耗散多项式动力学的非递归 Lindblad 量子化
A Nonrecursive Lindblad Quantization of Dissipative Polynomial Dynamics
浏览论文内容
中文总结 AI 辅助
本文提出一种非递归的 Lindblad 量子化方法，将任意平面多项式耗散流直接映射为开放量子系统，无需递归消除低阶项，并在半经典极限下恢复经典动力学特征，可用于设计具有指定经典结构的量子系统。
中文摘要 AI 辅助
我们提出了一种直接且非递归的构造方法，将任意平面多项式耗散流 $\dot{\alpha}=h(\alpha,\alpha^*)$ 映射为 Gorini--Kossakowski--Sudarshan--Lindblad 形式的开放量子系统。给定经典漂移的齐次分量，相应的哈密顿量和坍缩算符块在每个次数上通过代数方式独立获得。无需对低阶项进行递归消除：在大振幅极限 $|\alpha|\sim S\to\infty$ 下，由排序产生的低阶项被参数性地抑制，而平均场闭合为半经典局域态提供了指定的前导 $O(S)$ 漂移。这提供了一条从耗散经典动力学到显式开放量子系统实现的简单且系统的途径，但并未声称对经典流具有唯一的微观量子化。我们针对稳定不动点、Hopf 分岔和双稳态环流演示了该构造。相应的 Liouvillian 谱恢复了经典弛豫指数、极限环的径向 Floquet 指数和中性相位方向，以及双稳态情形下局部弛豫与环间切换之间的分离。这些例子表明，该构造不仅可用于分析给定的量子模型，还可用于在半经典极限下设计具有指定经典动力学结构的开放量子系统。
英文摘要
We present a direct and nonrecursive construction that maps an arbitrary planar polynomial dissipative flow $\dotα=h(α,α^*)$ to an open quantum system in Gorini--Kossakowski--Sudarshan--Lindblad form. Given the homogeneous components of the classical drift, the corresponding Hamiltonian and collapse-operator blocks are obtained algebraically and independently at each degree. No recursive cancellation of lower-order terms is required: in the large-amplitude limit $|α|\sim S\to\infty$, ordering-generated lower-degree terms are parametrically suppressed, while mean-field closure yields the prescribed leading $O(S)$ drift for semiclassically localized states. This provides a simple and systematic route from dissipative classical dynamics to explicit open-quantum-system realizations, without claiming a unique microscopic quantization of the classical flow. We demonstrate the construction for stable fixed points, a Hopf bifurcation, and a bistable-ring flow. The corresponding Liouvillian spectra recover the classical relaxation exponents, the radial Floquet exponent and neutral phase direction of a limit cycle, and the separation between local relaxation and inter-ring switching in the bistable case. These examples show that the construction can be used not only to analyze a given quantum model, but also to design open quantum systems with prescribed classical dynamical structures in the semiclassical limit.
发表机构
- Hebei University（河北大学）
- Hebei Key Laboratory of High-Precision Computation and Application of Quantum Field Theory（河北省量子场论高精度计算与应用重点实验室）
- Hebei Research Center of the Basic Discipline for Computational Physics（河北省计算物理学基础学科研究中心）
机构由 AI 辅助整理，请以论文原文为准。
