Unifying framework for amplification mechanisms: Spectral criticality, resonance, and nonnormality
Year: 2025
Type: article
Abstract: We bring together three key amplification mechanisms in linear dynamical systems: spectral criticality, resonance, and nonnormality. We present a unified linear framework that both distinguishes and quantitatively links these effects through two fundamental parameters: (1) the spectral distance to a conventional bifurcation or to a resonance and (2) a nonnormal index K (or condition number κ ) that measures the obliqueness of the eigenvectors. Closed-form expressions for the system's response in the form of the variance v ∞ of the observable responding to both Gaussian noise and periodic forcing reveal a general amplification law v ∞ = v 0 ( 1 + G ( K ) ) with nonnormal gain G ( K ) ∝ K 2 represented in universal phase diagrams. By reanalyzing a model of remote earthquake triggering based on breaking of Hamiltonian symmetry, we illustrate how our two-parameter framework significantly expands both the range of conditions under which amplification can occur and the magnitude of the resulting response, revealing a broad pseudocritical regime associated with large κ that previous single-parameter approaches overlooked. Similarly, in the non-Hermitian extensions of quantum optics provided by forward four-wave mixing experiments, we show the presence of a counterintuitive gain-from-loss effect that directly manifests nonnormal amplification in a propagating-wave setting. This predicts the possibility to engineer transient optical energy amplification without the need for true lasing or exact PT -symmetry breaking. Our framework applies to many other physical, natural, and social systems and offers diagnostic tools to distinguish true critical behavior from transient amplification driven by nonnormality.
Source: Physical Review Research
DOI: 10.1103/kdgw-shxf
Authors: Virgile Troude, Didier Sornette
Institution: Southern University of Science and Technology
Language: English
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $2,625
OpenAlex ID: W4416937975