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arXiv · 1007.4421

Scattering cross section resonance originating from a spectral singularity

Boris F. Samsonov
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Abstract

Using techniques of supersymmetric quantum mechanics, scattering properties of Hermitian Hamiltonians, which are related to non-Hermitian ones by similarity transformations, are studied. We have found that the scattering matrix of the Hermitian Hamiltonian coincides with the phase factor of the non-unitary scattering matrix of the non-Hermitian Hamiltonian. The possible presence of a spectral singularity in a non-Hermitian Hamiltonian translates into a pronounced resonance in the scattering cross section of its Hermitian counterpart. This opens a way for detecting spectral singularities in scattering experiments; although a singular point is inaccessible for the Hermitian Hamiltonian, the Hamiltonian "feels" the presence of the singularity if it is "close enough". We also show that cross sections of the non-Hermitian Hamiltonian do not exhibit any resonance behavior and explain the resonance behavior of the Hermitian Hamiltonian cross section by the fact that corresponding scattering matrix, up to a background scattering matrix, is a square root of the Breit-Wigner scattering matrix.

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Boris F. Samsonov. 2011-09-07. Scattering cross section resonance originating from a spectral singularity. https://doi.org/10.1088/1751-8113%2F44%2F39%2F392001

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