A Simple Data-Driven Level Finding Method of Quantum Many-Body Systems based on Statistical Outlier Detection

TL;DR

This paper introduces a straightforward data-driven approach that uses statistical outlier detection to identify new energy levels in quantum many-body systems solely from observed spectral lines, without prior knowledge of the levels.

Contribution

The paper presents a novel, simple method that reconstructs energy levels by analyzing the coincidence of multiple transition lines, distinguishing true levels from random combinations.

Findings

Successfully identified new energy levels in atomic systems.

Demonstrated effectiveness on publicly available spectral data.

Applicable to both atomic and nuclear systems.

Abstract

We report a simple and pure data-driven method to find new energy levels of quantum many-body systems only from observed line wavelengths. In our method, all the possible combinations are computed from known energy levels and wavelengths of unidentified lines. As each excited state exhibits many transition lines to different lower levels, the true levels should be reconstructed coincidentally from many level-line combinations, while the wrong combinations distribute randomly. Such a coincidence can be easily detected statistically. We demonstrate this statistical method by finding new levels for various atomic and nuclear systems from unidentified line lists available online.