Category: Physics

Summary: Estimating how short-range correlated disorder shifts the delocalization threshold in the Hatano-Nelson model.

The Hatano-Nelson model is a classic non-Hermitian system where asymmetry can keep part of the spectrum complex until disorder becomes strong enough to localize states. This experiment asks whether positively correlated diagonal disorder changes that delocalization threshold by creating longer favorable corridors than an IID disorder field would.

The script studies a periodic chain at fixed asymmetry and uses GPU-scale threshold mapping to compare correlated and uncorrelated disorder. The focus is the disorder strength where the complex spectrum collapses, signaling a change in transport and localization behavior.

That matters because correlated disorder is common in realistic media, yet most baseline threshold pictures assume independence. The project therefore measures how spatial memory in the disorder field alters a standard non-Hermitian localization boundary.

Method: GPU-accelerated threshold mapping in the periodic Hatano-Nelson chain, comparing correlated and IID diagonal disorder at fixed asymmetry.

What is measured: Critical disorder threshold, collapse of the complex spectrum, effect of disorder correlation, and finite-size threshold behavior.