Category: Physics

Summary: Finding the disorder-correlation level where a non-Hermitian mode relocalizes from bulk support to a boundary skin state.

Non-Hermitian systems can pile eigenmodes against a boundary through the skin effect, but disorder can suppress or reshape that behavior. This experiment asks when Markov-clustered asymmetric hopping is correlated enough to drive the dominant right eigenmode into a robust boundary-skin regime.

The model uses dense asymmetric operators with single-seed Markov disorder and repeatedly bisects the correlation parameter while increasing system size. At each stage it measures whether the leading mode is extended in the bulk or concentrated near the boundary.

That makes the experiment a direct threshold map for the onset of skin localization under correlated disorder. It links transport asymmetry and disorder memory in a way that standard clean-model analyses do not capture.

Method: Dense non-Hermitian eigensolve with iterative deepening and bisection on Markov disorder correlation, reading out right-eigenvector localization.

What is measured: Critical correlation threshold, boundary localization of the dominant mode, bulk-versus-skin support, and bracket width.