Non-Hermitian Physics: Exceptional Points & PT Symmetry
Gain-Loss Balance · Eigenvalue Coalescence · PT-Broken / Unbroken Phases
Re(E₊)
Re(E₋)
Im(E₊)
Im(E₋)
PT-Symmetric Dimer
Coupling κ
1.0
Gain/loss γ (current)
0.5
Scan γ range max
2.5
PT Unbroken
PT-symmetric dimer Hamiltonian:
H = [[iγ, κ], [κ, -iγ]]
Eigenvalues:
E± = ±√(κ² − γ²)
Exceptional point (EP):
γ = κ
→ eigenvalues coalesce
E = 0 (degenerate, eigenvectors merge)
PT-unbroken phase (γ < κ):
E± = ±√(κ²−γ²)
real
PT-broken phase (γ > κ):
E± = ±i√(γ²−κ²)
purely imaginary
→ exponential gain/loss in time