The Dual Canonical Formalism in the Quantum Junction Systems
  We have constructed a theory of dual canonical formalism, to study the quantum dual systems. In such a system, as the relationship between current and voltage of each, we assumed the duality conditions. As a simple example, we examined the duality between the SC / SI / SC junction and SI / SC / SI junction. We derived the relationship between the phase and the number of particles in a dual system of each other. 
Morishige Yoneda, Masaaki Niwa, Mitsuya Motohashi
cond-mat.mes-hall