Spontaneous breaking of continuous scale invariance and Efimovian-like dynamics in a driven-dissipative harmonic oscillator
Abstract
The Efimov effect manifests discrete scale invariance through a geometric series of three-body bound states. Analogous discrete scale symmetry has been observed in the Efimovian expansion of scale-invariant strongly interacting Fermi gases. However, it is unclear whether strong correlation is necessary. Here we investigate the spontaneous breaking of continuous scale invariance in a simple driven-dissipative harmonic oscillator whose driving and dissipation parameters scale as 1/t. By transforming to logarithmic time, we show that the dynamics is governed by a non-Hermitian superoperator whose spectral decomposition reveals the emergence of a pair of eigenmodes with opposite real parts and equal imaginary parts. This signals the spontaneous breaking of continuous scale invariance and gives rise to Efimovian-like oscillations: log-periodic decay oscillations obeying discrete scaling laws. The onset of oscillations coincides with a PT-symmetry breaking transition in logarithmic time. The Efimovian-like oscillations are robust against weak nonlinear interactions and perturbations. Our work implies that the spontaneous breaking of continuous temporal scale symmetry and the emergence of Efimovian-like dynamics can even be observed in a simple driven-dissipative system without many-body interactions.
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BibTeX
@misc{wu2026spontaneous,
title = {{Spontaneous breaking of continuous scale invariance and Efimovian-like dynamics in a driven-dissipative harmonic oscillator}},
author = {Zehui Wu and Jian Yu and Jian-Song Pan},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.34926},
eprint = {2609.34926},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.34926},
}
RIS
TY - UNPB
TI - Spontaneous breaking of continuous scale invariance and Efimovian-like dynamics in a driven-dissipative harmonic oscillator
AU - Zehui Wu
AU - Jian Yu
AU - Jian-Song Pan
PY - 2026
DA - 2026/09/28
PB - arXiv
DO - 10.48550/arxiv.2609.34926
UR - https://arxiv.org/abs/2609.34926
AB - The Efimov effect manifests discrete scale invariance through a geometric series of three-body bound states. Analogous discrete scale symmetry has been observed in the Efimovian expansion of scale-invariant strongly interacting Fermi gases. However, it is unclear whether strong correlation is necessary. Here we investigate the spontaneous breaking of continuous scale invariance in a simple driven-dissipative harmonic oscillator whose driving and dissipation parameters scale as 1/t. By transforming to logarithmic time, we show that the dynamics is governed by a non-Hermitian superoperator whose spectral decomposition reveals the emergence of a pair of eigenmodes with opposite real parts and equal imaginary parts. This signals the spontaneous breaking of continuous scale invariance and gives rise to Efimovian-like oscillations: log-periodic decay oscillations obeying discrete scaling laws. The onset of oscillations coincides with a PT-symmetry breaking transition in logarithmic time. The Efimovian-like oscillations are robust against weak nonlinear interactions and perturbations. Our work implies that the spontaneous breaking of continuous temporal scale symmetry and the emergence of Efimovian-like dynamics can even be observed in a simple driven-dissipative system without many-body interactions.
ER -