Neural Network Emulation of the Classical Limit in Quantum Systems via Learned Observable Mappings
This work addresses a foundational problem in quantum mechanics for physicists and philosophers, but it is incremental as it applies existing neural network methods to a new computational task.
The paper tackled the problem of understanding the classical limit in quantum systems by using a neural network to emulate how classical behavior emerges from the quantum harmonic oscillator as Planck's constant approaches zero, demonstrating machine learning as a complementary tool for exploring this foundational question.
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.