Fermion in a multi-kink-antikink soliton background, and exotic supersymmetry

TL;DR

This paper constructs and analyzes a fermion system in a multi-kink-antikink soliton background, revealing its exotic supersymmetry properties and connections to integrable equations and condensed matter physics.

Contribution

It explicitly constructs fermion bound and scattering states in a multi-kink-antikink background using exotic supersymmetry, linking soliton solutions to Dirac systems and integrable models.

Findings

Explicit fermion bound and scattering states derived

Exotic nonlinear supersymmetry identified in the Dirac system

Connection established between soliton backgrounds and the modified KdV equation

Abstract

We construct a fermion system in a multi-kink-antikink soliton background, and present in an explicit form all its trapped configurations (bound state solutions) as well as scattering states. This is achieved by exploiting an exotic N=4 centrally extended nonlinear supersymmetry of completely isospectral pairs of reflectionless Schrodinger systems with potentials to be n-soliton solutions for the Korteweg-de Vries equation. The obtained reflectionless Dirac system with a position-dependent mass is shown to possess its own exotic nonlinear supersymmetry associated with the matrix Lax-Novikov operator being a Darboux-dressed momentum. In the process, we get an algebraic recursive representation for the multi-kink-antikink backgrounds, and establish their relation to the the modified Korteweg-de Vries equation. We also indicate how the results can be related to the physics of self-consistent condensates based on the Bogoliubov-de Gennes equations.