Avalanches and Aging Driven by Parametric Amplification in Kerr Oscillator Networks
Abstract
Gain, loss, and nonlinearity shape the phase-space landscape of driven-dissipative systems, such as Kerr parametric oscillator (KPO) networks realized in superconducting, nanomechanical, and photonic arrays. Networks of KPOs exploit the stationary states of this landscape for Ising machines, bosonic error-correcting codes, and sensing. Yet how transients reach these states from a given initial condition remains largely unexplored. Here we show that KPO networks with nonlinear couplings can develop avalanches in their deterministic transient dynamics: rapid cascades of amplification between modes reminiscent of the relaxation avalanches of glassy systems. The mechanism is that parametric gain first activates the modes whose detuning it can overcome, and their nonlinear frequency shifts then pull dormant modes into the gain window one at a time. Dormant modes keep decaying while they wait for their turn, so every activation starts from a smaller seed and the intervals between activations grow geometrically. The network thus ages: the longer it has evolved, the slower it changes, and activations accumulate only logarithmically in time. In a 20-mode network, each dwell lasts about twice as long as the previous one.
Related
- Full-band reciprocal parametric amplification in coupled oscillator arrays
- Parametric amplification in a Kerr Oscillator based on Ne FIB Nanobridges
- Improving precision scaling via backaction-evading continuous measurement in a driven-dissipative Kerr parametric oscillator
- Semiconductor optical amplification of a diode-pumped 1-GHz Ti:sapphire oscillator
- Coherent-feedback-enhanced nonreciprocal entanglement via directional optical parametric amplification
BibTeX
@misc{gomez2026avalanches,
title = {{Avalanches and Aging Driven by Parametric Amplification in Kerr Oscillator Networks}},
author = {Alejandro S. Gómez and Javier del Pino},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.26573},
eprint = {2610.26573},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.26573},
}
RIS
TY - UNPB
TI - Avalanches and Aging Driven by Parametric Amplification in Kerr Oscillator Networks
AU - Alejandro S. Gómez
AU - Javier del Pino
PY - 2026
DA - 2026/10/22
PB - arXiv
DO - 10.48550/arxiv.2610.26573
UR - https://arxiv.org/abs/2610.26573
AB - Gain, loss, and nonlinearity shape the phase-space landscape of driven-dissipative systems, such as Kerr parametric oscillator (KPO) networks realized in superconducting, nanomechanical, and photonic arrays. Networks of KPOs exploit the stationary states of this landscape for Ising machines, bosonic error-correcting codes, and sensing. Yet how transients reach these states from a given initial condition remains largely unexplored. Here we show that KPO networks with nonlinear couplings can develop avalanches in their deterministic transient dynamics: rapid cascades of amplification between modes reminiscent of the relaxation avalanches of glassy systems. The mechanism is that parametric gain first activates the modes whose detuning it can overcome, and their nonlinear frequency shifts then pull dormant modes into the gain window one at a time. Dormant modes keep decaying while they wait for their turn, so every activation starts from a smaller seed and the intervals between activations grow geometrically. The network thus ages: the longer it has evolved, the slower it changes, and activations accumulate only logarithmically in time. In a 20-mode network, each dwell lasts about twice as long as the previous one.
ER -