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Unbounded Generators of Dynamical Semigroups

机译：动力半群的无穷生成器

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摘要

Dynamical semigroups have become the key structure for describing open system dynamics in all of physics. Bounded generators are known to be of a standard form, due to Gorini, Kossakowski, Sudarshan and Lindblad. This form is often used also in the unbounded case, but rather little is known about the general form of unbounded generators. In this paper we first give a precise description of the standard form in the unbounded case, emphasizing intuition, and collecting and even proving the basic results around it. We also give a cautionary example showing that the standard form must not be read too naively. Further examples are given of semigroups, which appear to be probability preserving to first order, but are not for finite times. Based on these, we construct examples of generators which are not of standard form.
机译：动力学半群已成为描述所有物理学中开放系统动力学的关键结构。由于Gorini，Kossakowski，Sudarshan和Lindblad，有界发生器是标准形式。这种形式也经常在无界情况下使用，但是对无界生成器的一般形式知之甚少。在本文中，我们首先对无边界情况下的标准形式进行精确描述，强调直觉，并收集甚至证明围绕它的基本结果。我们还给出了一个警告示例，表明不能过于天真地阅读标准表格。给出了半群的更多示例，这些半群似乎是概率保持一阶，​​但不是有限的时间。基于这些，我们构建了非标准形式的发电机示例。

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