Morphology of three-body quantum states from machine learning

David Huber, Oleksandr V. Marchukov, Hans Werner Hammer*, Artem G. Volosniev

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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 κ 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/κ ∈ [0, 1] and find no evidence of integrable cases beyond the limiting values 1/κ = 1 and 1/κ = 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.

Original languageEnglish
Article number065009
JournalNew Journal of Physics
Issue number6
StatePublished - Jun 2021
Externally publishedYes


  • Impurity systems
  • Machine learning
  • Quantum billiards
  • Quantum chaos


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