Non-Hermitian Exceptional Point (EP3)

Third-order exceptional point: three eigenvalues coalesce
1.00
0.00
1.00
Exceptional Points (EPs) are non-Hermitian degeneracies where both eigenvalues and eigenvectors coalesce.
At an EP3, three eigenvalues merge: the characteristic polynomial becomes (λ−λ₀)³ = 0.
The 3×3 Jordan form has off-diagonal 1s, giving power-law dynamics t²e^{λ₀t} instead of oscillations.
Left panel: eigenvalues in complex plane. Right panel: Riemann sheet topology near EP3.