Table 1 Comparison of four distinct wave-localization phenomena based on localization length, position, physical origin, and fate in the thermodynamic limit

From: Scale-tailored localization and its observation in non-Hermitian electrical circuits

 

Anderson

NHSE

SFL

STL

Loc. length

\({{{\mathcal{O}}}}(1)\)

\({{{\mathcal{O}}}}(1)\)

\({{{\mathcal{O}}}}(N)\)

\({{{\mathcal{O}}}}(l)\)

Position

bulk

boundary

impurity

boundary/impurity

Origin

wave interference

point gap

local impurity

long-range coupling

Theo. limit

✓

✓

× 

✓

  1. They include (1) Anderson localization, (2) NHSE: non-Hermitian skin effect, (3) SFL: scale-free localization, and (4) STL: scale-tailored localization. For Anderson localization or NHSE, the localization length or skin depth is finite. For SFL and STL, the localization length scales with the total system size and coupling range, respectively.
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