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Morphology of three-body quantum states from machine learning

Huber, David ; Marchukov, Oleksandr V. ; Hammer, Hans-Werner ; Volosniev, Artem G. (2021):
Morphology of three-body quantum states from machine learning. (Publisher's Version)
In: New Journal of Physics, 23 (6), IOP Publishing, ISSN 1367-2630,

Available under CC BY 4.0 International - Creative Commons, Attribution.

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Item Type: Article
Origin: Secondary publication via sponsored Golden Open Access
Status: Publisher's Version
Title: Morphology of three-body quantum states from machine learning
Language: English

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 thewave 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.

Journal or Publication Title: New Journal of Physics
Journal volume: 23
Number: 6
Publisher: IOP Publishing
Collation: 20 Seiten
Classification DDC: 500 Naturwissenschaften und Mathematik > 530 Physik
Divisions: 05 Department of Physics > Institute of Nuclear Physics
Date Deposited: 25 Aug 2021 12:37
Last Modified: 25 Aug 2021 12:37
Corresponding Links:
URN: urn:nbn:de:tuda-tuprints-193666
Additional Information:

Keywords: quantum billiards, machine learning, impurity systems, quantum chaos

URI: https://tuprints.ulb.tu-darmstadt.de/id/eprint/19366
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