Complementary variational theorems for inhomogeneous superconductors

We present complementary variational theorems for an inhomogeneous London superconductor, in which both the London penetration length lambda(L)(r) and permeability mu(r) vary randomly. A characteristic feature hers is the explicitly self-consistent coupling between the magnetic and supercurrent polarization effects due to these inhomogeneities. Our results may be important to composite systems containing magnetic (normal) and superconducting components. Applications of the theorems to such systems and their relationship to nonlinear composites will also be discussed.