  For theories with a sign problem there is no analog of the Banks-Casher
relation. This is true in particular for QCD at nonzero quark chemical
potential. However, for QCD-like theories without a sign problem the
Banks-Casher relation can be extended to the case of complex Dirac eigenvalues.
We derive such extensions for the zero-temperature, high-density limits of
two-color QCD, QCD at nonzero isospin chemical potential, and adjoint QCD. In
all three cases the density of the complex Dirac eigenvalues at the origin is
proportional to the BCS gap squared.
