Bogoliubov-de Gennes equation on graphs: A model for tree-branched Majorana wire network

Abstract

We consider Bogoliubov-de Gennes equation on a metric tree graph. Formulation of the problem for arbitrary graph topology is provided. Self-adjoint vertex boundary conditions are derived. Exact solutions of the problem is obtained for quantum tree graph. A quantum graph based model for tree-branched Majorana wire network is proposed.