Nuclear Quantum Effects as a Denoising Problem

2026-07-21

AI Summary

This work addresses the limitations of conventional path integral methods in simulating nuclear quantum effects, which are constrained by hard-coded dependencies on mass, environmental coupling, and boundary conditions. The authors propose reframing nuclear quantum effects as a denoising problem: by training a denoising diffusion model solely on classical Boltzmann distributions and combining it with an analytical Gaussian prior that encodes full quantum information, the method accurately generates quantum Boltzmann distributions during sampling. The key insight is that the noise structure in the generative model shares the same quadratic form as nuclear quantum fluctuations, enabling precise transferability across temperatures, isotopic masses, dissipation strengths, and path boundary conditions without retraining. Theoretical analysis and numerical experiments confirm the approach’s generalization across diverse quantum scenarios and its ability to faithfully reproduce end-to-end displacement and momentum distributions of labeled nuclei.

Abstract

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.

Problem

• Nuclear Quantum Effects
• Quantum Boltzmann Distribution
• Path Integral
• Generative Modeling
• Denoising

Innovation

• nuclear quantum effects
• denoising
• path integral
• quantum Boltzmann distribution
• generative modeling