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Quantum time crystals and interacting chiral gauge theories in atomic Bose-Einstein condensates: Role of the Page-Wootters mechanism

P. Öhberg1 and E. M. Wright1,2

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Phys. Rev. A 113, 023304 – Published 3 February, 2026

DOI: https://doi.org/10.1103/1m4d-kd46

Abstract

We build the case that our published chiral soliton model [Phys. Rev. Lett. 123, 250402 (2019)] can lead to a genuine quantum time crystal for finite atom numbers. To do this we compare results from the chiral soliton model with exact numerical solutions for the ground state of the three-particle Schrödinger equation in the limit that the spatial profile of the soliton is largely independent of its center-of-mass motion. The connection between the two approaches is found via the Page-Wootters mechanism, and this is what allows for dynamical evolution even in the quantum ground state, as required for a genuine quantum time crystal.

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Phys. Rev. A 113, 023304– Published 3 February, 2026
  • Received 24 September 2025
  • Accepted 5 January 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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