Initial broadband spectrum, due to sharp spatial gradient of the blink pulse,
Spectral narrowing or mode locking as coherent structures form,
Energy cascades resembling turbulence spectra in some regimes (notably for large A0A_0A0).
6. Geometric Interpretation of Spatio-temporal Dynamics
By mapping energy density (x,t)=I(x,t)2\rho(x,t) = |I(x,t)|^2(x,t)=I(x,t)2 onto a scalar curvature analog via:
R(x,t)2(x,t)R(x,t) \sim -\nabla^2 \rho(x,t)R(x,t)2(x,t)
we visualize time-evolving geometries as curvature fields. These "metric analogs" evolve from flat, structureless states to highly curved, domain-rich landscapes, thus mimicking cosmic evolution from homogeneity to complexity.
The spatio-temporal evolution reveals that even a minimal nonlinear field model, seeded by a blink excitation, is sufficient to generate rich geometric dynamics, including localized energy structures, topological transitions, and curvature analogs. This opens an experimental path to simulate and study analog cosmology with high fidelity in condensed matter systems.
C. Pattern Formation and Localized Structures
One of the most intriguing results of simulating the nonlinear field equation with blink excitation is the spontaneous emergence of structured, localized patterns in space and time. These self-organizing features are direct consequences of the interplay between nonlinearity, dissipation, and field gradients, and they offer a compelling analog to the complex structuring observed in early-universe scenarios and condensed matter systems alike.
1. Mechanisms of Pattern Formation
The evolution of the information field I(x,t)I(\vec{x}, t)I(x,t) exhibits a spontaneous symmetry breaking driven by the nonlinear term I2I\lambda |I|^2 II2I, especially after the system exits the initial high-energy blink phase. This leads to:
Instability amplification of specific wave modes,
Phase segregation, where neighboring domains adopt distinct phase values,
Amplitude modulation instabilities, allowing for envelope soliton formation.
Together, these processes give rise to spatially structured patterns with clear signatures:
Lattice-like nodal structures in 2D configurations,
Radial ring patterns from central excitation zones,
Filamentary webs in 3D configurations reminiscent of cosmic strings or domain walls.
2. Types of Emergent Structures
