Morphology of three-body quantum states from machine learning

• URL: http://arxiv.org/abs/2102.04961v2
• Date: Mon, 2 Aug 2021 14:09:47 GMT
• Title: Morphology of three-body quantum states from machine learning
• Authors: David Huber, Oleksandr V. Marchukov, Hans-Werner Hammer, and Artem G. Volosniev
• Abstract summary: We show that a triangular quantum billiard can be integrable or non-integrable. 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.
• Score: 18.56475227525833
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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