论文标题
局部和非本地主方程之间的相互作用：精确的和近似的动力学
The interplay between local and non-local master equations: exact and approximated dynamics
论文作者
论文摘要
主方程是描述开放量子系统演变的有用工具。为了表征动态的数学特征和物理起源，考虑同一系统的不同类型的主方程通常是有用的。在这里，我们得出了时间局部和整体差异描述之间的确切连接，重点是交换动力学类别。使用阻尼基础形式主义的使用使我们能够通过使用时间的函数，而其拉普拉斯仅转换，从而使一般过程从一个主方程到另一个方程，反之亦然。我们进一步分析了时间本地和整体分化的主方程的lindbladian形式，在其中我们解释了不同集合的Lindbladian运营商的外观。此外，我们研究了红场样的近似，该近似将精确的整数方程式转换为时间内定位的方程，以时空的时间为单位。除了将所得主方程的结构与与精确动力学相关的那些方程式相关联之外，我们还研究了近似值对马克维亚性的影响。特别是，我们表明，随着时间的流逝，粗晶片可能会引入记忆效应，从而导致违反动力学的划分性能。
Master equations are a useful tool to describe the evolution of open quantum systems. In order to characterize the mathematical features and the physical origin of the dynamics, it is often useful to consider different kinds of master equations for the same system. Here, we derive an exact connection between the time-local and the integro-differential descriptions, focusing on the class of commutative dynamics. The use of the damping-basis formalism allows us to devise a general procedure to go from one master equation to the other and vice-versa, by working with functions of time and their Laplace transforms only. We further analyze the Lindbladian form of the time-local and the integro-differential master equations, where we account for the appearance of different sets of Lindbladian operators. In addition, we investigate a Redfield-like approximation, that transforms the exact integro-differential equation into a time-local one by means of a coarse graining in time. Besides relating the structure of the resulting master equation to those associated with the exact dynamics, we study the effects of the approximation on Markovianity. In particular, we show that, against expectation, the coarse graining in time can possibly introduce memory effects, leading to a violation of a divisibility property of the dynamics.
