发表机构
Department of Chemistry, University of Chicago; James Franck Institute, University of Chicago; Courant Institute of Mathematical Sciences, New York University（芝加哥大学化学系; 芝加哥大学詹姆斯·弗兰克研究所; 纽约大学应用数学科学研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究核量子效应，提出仅基于经典玻尔兹曼统计训练去噪器，采样时与高斯分量组合产生量子玻尔兹曼分布，该组合在特定条件下精确且不变，能在多条件下精确转移，无需重训，揭示了生成噪声与量子涨落的关联。
AI 中文摘要
核量子效应可通过虚时路径积分严格捕捉，它将量子玻尔兹曼分布映射到经典复制品的环聚合物上。然而，核质量、与环境的耦合以及路径的边界条件在模拟或训练模型中仍然是固定的。本文表明，仅在经典玻尔兹曼统计上训练的去噪器，在采样时与携带整个量子背景的解析高斯分量组合，可产生核的量子玻尔兹曼分布。这种组合在训练噪声不超过目标系综的固有量子不确定性时存在且精确，并且在该界限允许的所有量子背景下都是不变的。我们在理论和数值实验中展示了在温度、同位素质量、耗散强度和路径边界条件之间的精确转移，无需重新训练。最后得出了标记核从开放虚时路径的端到端位移和动量分布。相同的不变性原则上也扩展到玻色子交换的置换边界条件，使用相同的去噪器。从这个角度看，生成建模的噪声和核的量子涨落是同一二次结构的两面。
英文摘要
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.
Comments9 pages, 3 figures
