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

• URL: http://arxiv.org/abs/2504.16334v1
• Date: Wed, 23 Apr 2025 00:58:11 GMT
• Title: Deep Neural Network Emulation of the Quantum-Classical Transition via Learned Wigner Function Dynamics
• Authors: Kamran Majid,
• Abstract summary: This paper introduces a novel approach employing deep neural networks to learn the dynamical mapping from initial quantum state parameters.<n>A deep feedforward neural network with an enhanced architecture was successfully trained for this prediction task, achieving a final training loss of 0.0390.<n>The implications of these findings for providing a new computational lens on the emergence of classicality are discussed.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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