These nonlinear structures serve as testbeds for emergent spacetime behavior, including:
Local control of analog curvature via tailored pulses,
Information trapping and release mimicking black hole evaporation,
Exploring causal structure and signal delay in curved emergent metrics.
They establish the groundwork for simulating early-universe topological defects and transitions, with experimental accessibility via condensed matter analogs such as magnonic lattices, optical solitons, or Josephson junction arrays.
III. Numerical Simulations
A. Blink Excitation Trigger: Initial Pulse Design
To explore the dynamic emergence of localized structures and curvature analogs within the nonlinear information field, we begin with the design of an appropriate blink excitation trigger---a sudden, spatially confined, and temporally brief pulse that mimics a localized fluctuation in the quantum vacuum. This "blink" serves as the analog of a primordial event in the cosmological narrative, akin to a fluctuation that seeds a universe.
1. Functional Form of the Initial Excitation
The initial condition for the information field I(x,t)I(\vec{x}, t)I(x,t) is specified as:
I(x,t=0)=A0exp(xx0222)ei0I(\vec{x}, t=0) = A_0 \exp\left(-\frac{|\vec{x} - \vec{x}_0|^2}{2\sigma^2}\right) \cdot e^{i\theta_0}I(x,t=0)=A0exp(22xx02)ei0 Itt=0=0\left.\frac{\partial I}{\partial t}\right|_{t=0} = 0tIt=0=0
Where:
A0A_0A0 is the amplitude of the excitation,
x0\vec{x}_0x0 is the spatial center of the pulse,
\sigma controls the spatial width (blink size),
0\theta_00 is the initial phase (uniform or randomized depending on the simulation class).
This form allows precise control of energy localization, phase coherence, and spatial extent. The initial pulse resembles a delta-like energy insertion, matching the "blink" nomenclature in both form and function.
2. Parameter Regimes for Structure Formation
