Spectral Singularities and Zero Energy Bound States

Abstract

Single particle scattering around zero energy is re-analysed in view of recent experiments with ultra-cold atoms, nano-structures and nuclei far from the stability valley. For non-zero orbital angular momentum the low energy scattering cross section exhibits dramatic changes depending on the occurrence of either a near resonance or a bound state or the situation in between, that is a bound state at zero energy. Such state is singular in that it has an infinite scattering length, behaves for the eigenvalues but not for the eigenfunctions as an exceptional point and has no pole in the scattering function. These results should be observable whenever the interaction or scattering length can be controlled.

5pages, 3 figures

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Cited by in corpus (6)

• Spectral singularities in PT-symmetric periodic finite-gap systems
• Characteristic dynamics near two coalescing eigenvalues incorporating continuum threshold effects
• Spectral Singularities and Zero Energy Bound States
• Resonant spectra of multipole-bound anions
• Evolution of electric-field-induced quasibound states and resonances in one-dimensional open quantum systems
• Characteristic influence of exceptional points in quantum dynamics