用神经网络模拟量子系统如何随普朗克常数变小趋向经典行为。
Neural Network Emulation of the Classical Limit in Quantum Systems via Learned Observable Mappings
- 训练神经网络学习量子谐振子的初始期望值与ℏ值到位置期望值演化的映射。
- 在ℏ趋近于零时，网络预测结果呈现经典力学规律，揭示量子-经典过渡特征。
- 为理解量子力学基础问题提供新工具，适合对量子哲学与机器学习交叉研究者。
量子力学的经典极限，通过严格变形量子化等框架形式化研究，仍是物理哲学中的深层课题。本文提出一种计算方法，利用神经网络模拟量子谐振子在普朗克常数ℏ趋于零时经典行为的涌现。我们构建并训练神经网络，学习从初始期望值和ℏ值到位置期望值随时间演化映射关系。通过分析网络在不同ℏ值下的预测表现，旨在揭示量子-经典过渡的计算特性。本工作展示了机器学习作为探索量子力学基础问题及其经典极限的补充工具的潜力。
原文摘要 · Abstract (English)
The classical limit of quantum mechanics, formally investigated through frameworks like strict deformation quantization, remains a profound area of inquiry in the philosophy of physics. This paper explores a computational approach employing a neural network to emulate the emergence of classical behavior from the quantum harmonic oscillator as Planck's constant $\hbar$ approaches zero. We develop and train a neural network architecture to learn the mapping from initial expectation values and $\hbar$ to the time evolution of the expectation value of position. By analyzing the network's predictions across different regimes of hbar, we aim to provide computational insights into the nature of the quantum-classical transition. This work demonstrates the potential of machine learning as a complementary tool for exploring foundational questions in quantum mechanics and its classical limit.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。