发表机构
Fudan University; Department of Physics and Center for Field Theory and Particle Physics, Fudan University; Key Laboratory of Nuclear Physics and Ion-beam Application (MOE), Fudan University（复旦大学; 复旦大学物理系与场论与粒子物理中心; 复旦大学核物理与离子束应用教育部重点实验室）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究针对单种粒子与其他粒子的散射过程，构建了散射纠缠熵，推导了其表达式并得到Tsallis、Rényi熵的相关结果，结论通用且模型无关。
AI 中文摘要
我们构建了单种粒子（记为$A$）与其余末态粒子间一般散射过程的纠缠熵。假设初态为纯动量本征态，我们证明粒子$A$的福克空间中的约化密度矩阵在零粒子、单粒子及多粒子态下为块对角形式，且在单粒子态的动量基下为对角形式。因此，假设末态中产生的粒子$A$不超过一个，我们可利用散射概率和微分截面写出粒子$A$的冯·诺依曼熵$S_A$。$S_A$包含总散射概率（或截面）与微分分布的信息，后者源于无限维动量希尔伯特空间的相空间分辨率因子。我们的结果具有普适性且与模型无关，因为我们考虑的是时间演化产生的完整末态（$S|i\rangle$）而非特定结果，且只要产生多个粒子$A$的概率为次领头阶，该结果就适用。我们还在该框架下得到了$n\geq2$、Tsallis熵和Rényi熵，发现领头阶下它们与总散射概率成正比，且不包含微分信息。
英文摘要
We construct the entanglement entropy of a general scattering process between one particle species (denoted as $A$) and the rest of the final state. Assuming a pure initial momentum eigenstate, we show that the reduced density matrix in particle $A$'s Fock space is block-diagonal in zero-, one- and multi-particle states, and is diagonal in the momentum basis for the one-particle state. As a result, we could write down the Von Neumann entropy of particle $A$, $S_A$, in terms of scattering probabilities and differential cross sections, assuming no more than one particle $A$ is produced in the final state. $S_A$ contains the information of both the total scattering probabilities (or cross sections) and the differential distributions --- the latter depends on a phase-space resolution factor as a result of the infinite-dimensional momentum Hilbert space. Our result is general and model-independent since we consider the full final state from time evolution ($S|i\rangle$) rather than a specific outcome, and is applicable as long as the probability for producing multiple particle $A$ is subleading. We also obtain the $n\geq2$ Tsallis and Rényi entropies in our framework and find out that, at the leading order, they are proportional to the total scattering probability and carry no differential information.
Comments9 pages, 0 figures
