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Solitons, chaos, and quantum phenomena: A deterministic approach to the Schrödinger equation

Damià Gomila*

  • *Contact author: damia@ifisc.uib-csic.es
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Phys. Rev. Research 7, 033276 – Published 23 September, 2025

DOI: https://doi.org/10.1103/l3xp-yrrv

Abstract

We show that the Schrödinger equation describes the ensemble mean dynamics of solitons in a Galilean invariant field theory where we interpret solitons as particles. On a zero background, solitons move classically, following Newton's second law; however, on a nonzero amplitude chaotic background, their momentum and position fluctuate fulfilling an exact uncertainty relation, which gives rise to the emergence of quantum phenomena. The Schrödinger equation for the ensemble of solitons is obtained from this exact uncertainty relation, and the amplitude of the background fluctuations is what corresponds to the value of ℏ. We confirm our analytical results running simulations of solitons moving against a potential barrier and comparing the ensemble probabilities with the predictions of the time-dependent Schrödinger equation, providing a deterministic version of the quantum tunneling effect. We conclude with a discussion of how our theory does not present statistical independence between measurement and experiment outcomes.

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Phys. Rev. Research 7, 033276– Published 23 September, 2025
  • Received 23 April 2025
  • Accepted 30 July 2025
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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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