PT-Symmetric Exceptional Point

A non-Hermitian Hamiltonian H = [[iγ, κ],[κ, -iγ]] with balanced gain (+γ) and loss (-γ) coupled by κ. Eigenvalues E± = ±√(κ²-γ²): real in the PT-unbroken phase (κ>γ), complex in broken phase (κ<γ), coalescing at the exceptional point κ=γ where eigenvectors also merge.

Eigenvalue Spectrum vs γ/κ
Dynamics |ψ₁(t)|², |ψ₂(t)|²
Complex Eigenvalue Plane
PT Phase: Unbroken — Real Eigenvalues
Iris Lab · PT symmetry · Exceptional points · Non-Hermitian physics