Time behaviour near to spectral singularities

Abstract

Spectral singularities such as exceptional points invoke specific physical effects. The present paper focuses upon the time dependent solutions of the Schrödinger equation. In a simple model it is demonstrated that - depending on initial conditions - within close proximity of exceptional points the time behaviour of the wave function displays characteristic features such as very fast decay or the opposite, i.e. very long life time. At the exceptional point the wave function typically has a linear term in time besides the usual exponential behaviour.

5 pages, 3 figures to appear in EPJ D

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Cited by in corpus (21)

• Non-Hermitian Physics
• The physics of exceptional points
• Signatures of three coalescing eigenfunctions
• Non-Hermitian topology: a unifying framework for the Andreev versus Majorana states controversy
• PT-Symmetric Sinusoidal Optical Lattices at the Symmetry-Breaking Threshold
• Nonorthogonal pairs of copropagating optical modes in deformed microdisk cavities
• Robustness of exceptional-point-based sensors against parametric noise: The role of Hamiltonian and Liouvillian degeneracies
• Fingerprints of exceptional points in the survival probability of resonances in atomic spectra
• Wave emission and absorption at spectral singularities
• On the time evolution at a fluctuating exceptional point
• Fano-Feshbach resonances in two-channel scattering around exceptional points
• Characteristic dynamics near two coalescing eigenvalues incorporating continuum threshold effects
• Harmonic inversion analysis of exceptional points in resonance spectra
• Non-divergent representation of non-Hermitian operator near the exceptional point with application to a quantum Lorentz gas
• Dressed bound states at chiral exceptional points
• Parity-time symmetry and coherent perfect absorption in a cooperative atom response
• Resonance in black hole ringdown: Benchmarking quasinormal mode excitation and extraction
• Spectral Singularities and Zero Energy Bound States
• Non-hermitian time evolution: from static to parametric instability
• Evolution of electric-field-induced quasibound states and resonances in one-dimensional open quantum systems
• Characteristic influence of exceptional points in quantum dynamics