Multichannel generalization of eigen-phase preserving supersymmetric transformations

TL;DR

This paper extends eigen-phase preserving supersymmetric transformations to multichannel Schrödinger equations with an even number of channels, enabling parametric deformations of the Hamiltonian while maintaining scattering eigen-phases.

Contribution

It introduces a generalization of EPP SUSY transformations to N>2 channels, showing they exist only for even N and characterizing their parametric effects.

Findings

EPP SUSY transformations exist only for even number of channels.

A single EPP SUSY transformation deforms the Hamiltonian with specific parameters.

Eigen-phase shifts of the scattering matrix remain unchanged after transformation.

Abstract

We generalize eigen-phase preserving (EPP) supersymmetric (SUSY) transformations to $N>2$ channel Schr\"odinger equation with equal thresholds. It is established that EPP SUSY transformations exist only in the case of even number of channels, $N=2M$. A single EPP SUSY transformation provides an $M(M-1)+2$ parametric deformation of the matrix Hamiltonian without affecting eigen-phase shifts of the scattering matrix.