Quantum Corral

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What Is It?

This experiment confines a two-dimensional lattice field inside a circular Dirichlet mask. A sinusoidal source at the centre drives the cavity while the drive frequency is swept across a range.

At certain frequencies, the cavity accepts energy efficiently and forms standing-wave patterns. The spectrum is measured from stored field energy rather than derived from an eigenvalue solver.

What It Tests

The experiment asks whether resonant cavity modes emerge from a local masked telegraph kernel when the geometry supplies only a circular boundary and a centre drive.

This makes it a useful confinement benchmark. If the lattice dynamics are behaving properly, energy peaks should appear at discrete frequencies and the field should settle into recognisable standing-wave patterns inside the corral.

How It Works

A circular mask clamps all exterior cells to zero. Interior cells evolve by a local four-neighbour telegraph update. Masked neighbours contribute zero, which gives the cavity its Dirichlet boundary condition.

The centre source is driven as amp·sin(ω·t). For each frequency, the field is allowed to warm up, then total stored energy is measured as Σ(φ²) + Σ(v²). The spectrum graph accumulates these measurements across the sweep.

The expected continuum reference is a circular Dirichlet cavity, where the lowest radial modes relate to zeros of the Bessel function J₀. The experiment does not compute those modes. It only drives the lattice and measures what the local update accepts.

What Is Not Hard-Coded

• No eigenvalue solver is used.
• No Bessel functions are evaluated.
• No analytic cavity solution is imposed.
• No standing-wave mode shape is painted into the renderer.

The wall, source, local update and energy measurement are the active ingredients. The resonant spectrum is allowed to appear or fail on those terms.

Why It Matters

Quantum Corral is a clean test because confinement makes the result difficult to bluff. A cavity has modes, gaps and energy peaks. If the local lattice kernel cannot produce them, later claims about bounded field structure become weaker.

For CAELIX, the result sits between simple propagation and more complex burdened structures. It shows how geometry alone can select a discrete spectrum from local dynamics, without putting the spectrum in by hand.