# Supersymmetrization of the Franke-Gorini-Kossakowski-Lindblad-Sudarshan equation

## TL;DR

This paper develops a method to incorporate supersymmetry into the FGKLS equation, enabling the study of quantum decoherence in supersymmetric systems interacting with environments, and constructs related isospectral quantum systems.

## Contribution

It introduces a novel prescription for supersymmetrizing the FGKLS equation and constructs pairs of isospectral quantum systems with this framework.

## Key findings

- Supersymmetrization of the FGKLS equation is achieved.
- Pairs of isospectral supersymmetric quantum systems are constructed.
- Examples illustrate the supersymmetric decoherence dynamics.

## Abstract

We investigate departures from the Hamiltonian dynamics such as the quantum decoherence in a supersymmetric quantum system due to its interaction with the environment. The effective description is given by the Franke-Gorini-Kossakowski-Lindblad-Sudarshan (FGKLS) equation. The prescription for supersymmetrization of this equation is elaborated and pairs of related isospectral quantum systems are built. We present some instructive examples of such a construction.