Morphology of three-body quantum states from machine learning

TL;DR

This paper uses machine learning to classify the morphology of three-body quantum states, distinguishing between integrable and non-integrable regimes with high accuracy based on wave function features.

Contribution

It introduces a neural network approach to analyze quantum state probability distributions, identifying key features like normalization and nodal lines for classification.

Findings

Neural networks classify quantum states with 97% accuracy.

Wave function features such as normalization and zero elements are decisive.

Machine learning effectively analyzes quantum state morphology in theory and experiments.

Abstract

The relative motion of three impenetrable particles on a ring, in our case two identical fermions and one impurity, is isomorphic to a triangular quantum billiard. Depending on the ratio $\kappa$ of the impurity and fermion masses, the billiards can be integrable or non-integrable (also referred to in the main text as chaotic). To set the stage, we first investigate the energy level distributions of the billiards as a function of $1/\kappa\in [0,1]$ and find no evidence of integrable cases beyond the limiting values $1/\kappa=1$ and $1/\kappa=0$. Then, we use machine learning tools to analyze properties of probability distributions of individual quantum states. We find that convolutional neural networks can correctly classify integrable and non-integrable states.The decisive features of the wave functions are the normalization and a large number of zero elements, corresponding to the existence of a nodal line. The network achieves typical accuracies of 97%, suggesting that machine learning tools can be used to analyze and classify the morphology of probability densities obtained in theory or experiment.