Spontaneous symmetry emergence in a Hermitian system of coupled oscillators without symmetry

T. T. Sergeev; E. S. Andrianov; A. A. Zyablovsky

doi:10.22331/q-2025-05-15-1746

Spontaneous symmetry emergence in a Hermitian system of coupled oscillators without symmetry

T. T. Sergeev, E. S. Andrianov, and A. A. Zyablovsky

Dukhov Research Institute of Automatics, 127055, 22 Sushchevskaya, Moscow Russia
Moscow Institute of Physics and Technology, 141700, 9 Institutskiy pereulok, Dolgoprudny Moscow region, Russia
Institute for Theoretical and Applied Electromagnetics, 125412, 13 Izhorskaya, Moscow Russia

Published:	2025-05-15, volume 9, page 1746
Editor:	Angelo Carollo
Eprint:	arXiv:2209.12497v6
Doi:	https://doi.org/10.22331/q-2025-05-15-1746
Citation:	Quantum 9, 1746 (2025).

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Abstract

Spontaneous symmetry breaking in systems with symmetry is a cornerstone phenomenon accompanying second-order phase transitions. Here, we predict the opposite phenomenon, namely, spontaneous symmetry emergence in a system that lacks symmetry. In the example of two coupled oscillators interacting non-symmetrically with a set of oscillators whose frequencies uniformly fill a finite frequency range, we demonstrate that the system state can acquire symmetry that is not inherent in the system Hamiltonian. The emergence of symmetry is manifested as a change in the system dynamics, which can be interpreted as a phase transition in a Hermitian system that lacks symmetry.

Featured image: The emergence of a symmetry in a system consisting of two coupled oscillators, one of which interacts with a reservoir of N oscillators. The symmetry emerges when the coupling strength between oscillators exceeds a critical value. The number of oscillators in the reservoir is 50 (the blue line), 100 (the orange line), 200 (the red line), and 400 (the black line).

Popular summary

Spontaneous symmetry breaking is a cornerstone phenomenon in physics that is often related to second-order phase transitions. In this work we consider a system of two coupled oscillators, one of which interacts with a reservoir represented by a finite set of oscillators. This system does not have symmetry with respect to permutation of oscillators. In the example of such a system, we predict a phenomenon that is opposite to spontaneous symmetry breaking, namely, spontaneous symmetry emergence in a system without symmetry. The emergence of symmetry manifests itself as a change in the system’s dynamics, which can be interpreted as a phase transition in such a system.

► BibTeX data

@article{Sergeev2025spontaneoussymmetry,
  doi = {10.22331/q-2025-05-15-1746},
  url = {https://doi.org/10.22331/q-2025-05-15-1746},
  title = {Spontaneous symmetry emergence in a {H}ermitian system of coupled oscillators without symmetry},
  author = {Sergeev, T. T. and Andrianov, E. S. and Zyablovsky, A. A.},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {9},
  pages = {1746},
  month = may,
  year = {2025}
}

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