量子更新过程
Quantum renewal processes
摘要：
给出了具有记忆核的主方程的一般构造，其解由完全正的保迹映射给出。这些动力学超越Lindblad范式的参考经典更新过程，使他们被称为量子更新过程。它们可以通过被跳跃中断的半群动力学来描述，被独立分布的时间间隔分开，遵循合适的等待时间分布。在这个框架中，可以进一步引入修改的过程，其中前几个事件遵循不同的分布。一个至关重要的作用，标志着一个重要的区别，就经典的情况下，是由运营商订购。事实上，对于相同的基本量子变换选择，不同的量子动力学出现。特别是，对于修改的过程的情况下，这是很自然的，考虑时间反转的操作符排序，其中最后几个事件分布不同。
英文摘要：
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.
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