Supersymmetric transformations for coupled channels with threshold differences

Abstract

The asymptotic behaviour of the superpotential of general SUSY transformations for a coupled-channel Hamiltonian with different thresholds is analyzed. It is shown that asymptotically the superpotential can tend to a diagonal matrix with an arbitrary number of positive and negative entries depending on the choice of the factorization solution. The transformation of the Jost matrix is generalized to "non-conservative" SUSY transformations introduced in Sparenberg et al (2006 J. Phys. A: Math. Gen. 39 L639). Applied to the zero initial potential the method permits to construct superpartners with a nontrivially coupled Jost-matrix. Illustrations are given for two- and three-channel cases.

17 pages, 3 explicit examples and figures added

References in corpus (2)

• Phase shift effective range expansion from supersymmetric quantum mechanics
• Multichannel coupling with supersymmetric quantum mechanics and exactly-solvable model for Feshbach resonance

Cited by in corpus (9)

• Single- and coupled-channel radial inverse scattering with supersymmetric transformations
• Exactly-solvable coupled-channel potential models of atom-atom magnetic Feshbach resonances from supersymmetric quantum mechanics
• Singular matrix Darboux transformations in the inverse scattering method
• Eigenphase preserving two-channel SUSY transformations
• Shadow poles in a coupled-channel problem calculated with Berggren basis
• Coupling between scattering channels with SUSY transformations for equal thresholds
• The $J$-matrix inverse scattering approach for coupled channels with different thresholds
• Spectral properties of non-conservative multichannel SUSY partners of the zero potential
• Multichannel generalization of eigen-phase preserving supersymmetric transformations