Analyzing quantum chaos in three-body systems with machine learning

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 of the impurity and fermion masses, the billiards can be integrable or non-integrable (also referred to as chaotic). 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 high accuracies, suggesting that machine learning tools can be used to analyze and classify the morphology of probability densities obtained in theory and experiment.