相互作用系统量子到经典转变中的关联与分支机制

中文摘要 AI 辅助

我们从约化动力学闭合的角度分析相互作用系统的量子到经典转变。玻姆轨迹被用作全波函数产生的概率流的诊断工具，而非另一套量子预测。保留坐标的闭合经典或半经典描述之所以能够出现，要么是因为相互作用诱导的关联被抑制，要么是因为所关注的观测量对剩余关联不敏感。我们使用三个模型来分离不同的机制。在硬核碰撞中，宽相对坐标波包的前沿在其中心之前到达边界，并通过反射和干涉产生空间不可分离性。在拉比模型中，当自旋-位置协方差阻止自旋动力学仅由平均振子坐标决定时，混合量子-经典埃伦费斯特近似失效。在内部态依赖力模型中，总平均位置满足精确的埃伦费斯特方程，而波函数分离为分支分辨的指针分量；因此，平均经典性并不意味着分支级经典性。这些例子表明，相互作用系统的量子到经典转变不仅受波包局域化控制，还受相互作用诱导的关联是否以及如何进入约化运动方程的控制。

英文摘要

We analyze the quantum-to-classical transition of interacting systems from the viewpoint of reduced dynamical closure. Bohmian trajectories are used as a diagnostic of the probability flow generated by the full wavefunction, rather than as an alternative set of quantum predictions. A closed classical or semiclassical description of a retained coordinate can emerge either because interaction-induced correlations are suppressed or because the observable of interest is insensitive to the correlations that remain. Three models are used to isolate distinct mechanisms. In a hard-core collision, the leading tail of a broad relative-coordinate wave packet reaches the boundary before its center and generates spatial nonseparability through reflection and interference. In the Rabi model, the mixed quantum-classical Ehrenfest approximation fails when spin-position covariances prevent the spin dynamics from being determined solely by the mean oscillator coordinate. In an internal-state-dependent force model, the total mean position obeys an exact Ehrenfest equation, while the wavefunction separates into branch-resolved pointer components; mean classicality therefore does not imply branch-level classicality. These examples show that the quantum-to-classical transition of interacting systems is controlled not only by wave-packet localization but also by whether and how interaction-induced correlations enter the reduced equations of motion.

发表机构

• School of Science and Engineering, The Chinese University of Hong Kong (Shenzhen)（香港中文大学（深圳）理工学院）

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