Category: Physics

Summary: Finding the bridge strength where two refuge-pinned lobes in a non-Hermitian Hatano-Nelson system merge and delocalize through a hostile corridor.

Non-Hermitian localization in Hatano-Nelson systems is sensitive to both disorder and spatial structure. This experiment asks when two localized refuge states, each pinned in its own favorable region, stop behaving independently because a connecting hostile bridge becomes strong enough to fuse them into a broader delocalized mode.

The script builds dense non-symmetric operators for a dual-refuge geometry and uses GPU iterative deepening to bisect the bridge-delocalization threshold. By following the leading mode rather than only the spectrum in bulk, it identifies the point where persistence spills out of the refuges and the two lobes effectively become one structure.

That makes the result useful as a geometric transition marker in a non-Hermitian setting. The experiment targets a refuge-corridor configuration that appears less directly mapped than standard single-impurity or coupled-chain localization studies.

Method: GPU dense non-symmetric eigensolves with iterative deepening and bisection on hostile bridge strength in a dual-refuge Hatano-Nelson operator.

What is measured: Critical bridge-delocalization threshold, localization profile of the leading mode, spectral stability indicators, and bracket width.