用去噪器模拟核量子效应,无需重训练即可跨温度、同位素等条件通用。
Nuclear Quantum Effects as a Denoising Problem

- 将量子效应建模为可解析的高斯噪声,与训练好的经典去噪器组合求解。
- 在不同温度、质量、耗散强度下精确转移,且无需重新训练。
- 适用于核量子效应模拟,尤其适合需快速切换参数的研究场景。
核量子效应可通过虚时路径积分严格描述,将量子玻尔兹曼分布映射为经典副本组成的环状聚合物。然而,核质量、环境耦合及路径边界条件在模拟或训练模型中被固定,尽管这些量子上下文仅通过已知闭式表达的二次作用量影响路径测度。本文表明:仅基于经典玻尔兹曼统计训练的去噪器,在采样时与携带全部量子信息的解析高斯组件组合,即可精确生成核的量子玻尔兹曼分布。该组合在训练噪声不超过目标系综固有量子不确定性的条件下存在且精确,并对所有满足此约束的量子情境保持不变。理论上和数值实验中均实现了温度、同位素质量、耗散强度及路径边界条件的精确迁移,无需重训练。该方法还可推导出标记核的端到端位移与动量分布,来自开放虚时路径。原则上,该不变性亦可扩展至玻色子交换的置换边界条件,使用相同去噪器。在此视角下,生成建模的噪声与核量子涨落实为同一二次结构的两面。
原文摘要 · Abstract (English)
Nuclear quantum effects are rigorously captured by imaginary-time path integrals, which map the quantum Boltzmann distribution onto a ring polymer of classical replicas. Yet the nuclear masses, the coupling to the environment, and the boundary conditions of the path remain hard-wired in the simulation or the trained model, even though this quantum context enters the path measure only through a quadratic action known in closed form. Here we show that a denoiser trained on classical Boltzmann statistics alone, composed at sampling time with an analytic Gaussian component carrying the entire quantum context, yields the quantum Boltzmann distribution of the nuclei. Such a composition exists and is exact whenever the training noise does not exceed the intrinsic quantum uncertainty of the target ensemble, and it is invariant across all quantum contexts admitted by this bound. We show exact transfer across temperature, isotopic mass, dissipation strength, and the boundary conditions of the path in theory and in numerical experiments, without retraining. The last yields the end-to-end displacement and momentum distributions of a tagged nucleus from open imaginary-time paths. The same invariance extends in principle to the permuted boundary conditions of bosonic exchange, with the identical denoiser. In this view, the noise of generative modeling and the quantum fluctuations of the nuclei are two faces of the same quadratic structure.
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