Category: Physics

Summary: Estimating the bandwidth prefactor where random band matrices cross from Wigner-Dyson to Poisson spectral statistics.

Random band matrices interpolate between fully mixed random matrices and nearly local systems, making them a classic model for localization and transport. This experiment asks for the finite-size threshold bandwidth where the spectrum stops showing level repulsion and instead looks Poisson-like.

The script generates symmetric band matrices, measures spacing statistics, and uses GPU-accelerated eigensolves with iterative deepening and bisection on the rescaled bandwidth. Carrying the bracket across larger matrix sizes turns the computation into a direct estimate of the critical prefactor in the expected square-root scaling law.

That prefactor is not known analytically. The value of the experiment is therefore quantitative: it builds a dense threshold map rather than relying on scattered exploratory sweeps.

Method: GPU dense symmetric eigensolves with iterative deepening and bisection on the rescaled bandwidth in random band matrices.

What is measured: Critical bandwidth prefactor, spacing-ratio crossover, implied critical bandwidth, system size reached, and bracket width.