Supersymmetrization of the Lindblad-Franke-GKS equation

We investigate departures from hamiltonian dynamics of a SUSY quantum system due to its interaction with environment that generates decoherence. The Lindblad-Franke-GKS equation is taken to approach the quantum dynamics of decoherence, the prescription for supersymmetrization of this equation is elaborated and pairs of related isospectral quantum systems are described. Some instructive examples of such a construction are built.