The Bogoliubov/de Gennes system, the AKNS hierarchy, and nonlinear quantum mechanical supersymmetry

TL;DR

This paper reveals that the Ginzburg-Landau expansion for the Bogoliubov-de Gennes Hamiltonian is governed by the AKNS hierarchy, uncovering a hidden nonlinear supersymmetry in quantum mechanics.

Contribution

It establishes a connection between the Ginzburg-Landau expansion, integrable nonlinear equations, and supersymmetry in the context of the Bogoliubov-de Gennes system.

Findings

Ginzburg-Landau expansion linked to AKNS hierarchy

Identification of hidden nonlinear supersymmetry

Mathematical framework for quantum integrability

Abstract

We show that the Ginzburg-Landau expansion of the grand potential for the Bogoliubov-de Gennes Hamiltonian is determined by the integrable nonlinear equations of the AKNS hierarchy, and that this provides the natural mathematical framework for a hidden nonlinear quantum mechanical supersymmetry underlying the dynamics.