有限密度下衰变与散射产生的味-动力学纠缠
Flavor--Kinetic Entanglement Production from Decay and Scattering at Finite Density
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中文总结 AI 辅助
该研究将散射-纠缠字典扩展到有限密度环境，通过味-动力学二分建立纠缠熵与碰撞概率的关联，并将其作为相变诊断，提出了一种表征热相结构的新方法。
中文摘要 AI 辅助
我们通过研究希尔伯特空间的味-动力学二分，将散射-纠缠字典扩展到有限密度环境中。我们证明，对动力学自由度求迹可将总分支变换概率直接映射到主导阶味-动力学线性纠缠熵。在有限密度下，真空分支变换概率被由与积分玻尔兹曼方程中相同的定向反应密度核构建的、占据数加权的碰撞概率所取代。所得可观测量是从介质中采样的一对粒子的浴平均味-动力学纠缠熵。作为原理验证，该框架被应用于O(N)单态标量扩展模型以探测热相变。在所研究的例子中，所得纠缠熵可用作基于碰撞的相变类型诊断，在一级相变处呈现有限不连续性，在连续相变处呈现非解析温度导数。这些例子提出了一种表征热相结构的新方法，与传统热力学序参量不同。
英文摘要
We extend the scattering-entanglement dictionary to finite-density environments by investigating the flavor--kinetic bipartition of the Hilbert space. We show that tracing over kinematic degrees of freedom maps the total branch-changing transition probability directly onto the leading flavor--kinetic linear entanglement entropy. At finite density, the vacuum branch-changing probability is replaced by an occupation-weighted collision probability, built from the same directed reaction-density kernel that enters the integrated Boltzmann equation. The resulting observable is the bath-averaged flavor--kinetic entanglement entropy of a pair sampled from the medium. As a proof of principle, this framework is applied to an $O(N)$ singlet-scalar extended model to probe thermal phase transitions. In the examples studied, the resulting entanglement entropy serves as a collision-based phase-transition-type diagnostic, exhibiting a finite discontinuity across a first-order phase transition and a nonanalytic temperature derivative for continuous transitions. These examples suggest a novel way to characterize thermal phase structures, distinct from traditional thermodynamic order parameters.
