Model G Tunneling Analogue

A toy 1D simulation of a tunneling-like effect in an SQK / Model G style continuous-medium framework.

Overview

This repository explores whether a localized organized excitation can:

• propagate through a medium,
• weaken in a hostile barrier region,
• and re-form beyond that barrier if enough coherence survives.

The project is not a semiconductor-accurate tunneling simulation. It is a conceptual analogue model intended to visualize a reaction-diffusion / field-based interpretation of tunneling.

Conceptual Interpretation

In this framework:

• the localized packet acts as an electron-like excitation,
• the barrier is a region where that excitation is disfavored,
• tunneling is interpreted as partial decay plus re-stabilization of organized structure.

Model

The toy model evolves a scalar field u(x,t) using:

• diffusion,
• rightward drift,
• nonlinear self-limiting growth,
• a suppressive barrier,
• and a recovery/trap region beyond the barrier.

The governing form is:

$$u_t = D u_{xx} - c u_x + (g(x) - s u^2) u$$

where g(x) includes a hostile barrier and a more favorable recovery region.

What the simulation measures

The code reports:

• Transmission: field norm beyond the barrier
• Reflection: field norm remaining on the left
• Barrier occupancy: field norm inside the barrier
• Peak beyond barrier: whether a localized packet re-forms on the right

Installation

pip install -r requirements.txt

Run

python simulation.py

##Typical Result

With tuned parameters, the simulation can show:

strong suppression in the barrier, nonzero transmission, and re-formation of a smaller packet beyond the barrier.

As barrier width increases, transmission drops sharply, giving a tunneling-like dependence on barrier thickness.

##Notes

This is a toy analogue model, not an experimentally validated replacement for conventional quantum tunneling theory.

It is best understood as a conceptual demonstration of how tunneling-like behavior might be described in a continuous-medium / reaction-diffusion ontology.

Possible Extensions scan barrier width and fit T(w) move from 1D to 2D test vortex-like packet structure replace the toy scalar field with a fuller multi-field Model G system