Huber, David; Marchukov, Oleksandr V.; Hammer, Hans Werner; Volosniev, ArtemIST Austria
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.
New Journal of Physics
We thank Aidan Tracy for his input during the initial stages of this project. We thank Nathan Harshman, Achim Richter, Wojciech Rzadkowski, and Dane Hudson Smith for helpful discussions and comments on the manuscript. This work has been supported by European Union's Horizon 2020 research and innovation program under the Marie Skłodowska-Curie Grant Agreement No. 754411 (AGV); by the German Aeronautics and Space Administration (DLR) through Grant No. 50 WM 1957 (OVM); by the Deutsche Forschungsgemeinschaft through Project VO 2437/1-1 (Project No. 413495248) (AGV and HWH); by the Deutsche Forschungsgemeinschaft through Collaborative Research Center SFB 1245 (Project No. 279384907) and by the Bundesministerium für Bildung und Forschung under Contract 05P18RDFN1 (HWH). HWH also thanks the ECT* for hospitality during the workshop 'Universal physics in Many-Body Quantum Systems—From Atoms to Quarks'. This infrastructure is part of a project that has received funding from the European Union's Horizon 2020 research and innovation program under Grant Agreement No. 824093. We acknowledge support by the Deutsche Forschungsgemeinschaft and the Open Access Publishing Fund of Technische Universität Darmstadt.
Huber D, Marchukov OV, Hammer HW, Volosniev A. Morphology of three-body quantum states from machine learning. New Journal of Physics. 2021;23(6). doi:10.1088/1367-2630/ac0576
Huber, D., Marchukov, O. V., Hammer, H. W., & Volosniev, A. (2021). Morphology of three-body quantum states from machine learning. New Journal of Physics. IOP Publishing. https://doi.org/10.1088/1367-2630/ac0576
Huber, David, Oleksandr V. Marchukov, Hans Werner Hammer, and Artem Volosniev. “Morphology of Three-Body Quantum States from Machine Learning.” New Journal of Physics. IOP Publishing, 2021. https://doi.org/10.1088/1367-2630/ac0576.
D. Huber, O. V. Marchukov, H. W. Hammer, and A. Volosniev, “Morphology of three-body quantum states from machine learning,” New Journal of Physics, vol. 23, no. 6. IOP Publishing, 2021.
Huber D, Marchukov OV, Hammer HW, Volosniev A. 2021. Morphology of three-body quantum states from machine learning. New Journal of Physics. 23(6), 065009.
Huber, David, et al. “Morphology of Three-Body Quantum States from Machine Learning.” New Journal of Physics, vol. 23, no. 6, 065009, IOP Publishing, 2021, doi:10.1088/1367-2630/ac0576.
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