STABILITY EQUATION AND TWO-COMPONENT EIGENMODE FOR DOMAIN WALLS IN A SCALAR POTENTIAL MODEL

Abstract

The connection between the supersymmetric quantum mechanics involving two-component eigenfunctions and the stability equation associated with two classical configurations is investigated and a matrix superpotential is deduced. The question of stability is ensured for the Bogomol'nyi–Prasad–Sommerfield (BPS) states on two domain walls in a scalar potential model containing up to fourth-order powers in the fields, which is explicit demonstrated using the intertwining operators in terms of two-by-two matrix superpotential in the algebraic framework of supersymmetry in quantum mechanics. Also, a non-BPS state is found to be nonstable via the fluctuation Hessian matrix.