Non-Gaussian Noise: A Minimal Structural Model Based on Spread–Contraction Dynamics

This work investigates the structural origin of non‑Gaussian quantum noise by introducing two universal degrees of freedom: spread and contraction. These two components appear broadly in quantum optics, measurement theory, and statistical physics, and they characterize how a distribution acquires smoothness, nonlocality, sharpness, or irreversibility. Using a minimal 1+1 dimensional dynamical model, we show that the competition between spread and contraction determines the shape of the distribution intensity p(x). When the ratio between the two crosses a critical value, the system undergoes a continuous yet abrupt transition through three regimes: Gaussian → non‑Gaussian → two‑component. The model reproduces key signatures of non‑Gaussianity—such as changes in kurtosis, skewness, and the emergence of two‑component spectra—without introducing additional parameters. This framework provides a unified structural perspective on phenomena including the disappearance of interference fringes, sudden contraction in weak measurements, and non‑Gaussian noise observed in optical state tomography and decoherence experiments. The spread–contraction plane serves as a general classification map for understanding how non‑Gaussian noise arises from the balance between smoothing and localization mechanisms, independent of any specific physical theory.