Addressing the Non-perturbative Regime of the Quantum Anharmonic Oscillator by Physics-Informed Neural Networks

TL;DR

This paper demonstrates how physics-informed neural networks can effectively solve the quantum anharmonic oscillator's Schrödinger equation, including regimes where traditional perturbative methods fail, by using an unsupervised deep learning approach.

Contribution

It introduces a novel application of PINNs to non-perturbative quantum systems, bridging solutions across different theoretical regimes, including real and imaginary frequencies.

Findings

Successfully computed eigenenergies and eigenfunctions for varying quartic interaction strengths.

Bridged solutions between perturbative, strong coupling, and pure quartic regimes.

Laid groundwork for applying PINNs to quantum field theory problems.

Abstract

The use of deep learning in physical sciences has recently boosted the ability of researchers to tackle physical systems where little or no analytical insight is available. Recently, the Physics-Informed Neural Networks (PINNs) have been introduced as one of the most promising tools to solve systems of differential equations guided by some physically grounded constraints. In the quantum realm, such approach paves the way to a novel approach to solve the Schroedinger equation for non-integrable systems. By following an unsupervised learning approach, we apply the PINNs to the anharmonic oscillator in which an interaction term proportional to the fourth power of the position coordinate is present. We compute the eigenenergies and the corresponding eigenfunctions while varying the weight of the quartic interaction. We bridge our solutions to the regime where both the perturbative and the strong coupling theory work, including the pure quartic oscillator. We investigate systems with real and imaginary frequency, laying the foundation for novel numerical methods to tackle problems emerging in quantum field theory.