的，即最后几次事件的分布不同。 显示英文摘要

摘要： We introduce a general construction of master equations with memory kernel whose solutions are given by completely positive trace preserving maps. These dynamics going beyond the Lindblad paradigm are obtained with reference to classical renewal processes, so that they are termed quantum renewal processes. They can be described by means of semigroup dynamics interrupted by jumps, separated by independently distributed time intervals, following suitable waiting time distributions. In this framework, one can further introduce modified processes, in which the first few events follow different distributions. A crucial role, marking an important difference with respect to the classical case, is played by operator ordering. Indeed, for the same choice of basic quantum transformations, different quantum dynamics arise. In particular, for the case of modified processes, it is natural to consider the time inverted operator ordering, in which the last few events are distributed differently.