Avalanches and Aging Driven by Parametric Amplification in Kerr Oscillator Networks

Alejandro S. Gómez; Javier del Pino

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arXiv · 2610.26573

Avalanches and Aging Driven by Parametric Amplification in Kerr Oscillator Networks

Alejandro S. Gómez·Javier del Pino

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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 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. While aging delays the approach to the stationary state, additive noise sets a floor on the seeds and unsticks the network, shortening the longest dwells first while the activation sequence survives to noise several orders of magnitude stronger.

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Alejandro S. Gómez, Javier del Pino. 2026-10-19. Avalanches and Aging Driven by Parametric Amplification in Kerr Oscillator Networks. https://arxiv.org/abs/2610.26573

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