Spectral Singularities and Zero Energy Bound States

Details Spectral Singularities and Zero Energy Bound States Spectral Singularities and Zero Energy Bound States

2011-05-16

arxiv.org/abs/1105.3141v1

Eur.Phys.J.D63:369-373,2011

Physics

Condensed Matter

Quantum Gases

5pages, 3 figures

Scientific paper

10.1140/epjd/e2011-20174-4

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.

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