Quasiparticle, charge, and energy conservation in weak‐coupling superconductors

The conservation of quasiparticles, electric charge, and energy in weak‐coupling superconductors is discussed and correlated with the interpretation of the quasiparticles as particle and hole excitations. The formulation employed is that of the Bogolyubov‐de Gennes equations. In the absence of spin‐dependent interactions these equations are written in the form of a time‐dependent Schrödinger equation with a two‐component wave function and a two‐by‐two matrix Hamiltonian. Accordingly, the desired conservation laws are discussed on much the same basis as in ordinary quantum theory. The generalization to permit nonlocal quasiparticle and pair potentials and spin‐dependent interactions is briefly presented.