Supersymmetric transformations for coupled channels with threshold differences

TL;DR

This paper analyzes the asymptotic behavior of superpotentials in supersymmetric quantum mechanics for coupled channels with different thresholds, generalizing transformations and constructing superpartners with nontrivial couplings.

Contribution

It introduces a generalized approach to SUSY transformations for coupled channels with thresholds, including non-conservative transformations and explicit construction of superpartners.

Findings

Superpotential asymptotically tends to a diagonal matrix with arbitrary entries.

Generalized transformation of the Jost matrix for non-conservative SUSY.

Constructed superpartners with nontrivially coupled Jost matrices for zero initial potential.

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.