Repulsion of Resonance States and Exceptional Points

1999/09/15 by W. D. Heiss · 1 voice · 10 citations
Materials Science · Physics and Astronomy · #Quantum chaos and dynamical systems #Solid-state spectroscopy and crystallography #Spectroscopy and Quantum Chemical Studies #quant-ph

paper · pdf · doi:10.1103/physreve.61.929

4 pages, latex, 3 figures, to appear in Phys.Rev.E

arxiv created 1999/09/15 · arxiv published 1999/09/15 · openalex publication_date 2000/01/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Level repulsion is associated with exceptional points which are square root singularities of the energies as functions of a (complex) interaction parameter. This is also valid for resonance state energies. Using this concept it is argued that level anti-crossing (crossing) must imply crossing (anti-crossing) of the corresponding widths of the resonance states. Further, itis shown that an encircling of an exceptional point induces a phase change of one wave function but not of the other. An experimental setup is discussed where this phase behaviour which differs from the one encountered at a diabolic point can be observed.

Cited by

• Eigenstates in coupled-channel scattering amplitude and their effects on spectrum
• Liouvillian and Hamiltonian exceptional points of atomic vapors: The spectral signatures of quantum jumps
• Universal quantum control by non-Hermitian Hamiltonian
• Exceptional Points of Non-hermitian Operators
• Asymmetric scattering and nonorthogonal mode patterns in optical microspirals
• Exceptional points in the spectra of atoms in external fields
• Renormalization and fixed points in Hilbert space
• Goos-Hänchen shift and localization of optical modes in deformed microcavities
• Formation of Long-Lived, Scarlike Modes near Avoided Resonance Crossings in Optical Microcavities
• Geometric phase for non-Hermitian Hamiltonians and its holonomy interpretation

Discussions

• Exceptional points do not strictly speaking require PT-symmetric Hamiltonians. From a mathematical point of view they are branch point singularities of a matrix or operator when the parameter which de [stackexchange, 3 points]