Huber, David ; Marchukov, Oleksandr V. ; Hammer, Hans-Werner ; Volosniev, Artem G. (2021)
Morphology of three-body quantum states from machine learning.
In: New Journal of Physics, 2021, 23 (6)
doi: 10.26083/tuprints-00019366
Artikel, Zweitveröffentlichung, Verlagsversion
Kurzbeschreibung (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 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.
| Typ des Eintrags: | Artikel |
|---|---|
| Erschienen: | 2021 |
| Autor(en): | Huber, David ; Marchukov, Oleksandr V. ; Hammer, Hans-Werner ; Volosniev, Artem G. |
| Art des Eintrags: | Zweitveröffentlichung |
| Titel: | Morphology of three-body quantum states from machine learning |
| Sprache: | Englisch |
| Publikationsjahr: | 2021 |
| Publikationsdatum der Erstveröffentlichung: | 2021 |
| Verlag: | IOP Publishing |
| Titel der Zeitschrift, Zeitung oder Schriftenreihe: | New Journal of Physics |
| Jahrgang/Volume einer Zeitschrift: | 23 |
| (Heft-)Nummer: | 6 |
| Kollation: | 20 Seiten |
| DOI: | 10.26083/tuprints-00019366 |
| URL / URN: | https://tuprints.ulb.tu-darmstadt.de/19366 |
| Zugehörige Links: | |
| Herkunft: | Zweitveröffentlichung aus gefördertem Golden Open Access |
| Kurzbeschreibung (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 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. |
| Status: | Verlagsversion |
| URN: | urn:nbn:de:tuda-tuprints-193666 |
| Zusätzliche Informationen: | Keywords: quantum billiards, machine learning, impurity systems, quantum chaos |
| Sachgruppe der Dewey Dezimalklassifikatin (DDC): | 500 Naturwissenschaften und Mathematik > 530 Physik |
| Fachbereich(e)/-gebiet(e): | 05 Fachbereich Physik 05 Fachbereich Physik > Institut für Kernphysik |
| Hinterlegungsdatum: | 25 Aug 2021 12:37 |
| Letzte Änderung: | 01 Sep 2021 10:48 |
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| Zugehörige Links: | |
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