高斯碰撞模型的记忆核与可分性
Memory kernel and divisibility of Gaussian Collisional Models
摘要：
在过去的几十年里，开放系统动力学中的记忆效应一直是人们感兴趣的主题。然而，量化这种影响的方法往往难以计算，而且可能缺乏分析洞察力。考虑到这一点，我们考虑高斯碰撞模型，其中非马尔可夫性通过相邻环境单元之间的额外相互作用引入。通过专注于连续变量高斯动力学，我们能够分析研究任意大小的模型。我们表明，动态可以投在马尔可夫嵌入的协方差矩阵，从而产生封闭形式的表达式的内存内核，管理的动态，一个数量，很少可以计算分析。基于中间映射的完全正性，对于可除性单调也是可能的。我们详细分析了两种类型的相互作用，分束器实现部分SWAP和双模压缩，纠缠的ancillas，并在同一时间，饲料激发到系统中。通过分析这两种典型情况下的记忆核和可分性，我们的结果有助于揭示量子域中记忆效应背后的复杂机制。
英文摘要：
Memory effects in the dynamics of open systems have been the subject of significant interest in the last decades. The methods involved in quantifying this effect, however, are often difficult to compute and may lack analytical insight. With this in mind, we consider Gaussian collisional models, where non-Markovianity is introduced by means of additional interactions between neighboring environmental units. By focusing on continuous-variable Gaussian dynamics, we are able to analytically study models of arbitrary size. We show that the dynamics can be cast in terms of a Markovian Embedding of the covariance matrix, which yields closed form expressions for the memory kernel that governs the dynamics, a quantity that can seldom be computed analytically. The same is also possible for a divisibility monotone, based on the complete positivity of intermediate maps. We analyze in detail two types of interactions, a beam-splitter implementing a partial SWAP and a two-mode squeezing, which entangles the ancillas and, at the same time, feeds excitations into the system. By analyzing the memory kernel and divisibility for these two representative scenarios, our results help to shed light on the intricate mechanisms behind memory effects in the quantum domain.
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