arXiv:2504.16334quant-phcs.LG2025-04被引 1

用神经网络模拟量子到经典的演化过程,直接预测相空间分布变化。

Deep Neural Network Emulation of the Quantum-Classical Transition via Learned Wigner Function Dynamics

  • 用深度网络学习初始量子态与普朗克常数对相空间分布的动态映射
  • 训练损失降至0.0390,能准确预测不同ℏ下的演化结果
  • 适合研究量子经典过渡的物理学者和机器学习应用者

当普朗克常数ℏ趋近于零时,量子力学如何涌现出经典行为,仍是物理学中的根本挑战。本文提出一种新方法,利用深度神经网络直接学习从一维谐振子高斯波包的初始参数及ℏ值,到时间演化后相空间中威格纳函数参数的映射关系。通过解析计算生成了全面的数据集,并采用增强型前馈神经网络成功完成训练,最终训练损失约为0.0390。该网络展现出前所未有的能力,可精确捕捉威格纳函数演化的内在规律,从而实现对量子-经典过渡的直接模拟。通过系统调节ℏ值,可预测相空间分布的演化。这一成果为理解经典性涌现提供了新的计算视角,相较于以往仅学习可观测量映射的研究,本方法通过相空间表示实现了更直接的建模路径。

原文摘要 · Abstract (English)

The emergence of classical behavior from quantum mechanics as Planck's constant $\hbar$ approaches zero remains a fundamental challenge in physics [1-3]. This paper introduces a novel approach employing deep neural networks to directly learn the dynamical mapping from initial quantum state parameters (for Gaussian wave packets of the one-dimensional harmonic oscillator) and $\hbar$ to the parameters of the time-evolved Wigner function in phase space [4-6]. A comprehensive dataset of analytically derived time-evolved Wigner functions was generated, and a deep feedforward neural network with an enhanced architecture was successfully trained for this prediction task, achieving a final training loss of ~ 0.0390. The network demonstrates a significant and previously unrealized ability to accurately capture the underlying mapping of the Wigner function dynamics. This allows for a direct emulation of the quantum-classical transition by predicting the evolution of phase-space distributions as $\hbar$ is systematically varied. The implications of these findings for providing a new computational lens on the emergence of classicality are discussed, highlighting the potential of this direct phase-space learning approach for studying fundamental aspects of quantum mechanics. This work presents a significant advancement beyond previous efforts that focused on learning observable mappings [7], offering a direct route via the phase-space representation.

量子经典过渡神经网络相空间威格纳函数

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