Morphology of three-body quantum states from machine learning
David Huber · Oleksandr V. Marchukov · Hans-Werner Hammer · Artem G. Volosniev
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 in the main text as chaotic). To set the stage, we first investigate the energy level distributions of the billiards as a function of and find no evidence of integrable cases beyond the limiting values and . 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.