essay · 2026-09-30

How is non-hermitian perturbation theory applied to elastodynamics

Research into non-Hermitian quantum mechanics reveals that extending perturbation theory beyond Hermitian systems requires specialized techniques like the Complex Absorbing Potential (CAP) and specific Hamiltonian partitioning schemes. The Epstein-Nesbet scheme is particularly effective because it partitions the full CAP-Schroedinger Hamiltonian to handle both many-body problems and resonance states effectively, as noted in studies of electronic resonances in molecules. When applied to autoionizing resonances like those in helium atoms using complex-rotation methods, this approach addresses issues where standard perturbation series radii are too small for convergence. This matters because it provides a rigorous mathematical foundation for analyzing unstable quantum systems that traditional Hermitian theories cannot describe locally or perturbatively.

Sources

• Elements of a non-Hermitian quantum theory without Hermitian conjugation - scalar product and scattering — 2015-01-06T19:08:51Z
• Non-Hermitian Generalization of Rayleigh-Schrödinger Perturbation Theory — 2024-12-06T16:30:19Z
• Non-Hermitian Rayleigh-Schroedinger Perturbation Theory — 2004-01-17T13:12:39Z
• Linking scalar elastodynamics and non-Hermitian quantum mechanics
• Linking Scalar Elastodynamics and Non-Hermitian Quantum...
• (PDF) Perturbation approach to the complex-rotation method
• Perspective on non-Hermitian elastodynamics
• Non-Hermitian Elastodynamics | Request PDF