量子化与镜像约化在非互易动力学哈密顿嵌入中不对易
Quantization and Mirror Reduction Do Not Commute in Hamiltonian Embeddings of Nonreciprocal Dynamics
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中文总结 AI 辅助
该研究证明非互易动力学的哈密顿嵌入在经典层面精确，但其正则量子化与镜像约化不对易，导致半经典奇异构造，并给出对数对应时间公式。
中文摘要 AI 辅助
哈密顿嵌入可以在扩大互易系统的不变流形上精确表示耗散的非互易经典动力学。我们证明，这种嵌入的正则量子化不必与约化到目标动力学对易。对于最近为成对非互易相互作用引入的镜像构造，不变流形是拉格朗日的。因此，对镜像条件的精确量子强制会移除动力学扇区，而不是产生约化流的量子类似物。如果仅在半经典层面施加约束，目标动力学的收缩会在共轭镜像方向产生逆转置展开。量子不确定性随后给出 $\ln D\ge\Xi(t)+n\ln[\pi/(\sigma\epsilon)]$，其中 $\Xi=-\ln|\det M|$ 是累积收缩，$D$ 是环面希尔伯特空间维数。一自由度和二自由度非互易模型的精确有限维外尔演化证实了所得的对数对应时间，包括当初始局域化尺度随 $\hbar$ 变化时其预测的变化。因此，经典嵌入是精确的，但其直接正则量子化是一种奇异半经典构造。
英文摘要
Hamiltonian embeddings can represent dissipative nonreciprocal classical dynamics exactly on invariant manifolds of enlarged reciprocal systems. We show that canonical quantization of such an embedding need not commute with reduction to the target dynamics. For the mirror construction recently introduced for pairwise nonreciprocal interactions, the invariant manifold is Lagrangian. Exact quantum enforcement of the mirror condition therefore removes the dynamical sector rather than producing a quantum analogue of the reduced flow. If the constraint is imposed only semiclassically, contraction of the target dynamics generates inverse-transpose expansion in the conjugate mirror directions. Quantum uncertainty then gives $\ln D\geΞ(t)+n\ln[π/(σε)]$, where $Ξ=-\ln|\det M|$ is the accumulated contraction and $D$ the torus Hilbert-space dimension. Exact finite-dimensional Weyl evolution of one- and two-degree-of-freedom nonreciprocal models confirms the resulting logarithmic correspondence time, including its predicted change when the initial localization scales with $\hbar$. Thus the classical embedding is exact, but its direct canonical quantization is a singular semiclassical construction.
发表机构
- Clemson University（克莱姆森大学）
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