Scattering cross-section resonance originating from a spectral singularity

作者：Samsonov Boris F^*

来源：Journal of Physics A-Mathematical and Theoretical, 2011, 44(39): 392001.

DOI：10.1088/1751-8113/44/39/392001

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 the corresponding scattering matrix, up to a background scattering matrix, is a square root of the Breit-Wigner scattering matrix.

• 出版日期2011-9-30