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  • Open Access

Unveiling semiclassical structures in eigenstates of a quantum chaotic system using neural networks

J. Montes1,*, F. Borondo2,†, and Gabriel G. Carlo3,‡

  • *Contact author: jmontes.3@alumni.unav.es
  • †Contact author: f.borondo@uam.es
  • ‡Contact author: g.carlo@conicet.gov.ar
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APS Open Sci. 1, 000176 – Published 21 October, 2026

DOI: https://doi.org/10.1103/9xdp-mwln

Abstract

Physics-informed neural networks and neural quantum states have consolidated a new paradigm to analyze and discover physical phenomena through constrained neural parametrizations. In this context, we investigate whether the semiclassical structure of the eigenfunctions of a quantum chaotic system can be unveiled through unsupervised learning. To this end, we train a “quantum dictionary,” formulated as an overcomplete autoencoder, that sparsely represents the eigenstates of the system, using as an illustration the quantum baker map. The only explicit physical information imposed on the dictionary atoms is their localization in phase space, without providing any kind of information about the periodic orbits of the corresponding classical system. The model achieves high fidelity in reconstructing held-out validation eigenstates not used in the gradient optimization of the dictionary. By comparing the learned atoms with an independently constructed “semiclassical dictionary,” we find that many of them develop scarlike Husimi-density concentrations around short periodic orbits. This result is interesting in two ways: Phase-space localization, combined with sparse reconstruction and dictionary diversity, can recover nontrivial semiclassical organization from spectral data and at the same time periodic orbits confirm their fundamental role in the structure of eigenfunctions of quantum systems with chaotic classical dynamics. More generally, our proposed architecture opens a route to learning representations whose atoms optimize other chosen physical properties.

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APS Open Sci. 1, 000176– Published 21 October, 2026
Vol. 1
  • Received 8 July 2026
  • Accepted 1 October 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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